Advertisement

Nanoprobing fracture length scales

  • W. W. Gerberich
  • W. M. Mook
  • M. J. Cordill
  • J. M. Jungk
  • B. Boyce
  • T. Friedmann
  • N. R. Moody
  • D. Yang
Conference paper

Abstract

Historically fracture behavior has been measured and modeled from the largest structures of earthquakes and ships to the smallest components of semiconductor chips and magnetic recording media. Accompanying this is an evolutionary interest in scale effects partially due to advances in instrumentation and partially to expanded supercomputer simulations. We emphasize the former in this study using atomic force microscopy, nanoindentation and acoustic emission to probe volumes small in one, two and three dimensions. Predominant interest is on relatively ductile Cu and Au films and semi-brittle, silicon nanoparticles. Measured elastic and plastic properties in volumes having at least one dimension on the order of 10 – 1000 nm, are shown to be state of stress and length scale dependent. These in turn are shown to affect fracture properties. All properties can vary by a factor of three dependent upon scale. Analysis of fracture behavior with dislocation-based, crack-tip shielding is shown to model both scale and stress magnitude effects.

Keywords

Fracture Toughness Acoustic Emission Strain Energy Release Rate Slow Crack Growth Indentation Size Effect 
These keywords were added by machine and not by the authors. This process is experimental and the keywords may be updated as the learning algorithm improves.

Preview

Unable to display preview. Download preview PDF.

Unable to display preview. Download preview PDF.

