Size of the Plastic Zone Produced by Nanoscratching

Abstract

Nanoscratching of ductile materials creates plastic zones surrounding the scratch groove. We approximate the geometry of these zones by a semicylinder with its axis oriented along the scratch direction. The radius and the length of the cylinder, as well as the length of the dislocations in the network created quantify the plasticity generated. Using molecular dynamics simulations, we characterize the plastic zones in six metals with fcc, bcc, and hcp crystal structures. We find that the plastic zone sizes after scratch are comparable to those after indent. Due to dislocation reactions, the dislocation networks simplify, reducing the total length of dislocations. As a consequence, the average dislocation density in the plastic zone stays roughly constant. Individually, we find exceptions from this simple picture. Fcc metals show strong plastic activity, which even increases during scratch. The hcp metals on the other side show the least plastic activity. Here the plasticity may be strongly reduced during scratch and particularly during tip withdrawal.

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Acknowledgements

IAA and HMU acknowledge support by the Deutsche Forschungsgemeinschaft via the Sonderforschungsbereich 926. CJR acknowledges support by ANPCyT PICT-2015-0342, SECTyP-UNCuyo, a donation by the Nvidia Corporation, and computational resources at Mendieta-CCAD-UNC through MinCyT-PDC-SNCAD.

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Correspondence to Herbert M. Urbassek.

Appendix 1: Depth Dependence of Scratching

Appendix 1: Depth Dependence of Scratching

Table 5 Influence of the scratch depth d on the radius of plastic zone, \(R_\mathrm{pl}\), and the plastic zone size factor, f

Besides the surface orientation and the scratch direction, scratching also depends on the scratching depth d. This quantity has been fixed to 3 nm in the main part of the work. In this Appendix, we vary it between \(d=2\) and 4 nm; however, we provide the results only for one fcc metal (Al), one bcc metal (Fe), and one hcp metal (Ti).

The results are summarized in Table 5. The results are quite consistent for the fcc and bcc materials. With increasing depth d, the size factor f increases. This increase is most pronounced for the hard material, Fe, and less dramatic for Al. We attribute this increase to the effects of dislocation mobility, which is influenced by cross-slip and the details of the stress field acting under the tip [51, 52]. In addition, the results after indent also apply in good approximation for the scratch, and the removal of the tip after scratch has only a minor influence on f. These latter assertions only fail for the most shallow scratch in Al.

For the hcp material, Ti, the scratch depth plays a larger role. For the two shallowest indents, \(d=2\) and 3 nm, the plastic zone is relatively small, and almost collapses after removal of the tip, resulting in \(f=1\) or even smaller. However, more stable results are obtained for the deepest indent, \(d=4\) nm. For this depth, the resulting f factor is around 3, in good agreement with the bcc results. Only the fcc size factor is larger for this scratch depth, around \(f=4\).

We conclude that for hcp materials, shallow indents and scratches tend to lose their plastic zones by dislocation annihilation at the surface. A similar result was obtained previously for too small tip sizes [6]. Deeper indents are needed to keep the plasticity surviving.

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Alabd Alhafez, I., Ruestes, C.J. & Urbassek, H.M. Size of the Plastic Zone Produced by Nanoscratching. Tribol Lett 66, 20 (2018). https://doi.org/10.1007/s11249-017-0967-9

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Keywords

  • Molecular dynamics
  • Nanoindentation
  • Scratching
  • Dislocations
  • Plasticity