Small scale, grain size and substrate effects in nano-indentation experiment of film-substrate systems

International Journal of Solids and Structures

Volumn 44, Issue 13, 2007, Pages 4492-4504

  Chen, S H ^a   Liu, L ^a   Wang, T C ^a  

^a INSTITUTE OF MECHANICS   (China)

Author keywords

Classical plasticity theory; FEM; Film substrate system; Indenter tip curvature; Nano indentation hardness; Strain gradient plasticity theory

Indexed keywords

FINITE ELEMENT METHOD; GRAIN SIZE AND SHAPE; NANOINDENTATION; PLASTICITY; STRAIN MEASUREMENT; THICKNESS MEASUREMENT;

CLASSICAL PLASTICITY THEORY; FILM-SUBSTRATE SYSTEM; INDENTER TIP CURVATURE; STRAIN GRADIENT PLASTICITY THEORY;

THIN FILMS;

EID: 34047152210     PISSN: 00207683     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijsolstr.2006.11.033     Document Type: Article

References (66)

1. Abu Al-Rub R., and 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. Plasticity 20 (2004) 1139-1182
2. Abu Al-Rub R., and Voyiadjis G.Z. A physically based gradient plasticity theory. Int. J. Plasticity 22 (2006) 654-684
3. Acharya A., and Bassani J.L. Lattice incompatibility and a general theory of crystal plasticity. J. Mech. Phys. Solids 48 (2000) 1565-1595
4. Bassani J. Incompatibility and a simple gradient theory of plasticity. J. Mech. Phys. Solids 49 (2001) 1983-1996
5. Chen S.H., and Wang T.C. A new hardening law for strain gradient plasticity. Acta Mater. 48 (2000) 3997-4005
6. Chen S.H., and Wang T.C. Strain gradient theory with couple stress for crystalline solids. Eur. J. Mech. A-Solids 20 (2001) 739-756
7. Chen S.H., and Wang T.C. A new deformation theory for strain gradient effects. Int. J. Plasticity 18 (2002) 971-995
8. Chen S.H., and Wang T.C. Finite element solutions for plane strain mode I crack with strain gradient effects. Int. J. Solids Struct. 39 5 (2002) 1241-1257
9. Chen S.H., and Wang T.C. Strain gradient effects in the particle-reinforced metal-matrix composites. Acta Mech. 157 1-4 (2002) 113-127
10. Chen S.H., and Wang T.C. Interface crack problems with strain gradient effects. Int. J. Fract. 117 1 (2002) 25-37
11. Chen S.H., Liu L., and Wang T.C. Size dependent nano-indentation of a soft film on a hard substrate. Acta Mater. 52 5 (2004) 1089-1095
12. Chen S.H., Tao C.J., and Wang T.C. A study of size-dependent micro-indentation. Acta Mech. 167 1-2 (2004) 57-71
13. Chen S.H., Liu L., and Wang T.C. Investigation of the mechanical properties of thin films by nano-indentation, considering the effects of thickness and different coating-substrate combinations. Surf. Coat. Technol. 191 (2005) 25-32
14. Dennis J.E., and Moré J.J. Quasi-Newton methods, motivation and theory. SIAM Rev. 19 1 (1977) 46-89
15. Duan H.L., Wang J., Huang Z.P., and Karihaloo B.L. Size-dependent effective elastic constants of solids containing nano-inhomogeneities with interface stress. J. Mech. Phys. Solids 53 (2005) 1574-1596
16. Fleck N.A., and Hutchinson J.W. A phenomenological theory for strain gradient effects in plasticity. J. Mech. Phys. Solids 41 (1993) 1825-1857
17. Fleck N.A., and Hutchinson J.W. Strain gradient plasticity. In: Hutchinson J.W., and Wu T.Y. (Eds). Advances in Applied Mechanics vol. 33 (1997), Academic Press, New York 295-361
18. Fleck N.A., Muller G.M., Ashby M.F., and Hutchinson J.W. Strain gradient plasticity: theory and experiment. Acta Metal. Mater. 42 (1994) 475-487
19. Gao H., and Huang Y. Taylor-based nonlocal theory of plasticity. Int. J. Solids Struct. 38 (2001) 2615-2637
