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Kinetics of length-scale dependent plastic deformation of gold microspheres

  • AZM Ariful Islam (a1) and Robert J. Klassen (a1)

The size and strain-rate dependence of plastic deformation in Au microspheres of diameter ranging from 0.8 to 6.0 µm was investigated at room-temperature using flat-punch micro-compression testing. The contact yield stress was observed to increase with decreasing microsphere diameter. The apparent activation volume, V*, associated with the rate dependent plastic deformation remained essentially constant between 4 and 6b 3 for 0.8 and 1.0 µm spheres over strains up to 20% whereas it increased from 12 to 42b 3 for the larger 3.0 and 6.0 µm diameter specimens. The initiation of plastic deformation within the microspheres was also found to be highly dependent upon sphere diameter and strain rate with associated V*, and apparent activation energy, Q*, values of 0.4b 3 and 0.02 eV for 0.8 µm diameter spheres increasing to 4.1b 3 and 0.16 eV for 6.0 µm diameter spheres. These values indicate that initial plasticity is controlled by heterogeneous nucleation events that are consistent with a surface self-diffusion mechanism.

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1. GreerJ.R., OliverW.C., and NixW.D.: Size dependence of mechanical properties of gold at the micron scale in the absence of strain gradients. Acta Mater. 53, 1821 (2005).
2. NixW.D., GreerJ.R., FengG., and LilleoddenE.T.: Deformation at the nanometer and micrometer length scales: Effects of strain gradients and dislocation starvation. Thin Solid Films 515, 3152 (2007).
3. KimJ-Y. and GreerJ.R.: Tensile and compressive behavior of gold and molybdenum single crystals at the nano-scale. Acta Mater. 57, 5245 (2009).
4. FrickC.P., ClarkB.G., OrsoS., SchneiderA.S., and ArztE.: Size effect on strength and strain hardening of small-scale [111] nickel compression pillars. Mater. Sci. Eng., A 489, 319 (2008).
5. UchicM.D., DimidukD.M., FlorandoJ.N., and NixW.D.: Sample dimensions influence strength and crystal plasticity. Science 305, 986 (2004).
6. PurkayasthaR. and McMeekingR.: A parameter study of intercalation of lithium into storage particles in a lithium-ion battery. Comput. Mater. Sci. 80, 2 (2013).
7. GreerJ. and NixW.: Nanoscale gold pillars strengthened through dislocation starvation. Phys. Rev. B 73, 245410 (2006).
8. GreerJ.R., WeinbergerC.R., and CaiW.: Comparing the strength of f.c.c. and b.c.c. sub-micrometer pillars: Compression experiments and dislocation dynamics simulations. Mater. Sci. Eng., A 493, 21 (2008).
9. MookW.M., NiederbergerC., BechelanyM., PhilippeL., and MichlerJ.: Compression of freestanding gold nanostructures: From stochastic yield to predictable flow. Nanotechnology 21, 55701 (2010).
10. SchneiderA.S., ClarkB.G., FrickC.P., and ArztE.: Correlation between activation volume and pillar diameter for Mo and Nb BCC Pillars. MRS Proc. 1185, 1185 (2009).
11. ShenoyV.B., PhillipsR., and TadmorE.B.: Nucleation of dislocations beneath a plane strain indenter. J. Mech. Phys. Solids 48, 649 (2000).
12. LiuY., Van der GiessenE., and NeedlemanA.: An analysis of dislocation nucleation near a free surface. Int. J. Solids Struct. 44, 1719 (2007).
13. SchuhC.A., MasonJ.K., and LundA.C.: Quantitative insight into dislocation nucleation from high-temperature nanoindentation experiments. Nat. Mater. 4, 617 (2005).
14. PaulW., OliverD., MiyaharaY., and GrütterP.H.: Minimum threshold for incipient plasticity in the atomic-scale nanoindentation of Au(111). Phys. Rev. Lett. 110, 1 (2013).
15. MordehaiD., LeeS-W., BackesB., SrolovitzD.J., NixW.D., and RabkinE.: Size effect in compression of single-crystal gold microparticles. Acta Mater. 59, 5202 (2011).
16. MordehaiD., KazakevichM., SrolovitzD.J., and RabkinE.: Nanoindentation size effect in single-crystal nanoparticles and thin films: A comparative experimental and simulation study. Acta Mater. 59, 2309 (2011).
17. LeeS-W., MordehaiD., RabkinE., and NixW.D.: Effects of focused-ion-beam irradiation and prestraining on the mechanical properties of FCC Au microparticles on a sapphire substrate. J. Mater. Res. 26, 1653 (2011).
18. WangZ-J., ShanZ-W., LiJ., SunJ., and MaE.: Pristine-to-pristine regime of plastic deformation in submicron-sized single crystal gold particles. Acta Mater. 60, 1368 (2012).
19. MookW.M., LundM.S., LeightonC., and GerberichW.W.: Flow stresses and activation volumes for highly deformed nanoposts. Mater. Sci. Eng., A 493, 12 (2008).
20. GallK., DiaoJ., and DunnM. L.: The strength of gold nanowires. Nano Lett. 4, 2431 (2004).
21. WeinbergerC.R., JenningsA.T., KangK., and GreerJ.R.: Atomistic simulations and continuum modeling of dislocation nucleation and strength in gold nanowires. J. Mech. Phys. Solids 60, 84 (2012).
