Size of the Plastic Zone Produced by Nanoscratching


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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  1. 1.

    Johnson, K.L.: Contact Mechanics. Cambridge University Press, Cambridge (1985)

    Google Scholar 

  2. 2.

    Fischer-Cripps, A.C.: Nanoindentation, 2nd edn. Springer, New York (2004)

    Google Scholar 

  3. 3.

    Durst, K., Backes, B., Göken, M.: Indentation size effect in metallic materials: correcting for the size of the plastic zone. Scr. Mater. 52, 1093–1097 (2005)

    Article  Google Scholar 

  4. 4.

    Ruestes, C.J., Bringa, E.M., Gao, Y., Urbassek, H.M.: Molecular dynamics modeling of nanoindentation. In: Tiwari, A., Natarajan, S. (eds.) Appl. Nanoindentation Adv. Mater., pp. 313–345. Wiley, Chichester, UK (2017). (Chap. 14)

  5. 5.

    Gao, Y., Ruestes, C.J., Tramontina, D.R., Urbassek, H.M.: Comparative simulation study of the structure of the plastic zone produced by nanoindentation. J. Mech. Phys. Solids 75, 58–75 (2015)

    Article  Google Scholar 

  6. 6.

    Alabd Alhafez, I., Ruestes, C.J., Gao, Y., Urbassek, H.M.: Nanoindentation of hcp metals: a comparative simulation study of the evolution of dislocation networks. Nanotechnology 27, 045706 (2016)

    Article  Google Scholar 

  7. 7.

    Komanduri, R., Chandrasekaran, N., Raff, L.M.: MD simulation of indentation and scratching of single crystal aluminum. Wear 240, 113–143 (2000)

    Article  Google Scholar 

  8. 8.

    Mulliah, D., Christopher, D., Kenny, S.D., Smith, R.: Nanoscratching of silver (100) with a diamond tip. Nucl. Instrum. Methods B 202, 294–299 (2003)

    Article  Google Scholar 

  9. 9.

    Mulliah, D., Kenny, S.D., Smith, R., Sanz-Navarro, C.F.: Molecular dynamic simulations of nanoscratching of silver (100). Nanotechnology 15, 243–249 (2004)

    Article  Google Scholar 

  10. 10.

    Jun, S., Lee, Y., Kim, S.Y., Im, S.: Large-scale molecular dynamics simulations of Al(111) nanoscratching. Nanotechnology 15, 1169–1174 (2004)

    Article  Google Scholar 

  11. 11.

    Fang, T.-H., Liu, C.-H., Shen, S.-T., Prior, S.D., Ji, L.-W., Wu, J.-H.: Nanoscratch behavior of multi-layered films using molecular dynamics. Appl. Phys. A 90, 753–758 (2008)

    Article  Google Scholar 

  12. 12.

    Zhang, J.J., Sun, T., Hartmaier, A., Yan, Y.D.: Atomistic simulation of the influence of nanomachininginduced deformation on subsequent nanoindentation. Comput. Mater. Sci. 59, 14–21 (2012)

    Article  Google Scholar 

  13. 13.

    Mulliah, D., Kenny, S.D., McGee, E., Smith, R., Richter, A., Wolf, B.: Atomistic modelling of ploughing friction in silver, iron and silicon. Nanotechnology 17, 1807–1818 (2006)

    Article  Google Scholar 

  14. 14.

    Lu, C., Gao, Y., Michal, G., Zhu, H., Huynh, N.N., Tieu, A.K.: Molecular dynamic simulation of effect of crystallographic orientation on nano-indentation/scratching behaviors of bcc iron. In: Luo, J., Meng, Y., Shao, T., Zhao, Q. (eds.) Adv. Tribol., pp. 562–563. Springer, Berlin (2010)

    Google Scholar 

  15. 15.

    Gao, Y., Ruestes, C.J., Urbassek, H.M.: Nanoindentation and nanoscratching of iron: atomistic simulation of dislocation generation and reactions. Comput. Mater. Sci. 90, 232–240 (2014)

    Article  Google Scholar 

  16. 16.

    Gao, Y., Brodyanski, A., Kopnarski, M., Urbassek, H.M.: Nanoscratching of iron: a molecular dynamics study of the influence of surface orientation and scratching direction. Comput. Mater. Sci. 103, 77–89 (2015)

    Article  Google Scholar 

  17. 17.

    Alabd Alhafez, I., Brodyanski, A., Kopnarski, M., Urbassek, H.M.: Influence of tip geometry on nanoscratching. Tribol. Lett. 65, 26 (2017)

    Article  Google Scholar 

  18. 18.

