Effect of Tip Roundness on the Nanoindentation of Fe Crystals


Indentation tips are never atomically sharp, but rounded at their end. We use atomistic simulation to study the effect of tip roundness for the particular case of a cube-corner pyramidal indenter by comparing the results of a spherical, a sharp cube-corner, and a rounded cube-corner tip during indention into bcc Fe. We find that as soon as the tip has indented so deeply that the spherical geometry does not hold any longer, strong deviations between the dislocation plasticity behavior show up. The rounded cube-corner tip produces less dislocations and a smaller plastic zone than the spherical indenter, when indented to the same depth. The results are better comparable, however, when the same displaced volume is considered. Finally, the dislocation nucleation mode is affected by the geometry, changing from homogeneous to heterogeneous nucleation as the tip changes from rounded to sharp. The cube-corner tips are found to produce more twinning and delay the formation of prismatic loops. For a penetration depth beyond the radius of the rounded cube-corner tip, atomic sharp pyramidal tips produce similar quantitative (hardness, dislocation density) and qualitative (pileup, dislocation arrangement) results compared to its rounded counterpart. Our results will prove important for understanding the differences between spherical indenter tips, as they are often used in simulation, and pyramidal tips, as they are used in experiment.

This is a preview of subscription content, log in to check access.

Fig. 1
Fig. 2
Fig. 3
Fig. 4
Fig. 5
Fig. 6
Fig. 7


  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.

    Armstrong, R.W., Elban, W.L., Walley, S.M.: Elastic, plastic, cracking aspects of the hardness of materials. Int. J. Mod. Phys. B 27, 1330004 (2013)

    Google Scholar 

  4. 4.

    Armstrong, R.W., Walley, S.M., Elban, W.L.: Crystal indentation hardness. Crystals 7, 21 (2017)

    Google Scholar 

  5. 5.

    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)

    CAS  Google Scholar 

  6. 6.

    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)

    CAS  Google Scholar 

  7. 7.

    Ruestes, C.J., Bringa, E.M., Gao, Y., Urbassek, H.M.: Molecular dynamics modeling of nanoindentation. In: Tiwari, A., Natarajan, S. (eds.) Applied Nanoindentation in Advanced Materials, Chapter 14, pp. 313–345. Wiley, Chichester (2017)

    Google Scholar 

  8. 8.

    Ruestes, C .J., Alabd Alhafez, I., Urbassek, H .M.: Atomistic studies of nanoindentation—A review of recent advances. Crystals 7, 293 (2017b)

    Google Scholar 

  9. 9.

    Van Vliet, K.J., Li, J., Zhu, T., Yip, S., Suresh, S.: Quantifying the early stages of plasticity through nanoscale experiments and simulations. Phys. Rev. B 67, 104105 (2003)

    Google Scholar 

  10. 10.

    Ma, X.-L., Yang, W.: Molecular dynamics simulation on burst and arrest of stacking faults in nanocrystalline Cu under nanoindentation. Nanotechnology 14, 1208 (2003)

    CAS  Google Scholar 

  11. 11.

    Zhu, T., Li, J., Van Vliet, K.J., Ogata, S., Yip, S., Suresh, S.: Predictive modeling of nanoindentation-induced homogeneous dislocation nucleation in copper. J. Mech. Phys. Sol. 52, 691 (2004)

    CAS  Google Scholar 

  12. 12.

    Liang, H., Woo, C.H., Huang, H., Ngan, A.H.W., Yu, T.X.: Crystalline plasticity on copper (001), (110), and (111) surfaces during nanoindentation. Comput. Model. Eng. Sci. 6, 105 (2004)

    Google Scholar 

  13. 13.

    Asenjo, A., Jaafar, M., Carrasco, E., Rojo, J.M.: Dislocation mechanisms in the first stage of plasticity of nanoindented Au (111) surfaces. Phys. Rev. B 73, 075431 (2006)

    Google Scholar 

  14. 14.

