Abstract
This work addresses the size effect encountered in nanoindentation experiments. It is generally referred to as the indentation size effect (ISE). Classical descriptions of the ISE show a decrease in hardness for increasing indentation depth. Recently new experiments have shown that after the initial decrease, hardness increases with increasing indentation depth. After this increase, finally the hardness decreases with increasing indentation. This work reviews the existing theories describing the ISE and presents new formulations that incorporate the hardening effect into the ISE. Furthermore, indentation experiments have been performed on several metal samples, to see whether the hardening effect was an anomaly or not. Finally, numerical simulations are performed using the commercial program ABAQUS.
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Abu Al Rub R.K., Voyiadjis G.Z.: Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro- and nano-indentation experiments. Int. J. Plast. 20(6), 1139–1182 (2004)
Voyiadjis, G.Z., Abu Al Rub, R.K.: Length scales in gradient plasticity. In: Ahzi, S., Cherkaoui, M., Khaleel, M.A., Zbib, H.M., Zikry, M.A., LaMatina, B. (eds.): Proceedings of the IUTAM Symposium on Multiscale Modeling and Characterization of Elastic-Inelastic Behavior of Engineering Materials, October 2002, pp. 167–174. Kluwer Academic Publishers, Morocco (2002)
Abu Al Rub R.K., Voyiadjis G.Z.: A physically based gradient plasticity theory. Int. J. Plast. 22(4), 654–684 (2006)
Almasri, A.H., Voyiadjis, G.Z.: Nanoindentation in FCC metals: experimental study. Acta Mechanica 18 (2009)
Lucas, B.N., Oliver, W.C. Phar, G.M., Loubet, J.-L.: Time-dependent deformation during indentation testing. Thin films: Stresses and mechanical properties VI. In: Proceedings of the Symposium, San Francisco, CA, USA, 8–12 Apr 1996, pp. 233–238 (1997)
Gao H., Huang Y.: Geometrically necessary dislocation and size-dependent plasticity. Scr. Mater. 48, 113–118 (2003)
Nix W.D., Gao H.: Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids. 46(3), 411–425 (1998)
Arsenlis A., Parks D.M.: Crystallographic aspects of geometrically-necessary and statistically stored dislocation density. Acta Mater. 7(5), 1597–1611 (1999)
Voyiadjis G.Z., Abu Al-Rub R.K.: Determination of the material intrinsic length scale of gradient plasticity theory. Int. J. Multiscale Comput. Eng. 2(3), 377–400 (2004)
Tabor D.: The Hardness of Metals. Clarendon Press, Oxford (1951)
Xue Z. et al.: The influence of indenter tip radius on the micro indentation hardness. Eng. Mater. Technol. 124(3), 371–379 (2002)
Yang B., Vehoff H.: Dependence of nanohardness upon indentation size and grain size—a local examination of the interaction between dislocations and grain boundaries. Acta Mater. 55(3), 849–856 (2007)
Voyiadjis G.Z., Abu Al-Rub R.K.: Gradient plasticity theory with a variable length scale parameter. Int. J. Solids Struct. 42(14), 3998–4029 (2005)
Voyiadjis, G.Z., Abu Al-Rub, R.K.: Thermodynamic Based Model for the Evolution Equation of the Backstress in Cyclic Plasticity, vol. 19, Issue 12. Elsevier, Baton Rouge (2003)
Armstrong, P.J., Frederick, C.O.: A Mathematical Representation of the Multiaxial Bauschinger Effect, vol. 21, no. 4. Berkeley Laboratories, Berkeley (1966)
Phillips A., Tang J.L., Ricciuti M.: Some new observations on yield surfaces. Acta Mech. 20(1–2), 23–39 (1984)
Chaboche J.-L., Rousselier G.: On the plastic and viscoplasic constitutive equations, part I: rules developed with internal variables concept. Part II: application of internal variable concepts to the 316 stainless steel. ASME J. Press. Vessel Technol. 105, 153–158 (1983)
Roylance, D. http://web.mit.edu/course/3/3.11/www/modules/ss.pdf. Accessed 23 Aug 2001
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Voyiadjis, G.Z., Peters, R. Size effects in nanoindentation: an experimental and analytical study. Acta Mech 211, 131–153 (2010). https://doi.org/10.1007/s00707-009-0222-z
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DOI: https://doi.org/10.1007/s00707-009-0222-z