    Alabd Alhafez, I., Urbassek, H.M.: Scratching of hcp metals: a molecular-dynamics study. Comput. Mater. Sci. 113, 187–197 (2016)

    Article  Google Scholar 

  19. 19.

    Mendelev, M.I., Kramer, M.J., Becker, C.A., Asta, M.: Analysis of semi-empirical interatomic potentials appropriate for simulation of crystalline and liquid Al and Cu. Philos. Mag. 88, 1723–1750 (2008)

    Article  Google Scholar 

  20. 20.

    Mishin, Y., Mehl, M.J., Papaconstantopoulos, D.A., Voter, A.F., Kress, J.D.: Structural stability and lattice defects in copper: Ab initio, tight-binding, and embedded-atom calculations. Phys. Rev. B 63, 224106 (2001)

    Article  Google Scholar 

  21. 21.

    Mendelev, M.I., Han, S., Srolovitz, D.J., Ackland, G.J., Sun, D.Y., Asta, M.: Development of new interatomic potentials appropriate for crystalline and liquid iron. Philos. Mag. 83, 3977–3994 (2003)

    Article  Google Scholar 

  22. 22.

    Dai, X.D., Kong, Y., Li, J.H., Liu, B.X.: Extended Finnis–Sinclair potential for bcc and fcc metals and alloys. J. Phys. Condens. Matter 18, 4527–4542 (2006)

    Article  Google Scholar 

  23. 23.

    Mendelev, M.I., Underwood, T.L., Ackland, G.J.: Development of an interatomic potential for the simulation of defects, plasticity, and phase transformations in titanium. J. Chem. Phys. 145, 154102 (2016)

    Article  Google Scholar 

  24. 24.

    Bertolino, G., Ruda, M., Pasianot, R., Farkas, D.: Atomistic simulation of the tension/compression response of textured nanocrystalline HCP Zr. Comput. Mater. Sci. 130, 172–182 (2017)

    Article  Google Scholar 

  25. 25.

    Pasianot, R.C., Monti, A.M.: A many body potential for \(\alpha\)-Zr. Application to defect properties. J. Nucl. Mater. 264, 198–205 (1999)

    Article  Google Scholar 

  26. 26.

    Shao, S., Medyanik, S.N.: Dislocation-interface interaction in nanoscale fcc metallic bilayers. Mech. Res. Commun. 37, 315–319 (2010)

    Article  Google Scholar 

  27. 27.

    Yaghoobi, M., Voyiadjis, G.Z.: Effect of boundary conditions on the MD simulation of nanoindentation. Comput. Mater. Sci. 95, 626–636 (2014)

    Article  Google Scholar 

  28. 28.

    Voyiadjis, G.Z., Yaghoobi, M.: Large scale atomistic simulation of size effects during nanoindentation: dislocation length and hardness. Mater. Sci. Eng. A 634, 20–31 (2015)

    Article  Google Scholar 

  29. 29.

    Ziegenhain, G., Urbassek, H.M., Hartmaier, A.: Influence of crystal anisotropy on elastic deformation and onset of plasticity in nanoindentation: a simulational study. J. Appl. Phys. 107, 061807 (2010)

    Article  Google Scholar 

  30. 30.

    Alcalá, J., Dalmau, R., Franke, O., Biener, M., Biener, J., Hodge, A.: Planar defect nucleation and annihilation mechanisms in nanocontact plasticity of metal surfaces. Phys. Rev. Lett. 109, 075502 (2012)

    Article  Google Scholar 

  31. 31.

    Ruestes, C.J., Stukowski, A., Tang, Y., Tramontina, D.R., Erhart, P., Remington, B.A., Urbassek, H.M., Meyers, M.A., Bringa, E.M.: Atomistic simulation of tantalum nanoindentation: effects of indenter diameter, penetration velocity, and interatomic potentials on defect mechanisms and evolution. Mater. Sci. Eng. A 613, 390–403 (2014)

    Article  Google Scholar 

  32. 32.

    Li, J., Fang, Q., Liu, Y., Zhang, L.: A molecular dynamics investigation into the mechanisms of subsurface damage and material removal of monocrystalline copper subjected to nanoscale high speed grinding. Appl. Surf. Sci. 303, 331–343 (2014)

    Article  Google Scholar 

  33. 33.

    Li, J., Liu, B., Luo, H., Fang, Q., Liu, Y., Liu, Y.: A molecular dynamics investigation into plastic deformation mechanism of nanocrystalline copper for different nanoscratching rates. Comput. Mater. Sci. 118, 66–76 (2016)

    Article  Google Scholar 

  34. 34.

    Kelchner, C.L., Plimpton, S.J., Hamilton, J.C.: Dislocation nucleation and defect structure during surface indentation. Phys. Rev. B 58, 11085–11088 (1998)

    Article  Google Scholar 

  35. 35.