    Tsuru, T., Shibutani, Y.: Anisotropic effects in elastic and incipient plastic deformation under (001), (110), and (111) nanoindentation of Al and Cu. Phys. Rev. B 75, 035415 (2007)

    Google Scholar 

  15. 15.

    Ju, S.-P., Wang, C.-T., Chien, C.-H., Huang, J.C., Jian, S.-R.: The nanoindentation responses of nickel surfaces with different crystal orientations. Mol. Simul. 33, 905 (2007)

    CAS  Google Scholar 

  16. 16.

    Carrasco, E., Rodríguez de la Fuente, O., Rojo, J.M.: Dislocation emission at the onset of plasticity during nanoindentation in gold. Philos. Mag. 88, 281 (2008)

    CAS  Google Scholar 

  17. 17.

    Ziegenhain, G., Urbassek, H.M.: Effect of material stiffness on hardness: a computational study based on model potentials. Philos. Mag 89, 2225–2238 (2009)

    CAS  Google Scholar 

  18. 18.

    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. Sol. 57, 1514–1526 (2009)

    CAS  Google Scholar 

  19. 19.

    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)

    Google Scholar 

  20. 20.

    Paul, W., Oliver, D., Miyahara, Y., Grütter, P.H.: Minimum threshold for incipient plasticity in the atomic-scale nanoindentation of Au(111). Phys. Rev. Lett. 110, 135506 (2013)

    Google Scholar 

  21. 21.

    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. Sol. 75, 58–75 (2015)

    CAS  Google Scholar 

  22. 22.

    Hagelaar, J.H.A., Bitzek, E., Flipse, C.F.J., Gumbsch, P.: Atomistic simulations of the formation and destruction of nanoindentation contacts in tungsten. Phys. Rev. B 73, 045425 (2006)

    Google Scholar 

  23. 23.

    Biener, M.M., Biener, J., Hodge, A.M., Hamza, A.V.: Dislocation nucleation in bcc Ta single crystals studied by nanoindentation. Phys. Rev. B 76, 165422 (2007)

    Google Scholar 

  24. 24.

    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)

    Google Scholar 

  25. 25.

    Christopher, D., Smith, R., Richter, A.: Atomistic modelling of nanoindentation in Fe and Ag. Nanotechnology 12, 372 (2001)

    CAS  Google Scholar 

  26. 26.

    Smith, R., Christopher, D., Kenny, S.D., Richter, A., Wolf, B.: Defect generation and pileup of atoms during nanoindentation of Fe single crystals. Phys. Rev. B 67, 245405 (2003)

    Google Scholar 

  27. 27.

    Lu, C., Gao, Y., Michal, G., Deng, G., Huynh, N.N., Zhu, H., Liu, X., Tieu, A.K.: Experiment and molecular dynamics simulation of nanoindentation of body centered cubic iron. J. Nanosci. Nanotechnol. 9, 7307 (2009a)

    CAS  Google Scholar 

  28. 28.

    Lu, C., Gao, Y., Michal, G., Huynh, N.N., Zhu, H.T., Tieu, A.K.: Atomistic simulation of nanoindentation of iron with different indenter shapes. Proc. IME J. 223, 977 (2009b)

    Google Scholar 

  29. 29.

    Kumar, N.N., Tewari, R., Durgaprasad, P.V., Dutta, B.K., Dey, G.K.: Active slip systems in bcc iron during nanoindentation: a molecular dynamics study. Comput. Mater. Sci. 77, 260 (2013)

    Google Scholar 

  30. 30.

    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)

    CAS  Google Scholar 

  31. 31.

    Alabd Alhafez, I., Ruestes, C.J., Bringa, E.M., Urbassek, H.M.: Influence of pre-existing plasticity on nanoindentation—An atomistic analysis of the dislocation fields produced. J. Mech. Phys. Solids 132, 103674 (2019a)

    Google Scholar 

  32. 32.