20. Gao H., Huang Y., Nix W.D., and Hutchinson J.W. Mechanism-based strain gradient plasticity-I. Theory. J. Mech. Phys. Solids 47 (1999) 1239-1263
21. Gerberich W.W., Tymiak N.I., Grunlan J.C., Horstemeyer M.F., and Baskes M.I. Interpretations of indentation size effects. J. Appl. Mech. 69 (2002) 433-442
22. Gurtin M.E. A gradient theory of single-crystal viscoplasticity that accounts for geometrically necessary dislocation. J. Mech. Phys. Solids 50 (2002) 5-32
23. Gurtin M.E. On a framework for small-deformation viscoplasticity: free energy, microforces, strain gradient. Int. J. Plasticity 19 (2003) 47-90
24. Haque M.A., and Saif M.T.A. Strain gradient effect in nanoscale thin films. Acta Mater. 51 (2003) 3053-3061
25. Hommel M., and Kraft O. Deformation behavior of thin copper films on deformable substrates. Acta Mater. 49 (2001) 3935-3947
26. Horstemeyer M.F., Baskes M.I., and Plimpton S.J. Length scale and time scale effects on the plastic flow of FCC metals. Acta Mater. 49 (2001) 4363-4374
27. Hu G., and Huang Z. Micromechanics of nonlinear composites. Key Eng. Mater. 274-276 (2004) 35-42
28. Huang Y., Gao H., Nix W.D., and Hutchinson J.W. Mechanism-based strain gradient plasticity-II. Analysis. J. Mech. Phys. Solids 48 (2000) 99-128
29. Huang Y., Xue Z., Gao H., Nix W.D., and Xia Z.C. A study of micro-indentation hardness tests by mechanism-based strain gradient plasticity. J. Mater. Res. 15 (2000) 1786-1796
30. Huang Y., Qu S., Hwang K.C., Li M., and Gao H. A conventional theory of mechanism-based strain gradient plasticity. Int. J. Plasticity 20 (2004) 753-782
31. Huang Y., Zhang F., Hwang K.C., Nix W.D., Pharr G.M., and Feng G. A model of size effects in nano-indentation. J. Mech. Phys. Solids 54 (2006) 1668-1686
32. Hwang K.C., Jiang H., Huang Y., Gao H., and Hu N. A finite deformation theory of strain gradient plasticity. J. Mech. Phys. Solids 50 (2002) 81-99
33. Johnson K.L. The correlation of indentation experiments. J. Mech. Phys. Solids 18 (1970) 115-126
34. Joslin D.L., and Oliver W.C. A new method for analyzing data from continuous depth-sensing micro-indentation tests. J. Mater. Res. 5 (1990) 123-126
35. Kreuzer H.G.M., and Pippan R. Discrete dislocation simulation of nano-indentation: the influence of obstacles and a limited number of dislocation sources. Philo. Magazine 85 (2005) 3301-3319
36. Liu X., and Hu G. A continuum micromechanical theory of overall plasticity for particulate composites including particle size effect. Int. J. Plasticity 21 (2005) 777-799
37. Lloyd D.J. Particle-reinforced aluminum and magnesium matrix composite. Int. Mater. Rev. 39 (1994) 1-23
38. Ma Q., and Clarke D.R. Size dependent hardness of silver single crystals. J. Mater. Res. 10 (1995) 853-863
39. 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. 13 (1998) 1300-1306
40. Nix W.D. Mechanical properties of tin films. Metal. Trans. 20A (1989) 2217-2245
41. Nix W.D., and Gao H. Indentation size effects in crystalline materials: a law for strain gradient plasticity. J. Mech. Phys. Solids 46 (1998) 411-425
42. Oliver W.C., and Pharr G.M. An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7 6 (1992) 1564-1583
43. Poole W.J., Ashby M.F., and Fleck N.A. Micro-hardness of annealed and work-hardened copper polycrystals. Scripta Mater. 34 (1996) 559-564
44. Pucha R.V., Ramakrishna G., Mahalingam S., and Sitaraman S.K. Modeling spatial strain gradient effects in thermo-mechanical fatigue of copper microstructures. Int. J. Fatigue 26 (2004) 947-957
45. Qu S., Huang Y., Nix W.D., Jiang H., Zhang F., and Hwang K.C. Indenter tip radius effect on the Nix-Gao relation in micro- and nano-indentation hardness experiments. J. Mater. Res. 19 (2004) 3423-3434