    Ziegenhain, G., Hartmaier, A., Urbassek, H.M.: Pair vs many-body potentials: influence on elastic and plastic behavior in nanoindentation of fcc metals. J. Mech. Phys. Solids 57, 1514–1526 (2009)

    Article  Google Scholar 

  36. 36.

    Plimpton, St.: Fast parallel algorithms for short-range molecular dynamics. J. Comput. Phys. 117, 1–19 (1995).

  37. 37.

    Stukowski, A.: Visualization and analysis of atomistic simulation data with OVITO—the Open Visualization Tool, Model. Simul. Mater. Sci. Eng. 18, 015012 (2010).

  38. 38.

    Henderson, A.: Paraview guide, a parallel visualization application. Kitware Inc. (2007).

  39. 39.

    Stukowski, A., Albe, K.: Extracting dislocations and non-dislocation crystal defects from atomistic simulation data. Model. Simul. Mater. Sci. Eng. 18, 085001 (2010)

    Article  Google Scholar 

  40. 40.

    Stukowski, A., Bulatov, V.V., Arsenlis, A.: Automated identification and indexing of dislocations in crystal interfaces. Model. Simul. Mater. Sci. Eng. 20, 085007 (2012)

    Article  Google Scholar 

  41. 41.

    Stukowski, A.: Structure identification methods for atomistic simulations of crystalline materials. Model. Simul. Mater. Sci. Eng. 20, 045021 (2012)

    Article  Google Scholar 

  42. 42.

    Stukowski, A., Arsenlis, A.: On the elastic-plastic decomposition of crystal deformation at the atomic scale. Model. Simul. Mater. Sci. Eng. 20, 035012 (2012)

    Article  Google Scholar 

  43. 43.

    Bowden, F.P., Tabor, D.: Friction, lubrication and wear: a survey of work during the last decade. Br. J. Appl. Phys. 17, 1521–1544 (1966)

    Article  Google Scholar 

  44. 44.

    Tsuru, T., Kaji, Y., Shibutani, Y.: Minimum energy motion and core structure of pure edge and screw dislocations in aluminum. J. Comput. Sci. Tech. 4, 185–193 (2010)

    Article  Google Scholar 

  45. 45.

    Muzyk, M., Pakiela, Z., Kurzydlowski, K.J.: Ab initio calculations of the generalized stacking fault energy in aluminium alloys. Scr. Mater. 64, 916–918 (2011)

    Article  Google Scholar 

  46. 46.

    Monnet, G., Terentyev, D.: Structure and mobility of the \(\frac{1}{2} \langle 111 \rangle \{112\}\) edge dislocation in BCC iron studied by molecular dynamics. Acta Mater. 57, 1416–1426 (2009)

    Article  Google Scholar 

  47. 47.

    Hafez Haghighat, S.M., von Pezold, J., Race, C.P., Körmann, F., Friak, M., Neugebauer, J., Raabe, D.: Influence of the dislocation core on the glide of the \(\frac{1}{2} \langle 111 \rangle \{110\}\) edge dislocation in bcc-iron. Comput. Mater. Sci. 87, 274–282 (2014)

    Article  Google Scholar 

  48. 48.

    Remington, T.P., Ruestes, C.J., Bringa, E.M., Remington, B.A., Lu, C.H., Kad, B., Meyers, M.A.: Plastic deformation in nanoindentation of tantalum: A new mechanism for prismatic loop formation. Acta Mater. 78, 378–393 (2014)

    Article  Google Scholar 

  49. 49.

    Tenckhoff, E.: Deformation Mechanisms, Texture, and Anisotropy in Zirconium and Zircaloy, ASTM Special Technical Publication, vol. 966. ASTM International, Philadelphia (1988)

    Google Scholar 

  50. 50.

    Gunkelmann, N., Alabd Alhafez, I., Steinberger, D., Urbassek, H.M., Sandfeld, S.: Nanoscratching of iron: a novel approach to characterize dislocation microstructures. Comput. Mater. Sci. 135, 181–188 (2017)

    Article  Google Scholar 

  51. 51.

    Po, G., Cui, Y., Rivera, D., Cereceda, D., Swinburne, T.D., Marian, J., Ghoniem, N.: A phenomenological dislocation mobility law for bcc metals. Acta Mater. 119, 123–135 (2016)

    Article  Google Scholar 

  52. 52.

    Dezerald, L., Rodney, D., Clouet, E., Ventelon, L., Willaime, F.: Plastic anisotropy and dislocation trajectory in bcc metals. Nat. Commun. 7, 11695 (2016)

    Article  Google Scholar 

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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).

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  • Molecular dynamics
  • Nanoindentation
  • Scratching
  • Dislocations
  • Plasticity