    Verkhovtsev, A.V., Yakubovich, A.V., Sushko, G.B., Hanauske, M., Solov’yov, A.V.: Molecular dynamics simulations of the nanoindentation process of titanium crystal. Comput. Mater. Sci. 76, 20–26 (2013)

    CAS  Google Scholar 

  33. 33.

    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)

    Google Scholar 

  34. 34.

    Avila, K.E., Küchemann, S., Alabd Alhafez, I., Urbassek, H.M.: Shear-transformation-zone activation during loading and unloading in nanoindentation of metallic glasses. Materials 12, 1477 (2019)

    CAS  Google Scholar 

  35. 35.

    Alabd Alhafez, I., Ruestes, C.J., Bringa, E.M., Urbassek, H.M.: Nanoindentation into a high-entropy alloy—An atomistic study. J. Alloys Compd. 803, 618–624 (2019b)

    Google Scholar 

  36. 36.

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

    CAS  Google Scholar 

  37. 37.

    Landman, U., Luedtke, W.D., Burnham, N.A., Colton, R.J.: Atomistic mechanisms and dynamics of adhesion, nanoindentation, and fracture. Science 248, 454 (1990)

    CAS  Google Scholar 

  38. 38.

    Luan, B., Robbins, M.O.: The breakdown of continuum models for mechanical contacts. Nature 435, 929 (2005)

    CAS  Google Scholar 

  39. 39.

    Wagner, R.J., Ma, L., Tavazza, F., Levine, L.E.: Dislocation nucleation during nanoindentation of aluminum. J. Appl. Phys. 104, 114311 (2008). https://doi.org/10.1063/1.3021305

    CAS  Article  Google Scholar 

  40. 40.

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

    Google Scholar 

  41. 41.

    Komanduri, R., Chandrasekaran, N., Raff, L.M.: Md simulation of atomic-scale friction. Phys. Rev. B 61, 14007 (2000)

    CAS  Google Scholar 

  42. 42.

    Kenny, S.D., Mulliah, D., Sanz-Navarro, C.F., Smith, R.: Molecular dynamics simulations of nanoindentation and nanotribology. Philos. Trans. R. Soc. A 363, 1949–1959 (2005)

    CAS  Google Scholar 

  43. 43.

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

    CAS  Google Scholar 

  44. 44.

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

    CAS  Google Scholar 

  45. 45.

    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)

    CAS  Google Scholar 

  46. 46.

    Banerjee, S., Naha, S., Puri, I.K.: Molecular simulation of the carbon nanotube growth mode during catalytic synthesis. Appl. Phys. Lett. 92, 233121 (2008)

    Google Scholar 

  47. 47.

    Allen, M. P., Tildesley, D. J. (eds.): Computer Simulation of Liquids ( Clarendon, Oxford, 1987)

  48. 48.

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

    CAS  Google Scholar 

  49. 49.

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

    Google Scholar 

  50. 50.

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

    Google Scholar 

  51. 51.

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

    Google Scholar 

  52. 52.

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

    Google Scholar 

  53. 53.

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

    Google Scholar 

  54. 54.

    Gerberich, W.W., Nelson, J., Lilleodden, E., Anderson, P., Wyrobek, J.: Indentation induced dislocation nucleation: the initial yield point. Acta Mater. 44, 3585–3598 (1996)

    CAS  Google Scholar 

  55. 55.

    Li, J., Van Vliet, K.J., Zhu, T., Yip, S., Suresh, S.: Atomistic mechanisms governing elastic limit and incipient plasticity in crystals. Nature 418, 307–310 (2002)

    CAS  Google Scholar 

  56. 56.

    Gunkelmann, N., Bringa, E.M., Kang, K., Ackland, G.J., Ruestes, C.J., Urbassek, H.M.: Polycrystalline iron under compression: plasticity and phase transitions. Phys. Rev. B 86, 144111 (2012)

    Google Scholar 

  57. 57.

    Yao, W.Z., Krill III, C.E., Albinski, B., Schneider, H.-C., You, J.H.: Plastic material parameters and plastic anisotropy of tungsten single crystal: a spherical micro-indentation study. J. Mater. Sci. 49, 3705 (2014)

    CAS  Google Scholar 

  58. 58.

