Dislocation-based model for predicting size-scale effects on the micro and nano indentation hardness of metallic materials

International Journal of Materials and Structural Integrity

Volumn 4, Issue 2-4, 2010, Pages 251-277

  Abu Al Rub, Rashid K ^a   Faruk, Abu N M ^a  

^a Department of Electrical and Computer Engineering   (United States)

Author keywords

Geometrically necessary dislocations; GNDs; Indentation size effect; ISE; Length scale; Micro indentation; Nano indentation; SSDs; Statistically stored dislocations

Indexed keywords

FORECASTING; NANOINDENTATION;

GEOMETRICALLY NECESSARY DISLOCATIONS; GNDS; INDENTATION SIZE EFFECTS; LENGTH SCALE; MICRO INDENTATION; SSDS; STATISTICALLY STORED DISLOCATIONS;

INDENTATION;

EID: 78651564383     PISSN: 17450055     EISSN: 17450063     Source Type: Journal    
DOI: 10.1504/IJMSI.2010.035209     Document Type: Article

References (56)

1. Abu Al-Rub, R.K. (2007) 'Prediction of micro and nano-indentation size effect from conical or pyramidal indentation', Mechanics of Materials, Vol. 39, pp.787-802
2. Abu Al-Rub, R.K. and Voyiadjis, G.Z. (2004a) 'Analytical and experimental determination of the material intrinsic length scale of strain gradient plasticity theory from micro- and nano-indentation experiments', Int. J. Plasticity, Vol. 20, pp.1139-1182.
3. Abu Al-Rub, R.K. and Voyiadjis, G.Z. (2004b) 'Determination of the material intrinsic length scale of gradient plasticity theory', International Journal of Multiscale Computational Engineering, Vol. 3, No. 3, pp.50-74.
4. Abu Al-Rub, R.K. and Voyiadjis, G.Z. (2006) 'A physically based gradient plasticity theory', Int. J. Plasticity, Vol. 22, pp.654-684.
5. Alkorta, J., Martinez-Esnaola, J.M. and Gil Sevillano, J. (2006) 'Detailed assessment of indentation size-effect in recrystallized and highly deformed niobium', Acta Materialia, Vol. 54, pp.3445-3452.
6. Arsenlis, A. and Parks, D.M. (1999) 'Crystallographic aspects of geometrically-necessary and statistically-stored dislocation density', Acta Materialia, Vol. 47, pp.1597-1611.
7. Arsenlis, A., Parks, D.M., Becker, R. and Bulatov, V.V. (2004) 'On the evolution of crystallographic dislocation density in non-homogeneously deforming crystals', J. Mech. Phys. Solids, Vol. 52, pp.1213-1246.
8. Ashby, M.F. (1970) 'The deformation of plastically non-homogenous alloys', Philos. Maga, Vol. 21, pp.399-424.
9. Begley, M.R. and Hutchinson, J.W. (1998) 'The mechanics of size-dependent indentation', J. Mech. Phys. Solids, Vol. 46, pp.2049-2068.
10. Biwa, S. and Storakers, B. (1995) 'An analysis of fully plastic Brinell indentation', J. Mech. Phys. Solids, Vol. 43, pp.1303-1333.
11. Busso, E.P., Meissonnier, F.T. and O'Dowd, N.P. (2000) 'Gradient-dependent deformation of two-phase single crystals', J. Mech. Phys. Solids, Vol. 48, pp.2333-2361.
12. Chiu, Y.L. and Ngan, A.H.W. (2002) 'A TEM investigation on indentation plastic zones in Ni3Al(Cr,B) single crystals', Acta Materialia, Vol. 50, pp.2677-2691.
13. De Guzman, M.S., Neubauer, G., Flinn, P. and Nix, W.D. (1993) 'The role of indentation depth on the measured hardness of materials', Material Research Symposium Proceedings, Vol. 308, pp.613-618.
14. Durst, K., Backes, B., Franke, O. and Goken, M. (2006) 'Indentation size effect in metallic materials: modeling strength from pop-in to macroscopic hardness using geometrically necessary dislocations', Acta Materialia, Vol. 54, pp.2547-2555.
15. Elmustafa, A.A. and Stone, D.S. (2002) 'Indentation size effect in polycrystalline F.C.C metals', Acta Mater, Vol. 50, pp.3641-3650.
