Determination of the microscale stress-strain curve and strain gradient effect from the micro-bend of ultra-thin beams

International Journal of Plasticity

Volumn 24, Issue 9, 2008, Pages 1606-1624

  Shi, Z F ^a   Huang, B ^b   Tan, H ^c   Huang, Y ^d   Zhang, T Y ^b   Wu, P D ^e   Hwang, K C ^a   Gao, H ^f  

^a TSINGHUA UNIVERSITY   (China)

^b HONG KONG UNIVERSITY OF SCIENCE AND TECHNOLOGY   (Hong Kong)

^c UNIVERSITY OF MANCHESTER   (United Kingdom)

^d NORTHWESTERN UNIVERSITY   (United States)

^e MCMASTER UNIVERSITY   (Canada)

^f Brown University   (United States)

Author keywords

Microscale uniaxial stress strain curve; Strain gradient effect; Thin beam

Indexed keywords

DEFLECTION (STRUCTURES); DEFORMATION; STRESS-STRAIN CURVES; ULTRATHIN FILMS;

MICROSCALE UNIAXIAL STRESS STRAIN CURVE; STRAIN GRADIENT EFFECT; THIN BEAMS;

BEAMS AND GIRDERS;

EID: 46549088176     PISSN: 07496419     EISSN: None     Source Type: Journal    
DOI: 10.1016/j.ijplas.2007.12.007     Document Type: Article

References (68)