22. DengC. and SansozF.: Effects of twin and surface facet on strain-rate sensitivity of gold nanowires at different temperatures. Phys. Rev. B: Condens. Matter Mater. Phys. 81, 1 (2010).
23. KellyA. and NicholsonR.B.: Strengthening Methods in Crystals (Halstead Press Division, Wiley, New York, 1972).
24. DaoM., LuL., ShenY.F., and SureshS.: Strength, strain-rate sensitivity and ductility of copper with nanoscale twins. Acta Mater. 54, 5421 (2006).
25. WangY.M., HamzaA.V., and MaE.: Activation volume and density of mobile dislocations in plastically deforming nanocrystalline Ni. Appl. Phys. Lett. 86, 241917 (2005).
26. JenningsA.T., LiJ., and GreerJ.R.: Emergence of strain-rate sensitivity in Cu nanopillars: Transition from dislocation multiplication to dislocation nucleation. Acta Mater. 59, 5627 (2011).
27. ZhuT., LiJ., SamantaA., LeachA., and GallK.: Temperature and strain-rate dependence of surface dislocation nucleation. Phys. Rev. Lett. 100, 25502 (2008).
28. WangY., HamzaA., and MaE.: Temperature-dependent strain rate sensitivity and activation volume of nanocrystalline Ni. Acta Mater. 54, 2715 (2006).
29. SomekawaH. and SchuhC.A.: Effect of solid solution elements on nanoindentation hardness, rate dependence, and incipient plasticity in fine grained magnesium alloys. Acta Mater. 59, 7554 (2011).
30. ZhuT., LiJ., OgataS., and YipS.: Mechanics of ultra-strength materials. MRS Bull. 34, 167 (2009).
31. RodriguezP.: Grain size dependence of the activation parameters for plastic deformation: Influence of crystal structure, slip system, and rate-controlling dislocation mechanism. Metall. Mater. Trans. A 35, 2697 (2004).
32. NixW.D. and LeeS.: Micro-pillar plasticity controlled by dislocation nucleation at surfaces. Philos. Mag. 91, 1084 (2011).
33. BhakhriV. and KlassenR.J.: The strain-rate dependence of the nanoindentation stress of gold at 300 K: A deformation kinetics-based approach. J. Mater. Res. 24, 1456 (2009).
34. KocksU.F., ArgonA.S., and AshbyM.F.: Thermodynamics and kinetics of slip. Prog. Mater. Sci. 19, 1 (1975).
35. KogutL. and EtsionI.: Elastic–plastic contact analysis of a sphere and a rigid flat. J. Appl. Mech. 69, 657 (2002).
36. MaharajD. and BhushanB.: Nanomanipulation, nanotribology and nanomechanics of Au nanorods in dry and liquid environments using an AFM and depth sensing nanoindenter. Nanoscale 6, 5838 (2014).
37. HeyerJ-K., BrinckmannS., Pfetzing-MicklichJ., and EggelerG.: Microshear deformation of gold single crystals. Acta Mater. 62, 225 (2014).
38. KamimuraY., EdagawaK., and TakeuchiS.: Experimental evaluation of the Peierls stresses in a variety of crystals and their relation to the crystal structure. Acta Mater. 61, 294 (2013).
39. HullD. and BaconD.: Introduction to Dislocations, 4th ed. (Butterworth-Heinemann, Jordan Hill, Oxford, 2001).
40. BrennerS.S.: Tensile strength of whiskers. J. Appl. Phys. 27, 1484 (1956).
41. BeiH., ShimS., PharrG.M., and GeorgeE.P.: Effects of pre-strain on the compressive stress–strain response of Mo-alloy single-crystal micropillars. Acta Mater. 56, 4762 (2008).
42. SalehiniaI., PerezV., and BahrD.F.: Effect of vacancies on incipient plasticity during contact loading. Philos. Mag. 92, 550 (2012).
43. OrowanE.: Problems of plastic gliding. Proc. Phys. Soc. 52, 8 (1940).
44. BhakhriV., WangJ., Ur-rehmanN., CiureaC., GiulianiF., and VandeperreL.J.: Instrumented nanoindentation investigation into the mechanical behavior of ceramics at moderately elevated temperatures. J. Mater. Res. 27, 65 (2011).
45. BaufeldB., MesserschmidtU., BartschM., and BaitherD.: Plasticity of cubic zirconia between 700 °C and 1150 °C observed by macroscopic compression and by in situ tensile straining tests. Key Eng. Mater. 97–98, 431 (1994).
46. PirouzP., DemenetJ.L., and HongM.H.: On transition temperatures in the plasticity and fracture of semiconductors. Philos. Mag. A 81, 1207 (2001).
47. WoP.C., ZuoL., and NganA.H.W.: Time-dependent incipient plasticity in Ni3Al as observed in nanoindentation. J. Mater. Res. 20, 489 (2005).
48. SmithJ.F. and ZhengS.: High temperature nanoscale mechanical property measurements. Surf. Eng. 16, 143 (2000).
49. ViereggeJ.: Nanoscale Creep Testing of Copper & Gold, Hysitron Inc application note, Minneapolis, MN.
50. LiuC.L., CohenJ.M., AdamsJ.B., and VoterA.F.: EAM study of surface self-diffusion. Surf. Sci. 253, 334 (1991).
51. ChenL.Y., HeM., ShinJ., RichterG., and GianolaD.S.: Measuring surface dislocation nucleation in defect-scarce nanostructures. Nat. Mater. 14, 707 (2015).
52. LiJ.: Dislocation nucleation: Diffusive origins. Nat. Mater. 14, 656 (2015).
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