16. Feng, G. and Nix, W.D. (2004) 'Indentation size effect in MgO', Scripta Mater, Vol. 51, pp.599-603.
17. Fleck, N.A., Muller, G.M., Ashby, M.F. and Hutchinson, J.W. (1994) 'Strain gradient plasticity: theory and experiment', Acta Metallurgica et Materialia, Vol. 42, pp.475-487.
18. Gao, H., Huang, Y., Nix, W.D. and Hutchinson, J.W. (1999) 'Mechanism-based strain gradient plasticity - I. theory', J. Mech. Phys. Solids, Vol. 47, pp.1239-1263.
19. Gerberich, W.W., Tymiak, N.I., Grunlan, J.C., Horstemeyer, M.F. and Baskes, M.I. (2002) 'Interpretation of indentation size effects', ASME Tras., Journal of Applied Mechanics, Vol. 69, pp.433-442.
20. Haque, M.A. and Saif, M.T.A. (2003) 'Strain gradient effect in nanoscale thin films', Acta Materialia, Vol. 51, pp.3053-3061.
21. Hill, R., Storakers, B. and Zdunek, A.B. (1989) 'A theoretical study of the Brinell hardness test', Proceedings of the Royal Society of London Series A Mathematical Physical and Engineering Sciences, Vol. 423, No. 1865, pp.301-330.
22. Huang, Y., Zhang, F., Hwang, K.C., Nix, W.D., Pharr, G.M. and Feng, G. (2006) 'A model of size effects in nano-indentation', J. Mech. Phys. Solids, Vol. 54, pp.1668-1686.
23. Huber, N., Nix, W.D. and Gao, H. (2002) 'Identification of elastic-plastic material parameters from pyramidal indentation of thin films', Proceedings of the Royal Society of London Series A, Vol. 458, No. 2023, pp.1593-1620.
24. Johnson, K.L. (1970) 'The correlation of indentation experiments', J. Mech. Phys. Solids, Vol. 18, pp.115-126.
25. Kim, J.Y., Kang, S.K., Greer, J.R. and Kwon, D. (2008) 'Evaluating plastic flow properties by characterizing indentation size effect using a sharp indenter', Acta Materialia, Vol. 56, pp.3338-3343.
26. Kiser, M.T., Zok, F.W. and Wilkinson, D.S. (1996) 'Plastic flow and fracture of a particulate metal matrix composite', Acta Mater, Vol. 44, pp.3465-3476.
27. Kocks, U.F. (1966) 'A statistical theory of flow stress and work hardening', Phil. Mag, Vol. 13, p.541.
28. Kramer, D., Huang, H., Kriese, M., Rohack, J., Nelson, J., Wright, A., Bahr, D. and Gerberich, W.W. (1999) 'Yield strength predictions from the plastic zone around nanocontacts', Acta Materialia, Vol. 47, p.333-343.
29. Lim, Y.Y. and Chaudhri, Y.Y. (1999) 'The effect of the indenter load on the nanohardness of ductile metals: an experimental study of polycrystalline work-hardened and annealed oxygen-free copper', Philoso. Maga, Vol. A79, No. 12, pp.2979-3000.
30. Lloyd, D.J. (1994) 'Particle reinforced aluminum and magnesium matrix composites', Int. Mater. Rev, Vol. 39, pp.1-23.
31. Ma, Q. and Clarke, D.R. (1995) 'Size dependent hardness in silver single crystals', Journal of Materials Research, Vol. 10, pp.853-863.
32. Mughrabi, H. (2001) 'On the role of strain gradients and long-range internal stresses in the composite model of crystal plasticity', Materials Science and Engineering, Vol. A317, pp.171-180.
33. Manika, I. and Maniks, J. (2006) 'Size effects in micro- and nano-scale indentation', Acta Materialia, Vol. 54, pp.2049-2056.
34. McElhaney, K.W., Valssak, J.J. and Nix, W.D. (1998) 'Determination of indenter tip geometry and indentation contact area for depth sensing indentation experiments', Journal of Materials Research, Vol. 13, pp.1300-1306.
35. Nan, C-W. and Clarke, D.R. (1996) 'The influence of particle size and particle fracture on the elastic/plastic deformation of metal matrix composites', Acta Mater, Vol. 44, pp.3801-3811.