1. Abu Al-Ruh R.K., and Voyiadjis G.Z. A physically based gradient plasticity theory. International Journal of Plasticity 22 (2006) 654-684
2. Acharya A., and Beaudoin A.J. Grain-size effect in viscoplastic polycrystals at moderate strains. Journal of the Mechanics and Physics of Solids 48 (2000) 2213-2230
3. Aifantis E.C. On the microstructural origin of certain inelastic models. Journal of Engineering Materials and Technology - Transactions of the ASME 106 (1984) 326-330
4. American Institute of Physics handbook, 1972. McGraw-Hill, New York.
5. Arsenlis A., and Parks D.M. Crystallographic aspects of geometrically-necessary and statistically stored dislocation density. Acta Materialia 47 (1999) 1597-1611
6. Ashby M.F. The deformation of plastically non-homogeneous alloys. Philosophical Magazine 21 (1970) 399-424
7. Bassani J.L. Incompatibility and a simple gradient theory of plasticity. Journal of the Mechanics and Physics of Solids 49 (2001) 1983-1996
8. Beaudoin A.J., and Acharya A. A model for rate-dependent flow of metal polycrystals based on the slip plane lattice incompatibility. Materials Science and Engineering A 309 (2001) 411-415
9. Bishop J.F.W., and Hill R. A theory of plastic distortion of a polycrystalline aggregate under combined stresses. Philosophical Magazine 42 (1951) 414-427
10. Bishop J.F.W., and Hill R. A theoretical derivation of the plastic properties of a polycrystalline facecentered metal. Philosophical Magazine 42 (1951) 1298-1307
11. Busso E.P., Meissonnier F.T., and O'Dowd N.P. Gradient-dependent deformation of two-phase single crystals. Journal of the Mechanics and Physics of Solids 48 (2000) 2333-2361
12. Cheong K.S., Busso E.P., and Arsenlis A. A study of microstructural length scale effects on the behaviour of FCC polycrystals using strain gradient concepts. International Journal of Plasticity 21 (2005) 1797-1814
13. de Borst R., and Mühlaus H.B. Gradient-dependent plasticity: formulation and algorithmic aspects. International Journal for Numerical Methods in Engineering 35 (1992) 521-539
14. Douglass, M.R., 1998. Lifetime estimates and unique failure mechanisms of the digital micromirror device (DMD). In: Annual Proceedings-Reliability Physics Symposium (Sponsored by IEEE), 31 March-2 April 1998, pp. 9-16. Available from: .
15. Elssner G., Korn D., and Ruhle M. The influence of interface impurities on fracture energy of UHV diffusion-bonded metal-ceramic bicrystals. Scripta Metallurgica et Materialia 31 (1994) 1037-1042
16. Evers L.P., Parks D.M., Brekelmans W.A.M., and Geers M.G.D. Crystal plasticity model with enhanced hardening by geometrically necessary dislocation accumulation. Journal of the Mechanics and Physics of Solids 50 (2002) 2403-2424
17. Feng G., and Nix W.D. Indentation size effect in MgO. Scripta Materialia 51 (2004) 599-603
18. Fleck N.A., and Hutchinson J.W. A phenomenological theory for strain gradient effects in plasticity. Journal of the Mechanics and Physics of Solids 41 (1993) 1825-1857
19. 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
20. Fleck N.A., and Hutchinson J.W. A reformulation of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 49 (2001) 2245-2271
21. Fleck N.A., Muller G.M., Ashby M.F., and Hutchinson J.W. Strain gradient plasticity: theory and experiments. Acta Metallurgica et Materialia 42 (1994) 475-487
22. Hertzberg R.W. Deformation and Fracture Mechanics of Engineering Materials (1989), John Wiley & Sons, New York pp. 7
23. Gao H., Huang Y., and Nix W.D. Modeling plasticity at the micrometer scale. Naturwissenschaften 86 (1999) 507-515
24. Gao H., Huang Y., Nix W.D., and Hutchinson J.W. Mechanism-based strain gradient plasticity- I. Theory. Journal of the Mechanics and Physics of Solids 47 (1999) 1239-1263
25. Gao H., and Huang Y. Taylor-based nonlocal theory of plasticity. International Journal of Solids and Structure 38 (2001) 2615-2637
26. Gao H., and Huang Y. Geometrically necessary dislocation and size-dependent plasticity. Scripta Materialia 48 (2003) 113-118
27. Haque M.A., and Saif M.T.A. Strain gradient effect in nanoscale thin films. Acta Materialia S1 (2003) 3053-3061
28. Huang, B., 2005. Mechanical Characterization of Thin Films. Doctor Dissertation of the Hong Kong University of Science and Technology (Chapter 5).
29. Huang B., and Zhang T.Y. Microbridge tests: II. On buckled thin gold films. Journal of Micromechanics and Microengineering 16 (2006) 134-142
30. Huang Y., Gao H., Nix W.D., and Hutchinson J.W. Mechanism-based strain gradient plasticity - II. Analysis. Journal of the Mechanics and Physics of Solids 48 (2000) 99-128
31. Huang Y., Xue Z., Gao H., Nix W.D., and Xia Z.C. A study of microindentation hardness tests by mechanism-based strain gradient plasticity. Journal of Materials Research 15 (2000) 1786-1796
32. Huang Y., Qu S., Hwang K.C., Li M., and Gao H. A conventional theory of mechanism-based strain gradient plasticity. International Journal of Plasticity 20 (2004) 753-782
33. Huang Y., Zhang F., Hwang K.C., Nix W.D., Pharr G.M., and Feng G. A model of size effects in nano-indentation. Journal of the Mechanics and Physics of Solids 54 (2006) 1668-1686
34. Hwang K.C., Jiang H., Huang Y., Gao H., and Hu N. A finite deformation theory of strain gradient plasticity. Journal of the Mechanics and Physics of Solids 50 (2002) 81-99
35. Hwang K.C., Jiang H., Huang Y., and Gao H. Finite deformation analysis of mechanism-based strain gradient plasticity: torsion and crack tip field. International Journal of Plasticity 19 (2003) 235-251
36. Hwang K.C., Guo Y., Jiang H., Huang Y., and Zhuang Z. The finite deformation theory of Taylor-based nonlocal plasticity. International Journal of Plasticity 20 (2004) 831-839
