Gradient effects in micro-/nanoindentation

References

• Nix W. D. and Gao H.: ‘Indentation size effects in crystalline materials: a law for strain gradient plasticity’, J. Mech. Phys. Solids, 1998, 46, 411–425.
   Web of Science ®Google Scholar
• Aifantis E. C.: ‘On the microstructural origin of certain inelastic models’, Trans. ASME, J. Eng. Mater. Technol., 1984, 106, 326–330.
   Web of Science ®Google Scholar
• Tsagrakis I., Konstantinidis A. and Aifantis E. C.: ‘Strain gradient and wavelet interpretation of size effects in yield and strength’, Mech. Mater., 2003, 35, 733–745.
   Web of Science ®Google Scholar
• Aifantis E. C.: ‘Gradient plasticity’, in ‘Handbook of materials behavior models’, (ed. Lemaitre J.), 291–307; 2001, New York, Academic Press.
   Google Scholar
• Johnson K. L.: ‘The correlation of indentation experiments’, J. Mech. Phys. Solids, 1970, 18, 115–126.
   Web of Science ®Google Scholar
• Aifantis E. C.: ‘On the role of gradients in the localization of deformation and fracture’, Int. J. Eng. Sci., 1992, 30, 1279–129. (see also E. C. Aifantis: ‘Strain gradient interpretation of size effects’, Int. J. Fract., 1999, 95, 299–314)
   Google Scholar
• Aifantis E. C.: ‘Gradient nanomechanics: applications to deformation, fracture, and diffusion in nanopolycrystals’, Metall. Mater. Trans. A, 2011, 42A, 2985–2998.
   Web of Science ®Google Scholar
• Altan B. S. and Aifantis E. C.: ‘On some aspects in the special theory of gradient elasticity’, J. Mech. Behav. Biomed. Mater., 1997, 8, 231–282.
   Google Scholar
• Askes H. and Aifantis E. C.: ‘Gradient elasticity in statics and dynamics: an overview of formulations, length scale identification procedures, finite element implementations and new results’, Int. J. Solids Struct., 2011, 48, 1962–1990.
   Web of Science ®Google Scholar
• Bull S. J., Page T. F. and Yoffe E. H.: Philos. Mag. Lett., 1989, 59, 281. (see also J. R. Barber: ‘Elasticity’; 2002, Dordrecht, Springer)
   Web of Science ®Google Scholar
• McElhaney K. W., Vlassak J. J. and Nix W. D.: ‘Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments’, J. Mater. Res., 1998, 10, 1300–1306.
   Web of Science ®Google Scholar
• Aifantis E. C.: ‘Pattern formation in plasticity’, Int. J. Eng. Sci., 1995, 33, 2161–2178.
   Web of Science ®Google Scholar
• Hill R.: ‘The mathematical theory of plasticity’; 1950, Oxford, Clarendon Press.
   Google Scholar
• Tsagrakis I., Efremidis G., Konstantinidis A. and Aifantis E. C.: ‘Deformation vs. flow and wavelet-based models of gradient plasticity: examples of axial symmetry’, Int. J. Plast., 2006, 22, 1456–1485.
   Web of Science ®Google Scholar
• Mokios G. P. and Aifantis E. C.: ‘Gradient plasticity solution of an expanding spherical cavity with application in indentation’, Proc. 8th HSTAM Int. Cong. on ‘Mechanics’, Patras, Greece, July 2007, HSTAM, 607–614.
   Google Scholar
• Mokios G. P. and Aifantis E. C.: ‘A gradient elasticity approach to the indentation size effect at very small depths’, J. Mech. Behav. Biomed. Mater., 2011, 20, 35–40.
   Google Scholar
• Tymiak N. I., Kramer D. E., Bahr D. F., Wyrobek T. J. and Gerberich W. W.: ‘Plastic strain and strain gradients at very small indentation depths’, Acta Mater., 2001, 49, 1021–1034.
   Web of Science ®Google Scholar
• Fleck N. A., Muller G. M., Ashby M. F. and Hutchinson J. W.: ‘Strain gradient plasticity: theory and experiment’, Acta Metall. Mater., 1994, 42, 475–487.
   Google Scholar
• Fleck N. A. and Hutchinson J. W.: ‘An assessment of a class of strain gradient plasticity theories’, J. Mech. Phys. Solids, 2001, 49, 2245–2272. [see also N. A. Fleck and J. W. Hutchinson: ‘A phenomenological theory for strain gradient effects in plasticity’, J. Mech. Phys. Solids, 1993, 41, 1825–1857; N. A. Fleck and J. W. Hutchinson: ‘Strain gradient plasticity’, in ‘Advances in applied mechanics’, (ed. J. W. Hutchinson and T. W. Wu), Vol. 33, 295–361; 1997, New York, Academic Press].
   Web of Science ®Google Scholar
• Gurtin M. E. and Anand L.: ‘Thermodynamics applied to gradient theories involving the accumulated plastic strain: the theories of Aifantis and Fleck & Hutchinson and their generalization’, J. Mech. Phys. Solids, 2009, 57, 405–421.
   Web of Science ®Google Scholar
• Brown L. M.: ‘Slip circle constructions for inhomogeneous rotational flow’, Mater. Sci. Forum, 2007, 550, 105–117. [see also L. M. Brown: ‘Slip circle constructions for plasticity of polycrystals’, in ‘Plasticity, failure and fatigue in structural materials – from macro to nano (Proc. Hael Mughrabi Honorary Symp.)’, (ed. K. J. Hsia et al.); 2008, Warrendale, PA, TMS].
   Google Scholar