36. Needleman, A. and Gil Sevillano, J. (2003) 'Preface to the viewpoint set on: geometrically necessary dislocations and size dependent plasticity', Scripta Materialia, Vol. 48, No. 2, pp.109-211.
37. Nix, W.D. and Gao, H. (1998) 'Indentation size effects in crystalline materials: a law for strain gradient plasticity', J. Mech. Phys. Solids, Vol. 46, pp.411-425.
38. Nye, J.F. (1953) 'Some geometrical relations in dislocated crystals', Acta Metallurgica, Vol. 1, pp.153-162.
39. Orowan, E. (1948) Discussion in Symposium on Internal Stresses in Metals and Alloys, p.451, Institute of Metals, London.
40. Poole, W.J., Ashby, M.F. and Fleck, N.A. (1996) 'Micro-hardness of annealed and work-hardened copper polycrystals', Scripta Materialia, Vol. 34, pp.559-564.
41. Qiu, X., Huang, Y., Nix, W.D., Hwang, K.C. and Gao, H. (2001) 'Effect of intrinsic lattice resistance in strain gradient plasticity', Acta Mater, Vol. 49, pp.3949-3958.
42. Qu, S., Huang, Y., Nix, W.D., Jiang, H., Zhang, F. and Hwang, K.C. (2004) 'Indenter tip radius effect on the Nix-Gao relation in micro- and nanoindentation hardness experiments', J. Mater. Res, Vol. 19, pp.3423-3434.
43. Saha, R., Xue, Z., Huang, Y. and Nix, W.D. (2001) 'Indentation of a soft metal film on a hard substrate: strain gradient hardening effects', J. Mech. Phys. Solids, Vol. 49, pp.1997-2014.
44. Shrotriya, P., Allameh, S.M., Lou, J., Buchheit, T. and Soboyejo, W.O. (2003) 'On the measurement of the plasticity length scale parameter in LIGA nickel foils', Mechanics of Materials, Vol. 35, pp.233-243.
45. Stolken, J.S. and Evans, A.G. (1998) 'A microbend test method for measuring the plasticity length-scale', Acta Mater, Vol. 46, pp.5109-5115.
46. Stelmashenko, N.A., Walls, M.G., Brown, L.M. and Milman, Y.V. (1993) 'Microindentation on W and Mo oriented single crystals: an STM study', Acta Metallurgica et Materialia, Vol. 41, pp.2855-2865.
47. Swadener, J.G., George, E.P. and Pharr, G.M. (2002) 'The correlation of the indentation size effect measured with indenters of various shapes', J. Mech. Phys. Solids, Vol. 50, pp.681-694.
48. Tabor, D. (1951) The Hardness of Metals, Clarendon Press, Oxford.
49. Taylor, G.I. (1938) 'Plastic strain in metals', J. Inst. Metals, Vol. 62, pp.307-324.
50. Voyiadjis, G.Z. and Abu Al-Rub, R.K. (2005) 'Gradient plasticity theory with a variable length scale parameter', International Journal of Solids and Structures, Vol. 42, pp.3998-4029.
51. Voyiadjis, G.Z. and Abu Al-Rub, R.K. (2009) Nonlocal Continuum Damage and Plasticity: Theory and Computation, World Scientific Publishing Co Pte Ltd., UK.
52. Xue, Z., Huang, Y., Hwang, K.C. and Li, M. (2002) 'The influence of indenter tip radius on the micro-indentation hardness', ASME J. Eng. Mater. Technol, Vol. 124, pp.371-379.
53. Yuan, H. and Chen, J. (2001) 'Identification of the intrinsic material length in gradient plasticity theory from micro-indentation tests', Int. J. Solids and Structures, Vol. 38, pp.8171-8187.
54. Zhang, F., Saha, R., Huang, Y., Nix, W. D., Hwang, K.C., Qu, S. and Li, M. (2005) 'Indentation of a hard film on a soft substrate: strain gradient hardening effects', Int. J. Plasticity, Vol. 23, pp.25-43. (Pubitemid 44402984)
55. Zhao, M., Slaughter, W.S., Li, M. and Mao, S.X. (2003) 'Material-length-scale-controlled nanoindentation size effects due to strain-gradient plasticity', Acta Materialia, Vol. 51, pp.4461-4469.
56. Zong, Z., Lou, J., Adewoye, O.O., Elmustafa, A.A., Hammad, F. and Soboyejo, W.O. (2006) 'Indentation size effect in the nano- and micro-hardness of fcc single crystal metals', Metarials Science and Engineering, Vol. A434, pp.178-187.