37. Jiang H., Huang Y., Zhuang Z., and Hwang K.C. Fracture in mechanism-based strain gradient plasticity. Journal of the Mechanics and Physics of Solids 49 (2001) 979-993
38. Kocks U.F. The relation between polycrystal deformation and single crystal deformation. Metallurgical and Materials Transactions 1 (1970) 1121-1144
39. Lasry D., and Belytschko T. Localization limiters in transient problems. International Journal of Solids and Structures 24 (1988) 581-597
40. Lloyd D.J. Particle reinforced aluminum and magnesium matrix composites. International Materials Reviews 39 (1994) 1-23
41. McElhaney K.W., Vlasssak J.J., and Nix W.D. Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments. Journal of Materials Research 13 (1998) 1300-1306
42. Mühlaus H.B., and Aifantis E.C. A variational principle for gradient plasticity. International Journal of Solids and Structures 28 (1991) 845-857
43. Nix W.D., and Gao H. Indentation size effects in crystalline materials: a lawfor strain gradient plasticity. Journal of the Mechanics and Physics of Solids 46 (1998) 411-425
44. Nye J. Some geometrical relations in dislocated crystals. Acta Metallurgica et Materialia 1 (1953) 153-162
45. Qiu X., Huang Y., Nix W.D., Hwang K.C., and Gao H. Effect of intrinsic lattice resistance in strain gradient plasticity. Acta Materialia 49 (2001) 3949-3958
46. Qiu X., Huang Y., Wei Y., Gao H., and Hwang K.C. The flow theory of mechanism-based strain gradient plasticity. Mechanics of Materials 35 (2003) 245-258
47. Qu S., Huang Y., Nix W.D., Jiang H., Zhang F., and Hwang K.C. The indenter tip radius effet on the Nix-Gao relation in micro- and nanoindentation hardness experiments. Journal of Materials Research 19 (2004) 3423-3434
48. Qu S., Siegmund T., Huang Y., Wu P.D., Zhang F., and Hwang K.C. A study of particle size effect and interface fracture in aluminum alloy composites via an extend conventional theory of mechanism-based strain gradient plasticity. Composites Science and Technology 65 (2005) 1244-1253
49. 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. International Journal of Plasticity 22 (2006) 1265-1286
50. Saha R., Xue Z., Huang Y., and Nix W.D. Indentation of a soft metal film on a hard substrate: strain gradient hardening effects. Journal of the Mechanics and Physics of Solids 49 (2001) 1997-2014
51. Saha R., and Nix W.D. Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Materialia 50 (2002) 23-28
52. Shi M.X., Huang Y., Gao H., and Hwang K.C. Non-existence of separable crack tip field in mechanism-based strain gradient plasticity. International Journal of Solids and Structures 37 (2000) 5995-6010
53. Shi M., Huang Y., Jiang H., Hwang K.C., and Li M. The boundary-layer effect on the crack tip field in mechanism-based strain gradient plasticity. International Journal of Fracture 112 (2001) 23-41
54. Shrotriya P., Allameh S.M., Lou J., Buchheit T., and Soboyejo W.O. On the measurement of the plasticity length scale parameter in LIGA nikel foiles. Mechanics of Materials 35 (2003) 233-243
55. Sluys L.J., de Borst R., and Mühlaus H.B. Wave-propagation, localization and dispersion in a gradient-dependent medium. International Journal of Solids and Structures 30 (1993) 1153-1171
56. Stelmashenko N.A., Walls A.G., Brown L.M., and Milman Y.V. Microindentation on W and Mooriented single crystals: an STM study. Acta Metallurgica et Materialia 41 (1993) 2855-2865
57. Stolken J.S., and Evans A.G. A microbend test method for measuring the plasticity length scale. Acta Materialia 46 (1998) 5109-5115
58. Swadener J.G., George E.P., and Pharr G.M. The correlation of the indentation size effect measured with indenters of various shapes. Journal of the Mechanics and Physics of Solids 50 (2002) 681-694
59. Taylor G.I. The mechanism of plastic deformation of crystals. Part I. - theoretical. Proceedings of the Royal Society of London A 145 (1934) 362-387
60. Taylor G.I. Plastic strain in metals. Journal of the Institute of Metals 62 (1938) 307-324
61. Uchic M.D., Dimiduk D.M., Florando J.N., and Nix W.D. Oxide surface films on metal crystals-response. Science 306 (2004) 1134-1135
62. Voyiadjis G.Z., Aby Al-Ruba R.K., and Palazottob A.N. Thermodynamic framework for coupling of non-local viscoplasticity and non-local anisotropic viscodamage for dynamic localization problems using gradient theory. International Journal of Plasticity 20 (2004) 981-1038
63. Wang W., Huang Y., Hsia K.J., Hu K.X., and Chandra A. A study of microbend test by strain gradient plasticity. International Journal of Plasticity 19 (2003) 365-382
64. Xue Z., Huang Y., and Li M. Particle size effect in metallic materials: a study by the theory of mechanism-based strain gradient plasticity. Acta Materialia 50 (2002) 149-160
65. Xue Z., Saif M.T.A., and Huang Y. The strain gradient effect in microelectromechanical systems (MEMS). Journal of Microelectromechanical Systems 11 (2002) 27-35
66. Zbib H.M., and Aifantis E.C. On the localization and postlocalization behavior of plastic deformation. Part I. On the initiation of shear bands; Part II. On the evolution and thickness of shear bands; Part III. On the structure and velocity of Portevin-Le Chatelier bands. Res Mechanica 23 (1988) 261-277 279-292, 293-305
67. Zhang T.Y., Su Y.J., Qian C.F., Zhao M.H., and Chen L.Q. Microbridge testing of silicon nitride thin films deposited on silicon wafers. Acta Materialia 48 (2000) 2843-2857
68. Zhang F., Saha R., Huang Y., Nix W.D., Hwang K.C., Qu S., and Li M. Indentation of a hard film on a soft substrate: strain gradient effects. International Journal of Plasticity 23 (2007) 25-43