    Terentyev, D.A., Osetsky, Y.N., Bacon, D.J.: Effects of temperature on structure and mobility of the \(<\)1 0 0\(>\) edge dislocation in body-centred cubic iron. Acta Mater. 58, 2477 (2010)

    CAS  Google Scholar 

  59. 59.

    Kelly, A., Knowles, K .M.: Crystallography and Crystal Defects, 2nd edn. Wiley, Chichester (2012)

    Google Scholar 

  60. 60.

    Alabd Alhafez, I., Urbassek, H .M.: Influence of tip adhesion on nanoindentation and scratching. Model. Simul. Mater. Sci. Eng 27, 065014 (2019)

    Google Scholar 

  61. 61.

    Gao, Y., Lu, C., Huynh, N.N., Michal, G., Zhu, H.T., Tieu, A.K.: Molecular dynamics simulation of effect of indenter shape on nanoscratch of Ni. Wear 267, 1998 (2009)

    CAS  Google Scholar 

  62. 62.

    Zhu, P.-Z., Hu, Y.-Z., Wang, H., Ma, T.-B.: Study of effect of indenter shape in nanometric scratching process using molecular dynamics. Mater. Sci. Eng. A 528, 4522 (2011)

    Google Scholar 

  63. 63.

    Ma, L., Morris, D.J., Jennerjohn, S.L., Bahr, D.F., Levine, L.E.: The role of probe shape on the initiation of metal plasticity in nanoindentation. Acta Mater. 60, 4729–4739 (2012)

    CAS  Google Scholar 

  64. 64.

    Goel, S., Cross, G., Stukowski, A., Gamsjäger, E., Beake, B., Agrawal, A.: Designing nanoindentation simulation studies by appropriate indenter choices: case study on single crystal tungsten. Comput. Mater. Sci. 152, 196–210 (2018)

    CAS  Google Scholar 

  65. 65.

    Oliver, D., Paul, W., El Ouali, M., Hagedorn, T., Miyahara, Y., Qi, Y., Grütter, P.: One-to-one spatially matched experiment and atomistic simulations of nanometre-scale indentation. Nanotechnology 25, 025701 (2013)

    Google Scholar 

  66. 66.

    Vishnubhotla, S.B., Chen, R., Khanal, S.R., Hu, X., Martini, A., Jacobs, T.D.B.: Matching atomistic simulations and in situ experiments to investigate the mechanics of nanoscale contact. Tribol. Lett. 67, 97 (2019)

    Google Scholar 

Download references


HMU acknowledges support by the Deutsche Forschungsgemeinschaft (DFG, German Research Foundation)—Project Number 172116086—SFB 926. CJR and MCZ acknowledge support by ANPCyT PICT-2015-0342, SiiP-UNCuyo-2019-M088, a donation by the Nvidia Corporation, and computational resources at TOKO-FCEN-UNCuyo cluster. EMB thanks funding from SIIP-UNCuyo-2019-2021 grant. The work by MCZ was supported by an EVC scholarship from Consejo Interuniversitario Nacional - Argentina.

Author information



Corresponding author

Correspondence to Carlos J. Ruestes.

Additional information

Publisher's Note

Springer Nature remains neutral with regard to jurisdictional claims in published maps and institutional affiliations.

Electronic supplementary material

Below is the link to the electronic supplementary material.

Electronic supplementary material 1 (AVI 1560 kb)

Electronic supplementary material 1 (AVI 1560 kb)

Rights and permissions

Reprints and Permissions

About this article

Verify currency and authenticity via CrossMark

Cite this article

Zonana, M.C., Ruestes, C.J., Bringa, E.M. et al. Effect of Tip Roundness on the Nanoindentation of Fe Crystals. Tribol Lett 68, 56 (2020). https://doi.org/10.1007/s11249-020-01295-9

Download citation


  • Molecular dynamics
  • Nanoindentation
  • Dislocations
  • Plasticity