46. Qu S., Huang Y., Pharr G.M., and Hwang K.C. The indentation size effect in the spherical indentation of iridium: A study via the conventional theory of mechanism-based strain gradient plasticity. Int. J. Plasticity 22 (2006) 1265-1286
47. Saha R., and Nix W.D. Effects of the substrate on the determination of thin film mechanical properties by nano-indentation. Acta Mater. 50 (2002) 23-38
48. Saha R., Xue Z., Huang Y., and Nix W.D. Indentation of a soft metal film on a hard substrate: strain gradient hardening effects. J. Mech. Phys. Solids 49 (2001) 1997-2014
49. Schwaiger R., and Kraft O. Analyzing the mechanical behavior of thin films using nano-indentation, cantilever microbeam deflection, and finite element modeling. J. Mater. Res. 19 1 (2004) 315-324
50. Shrotriya P., Allameh S.M., Lou J., Buchheit T., and Soboyejo W.O. On the measurement of the plasticity length-scale parameter in LIGA nickel foils. Mech. Mater. 35 (2003) 233-243
51. Smyshlyaev V.P., and Fleck N.A. The role of strain gradients in the grain size effect for polycrystals. J. Mech. Phys. Solids 44 (1996) 465-495
52. Stelmashenko N.A., Walls A.G., Brwon L.M., and Milman Y.V. Micro-indentation on W and Mo oriented single crystals: an STM study. Acta Metal. Mater. 41 (1993) 2855-2865
53. Stolken J.S., and Evans A.G. A microbend test method for measuring the plasticity length scale. Acta Mater. 46 (1998) 5109-5115
54. Suresh S., Nieh T.G., and Choi B.W. Nano-indentation of cooper thin films on silicon substrates. Scripta Mater. 41 (1999) 951-957
55. Swaddiwudhipong S., Poh L.H., Hua J., Liu Z.S., and Tho K.K. Modeling nano-indentation tests of glass polymers using finite elements with strain gradient plasticity. Mater. Sci. Eng. A 404 (2005) 179-187
56. Swaddiwudhipong S., Hua J., Tho K.K., and Liu Z.S. Finite element modeling for materials with size effect. Model. Simul. Mater. Sci. Eng. 14 (2006) 1127-1137
57. Swaddiwudhipong S., Tho K.K., Hua J., and Liu Z.S. Mechanism-based strain gradient plasticity in C0 axisymmetric element. Int. J. Solids Struct. 43 (2006) 1117-1130
58. Swadener J.G., Taljat B., and Pharr G.M. Measurement of residual stress by load and depth sensing indentation with spherical indenters. J. Mater. Res. 16 (2001) 2091-2102
59. Swadener J.G., George E.P., and Pharr G.M. The correlation of the indentation size effect measured with indenters of various shapes. J. Mech. Phys. Solids 50 (2002) 681-694
60. Venkatraman R., and Bravman J.C. Separation of film thickness and grain-boundary strengthening effects in al thin-films on Si. J. Mater. Res. 7 (1992) 2040-2048
61. Voyiadjis G.Z., and Abu Al-Rub R.K. Gradient plasticity theory with a variable length scale parameter. Int. J. Solids Struct. 42 (2005) 3998-4029
62. Wei Y. Hardness solution form for elastic-plastic material considering the indenter tip curvature effect. Acta Mech. Sin. 35 (2003) 509-512 (in Chinese)
63. Wei Y., and Hutchinson J.W. Steady-state crack growth and work of fracture for solids characterized by strain gradient plasticity. J. Mech. Phys. Solids 45 (1997) 1253-1273
64. Wei Y., and Hutchinson J.W. Hardness trends in micro scale indentation. J. Mech. Phys. Solids 51 (2003) 2037-2056
65. Wei Y., Wang X., Zhao M., Cheng C.M., and Bai Y. Size effect and geometrical effect of solids in micro-indentation test. Acta Mech. Sin. 19 (2003) 59-70
66. Xue Z., Huang Y., Hwang K.C., and Li M. The influence of indenter tip radius on the micro-indentation hardness. J. Eng. Mater. Tech. 124 (2002) 371-379