References

  1. Anderson, P.M. and Rice, J.R. (1986). Dislocation emission from cracks in crystals or along crystal interfaces. Scripta Metallurgica, 20, 1467–1472.CrossRefGoogle Scholar
  2. ASM Handbook on Fatigue and Fracture (1996). ASM International Materials, 19, Park, OH.Google Scholar
  3. Bazant, Z.P. (2004). Scaling theory for quasibrittle structural failure, PHAS, 101, National Academy of Sciences, September.Google Scholar
  4. Becit, M.R. (1979). Fracture of a surface layer bonded to a half space. International Journal of Engineering and Science 17, 287–295.CrossRefGoogle Scholar
  5. Begley, M.R. and Ambriso, J.M. (2003). Channel cracking during thermal cycling of thin film multilayers. International Journal of Fracture 119/120, 325–338.CrossRefGoogle Scholar
  6. Belytschko, T., Xiao, S.P., Schatz, G.C. and Ruoff, R.S. (2004). Atomistic Simulations of Nanotube Fracture, Dept. of Mechanical Engineering Northwestern Unversity, www.tam.northwestern.edu/tb/nano/tubefrac.Google Scholar
  7. Binnig, G., Quate, C.F. and Gerber, C. (1987). Atomic force microscope. Physical Review Letters 56, 930–933.CrossRefGoogle Scholar
  8. Chen, Y.T., Atteridge, D.G. and Gerberich, W.W. (1981). Dislocation dynamics of Fe-binary alloys: I. Low temperature plastic flow. Acta Metallurgica 29, 1171–1185.CrossRefGoogle Scholar
  9. Christensen, N.E., Ruoff, A.L. and Rodriguez, C.O. (1995). Pressure strengthening: a way to multimegabar static pressures. Physical Review B 52, 9121–9124.CrossRefGoogle Scholar
  10. Corcoran, S.G., Colton, R.J., Lilleodden, E.T. and Gerberich, W.W. (1997). Anamolous plastic deformation of surfaces: nanoindenation of gold single crystals. Physical Review B 55, 16057–16060.CrossRefGoogle Scholar
  11. Cordill, M.J., Bahr, D.F., Moody, N.R. and Gerberich, W.W. (2004). Recent developments in thin film adhesion measurement. IEEE Transactions on Device Manufacturing and Reliability 4, 163–168.CrossRefGoogle Scholar
  12. Cordill, M.J., Moody, N.R. and Bahr, D.F. (2005). The effects of plasticity on adhesion of hard films on ductile interlayers, Acta Materialia, accepted.Google Scholar
  13. Curtin, W.A. and Miller, R.E. (2003). Atomistic/continuum coupling in computational materials science. Modelling and Simulation in Materials Science and Engineering 11, R33–R68.CrossRefGoogle Scholar
  14. Fleischmann, P., Lakestani, F., Baboux, J.C. and Rouby, D. (1977). Spectral and energy analysis of a moving ultrasonic source-application of acoustic emission to aluminum during plastic deformation. Materials Science and Engineering 29, 205–212.CrossRefGoogle Scholar
  15. Gall, K., Diao, J. and Dunn, M. (2004). Strength of gold nanowires. Nanoletters 4, 2431–2436.Google Scholar
  16. Gall, K., Diao, J., Dunn, M.L., Haftel, M., Bernstein, N. and Mehl, M.J. (2005). Tetragonal Phase Transformation in Gold Nanowires, Journal of Engineering Materials and Technology, submitted.Google Scholar
  17. Garzke, Jr., W.H, Brown, D.K., Matthias, P.K., Cullimore, R., Wood, D., Livingston, D., Leighty, H.P., Foecke, T. and Sandiford, A. (1997). Titanic, the Anatomy of a Disaster, Report from the Marine/Forensic Panel (SD-7), Soc. Of Naval Architects and Marine Engineers, 1.1–1.47.Google Scholar
  18. Gerberich, W.W. and Jatavallabhula, K. (1980). A review of acoustic emission from source controlled by grain size and particle fracture, in Nondestructive Evaluation, (edited by Buck, O. and Wolf, S.M.) TMS, Warrendale, PA, 319–348.Google Scholar
  19. Gerberich, W.W. (1985). Interaction of microstructure and mechanism in defining KIc, KIscc, or ΔKth values In: Fracture: Interactions of Microstructure, Mechanisms, and Mechanics, (edited by Wells, J.M. and Landes, J.D.,) TMS, Warrendale, PA, 49.Google Scholar
  20. Gerberich, W.W., Yu, W., Kramer, D., Strojny, A., Bahr, D.F, Lilleodden, E.T. and Nelson, J. (1993). Elastic loading and elastoplastic unloading from nanometer level indentations for modulus determinations. Journal of Materials Research 13, 421–439.Google Scholar
  21. Gerberich, W.W., Volinsky, A.A. and Tymiak, N.I. (2000). A brittle to ductile transition in adhered thin films. Materials Research Society Symposium 594, 51–363.Google Scholar
  22. Gerberich, W.W., Tymiak, N.I., Grunlan, J.C., Horstemeyer, M.F. and Baskes, M.I. (2002). Interpretations of indentation size effects. Journal of Applied Mechanics 69, 433–442.CrossRefGoogle Scholar
  23. Gerberich, W.W., Mook, W.M, Perrey, C.R., Carter, C.B., Baskes, M.I., Mukherjee, R., Gidwani, A., Heberlein, J., McMurry, P.H. and Girshick, J.L. (2003). Superhard silicon nanospheres. Journal on the Mechanics and Physics of Solids 51, 979–992.CrossRefGoogle Scholar
  24. Gerberich, W.W., Jungk, J.M., Li, M., Volinsky, A.A., Hoehn, J.W. and Yoder, K. (2003a). Length scales for the fracture of nanostructures. International Journal of Fracture 119/120, 387–405.CrossRefGoogle Scholar
  25. Gerberich, W.W., Jungk, J.M. and Mook, W.M. (2003b). Crack-dislocation interactions. in Comprehensive Structural Integrity: Interfacial and Nanoscale Failure, (edited by Gerberich, W. and Yang, W.), ch. 10, 357–382.Google Scholar
  26. Gerberich, W.W., Cordill, M.J, Mook, W.M., Moody, N.R., Perrey, C.R., Carter, C.B., Mukherjee, R. and Girshick, S.L. (2005). A boundary constraint energy balance criterion for small volume deformation. Acta Materialia, accepted.Google Scholar
  27. Gerberich, W.W., Mook, W.M., Cordill, M.J., Carter, C.B., Perrey, C.R., Heberlein, J. and Girshick, S.L. (2005a). Reverse plasticity in single crystal silicon nanospheres. International Journal of Plasticity, accepted.Google Scholar
  28. Griffith, A.A. (1921). The phenomena of rupture and flow in solids. Philosophical Transactions of the Royal Society of London A221, 163–198.Google Scholar
  29. Griffith, A.A. (1925). The theory of rupture. Proceedings of the 1st Congress on Applied Mechanics, Delft, 55–63.Google Scholar
  30. Hall, E.O. (1951). The deformation and ageing of mild steel III. Discussion of results. Proceedings of Physical Science B 64, 747–753.CrossRefGoogle Scholar
  31. Hansen, N. (2004). Hall-Petch relation and boundary strengthening. Scripta Metallurgica 51, 801–806.Google Scholar
  32. Horstemeyer, M.F. and Baskes, M.I. (1991). Atomistic finite deformation simulations: a discussion on length scale effects in relation to mechanical stresses. Transactions of the ASME. Journal of Engineering Materials and Technology 121, 114–119.Google Scholar
  33. Huang, H. and Gerberich, W.W. (1992). Crack-tip dislocation emission arrangements for equilibrium-II. Comparisons to analytical and computer simulation models. Acta Metallurgica et Materialia 40, 2873.CrossRefGoogle Scholar
  34. Huang, H. and Spaepen, F. (2000). Tensile testing of free-standing Cu, Ag and Al thin films and Ag/Cu multilayers. Acta Materialia 48, 3261–3269.CrossRefGoogle Scholar
  35. Hughes, D.A. (2004). Sandia National Laboratories, Livermore, CA, private communication.Google Scholar
  36. Hutchinson, J.W. (1968). Singular behaviour at the end of a tensile crack in a hardening material. Journal of the Mechanics and Physics of Solids 16, 3–31.Google Scholar
  37. Irwin, G.R. (1948). Fracture dynamics. In: Fracturing of Metals, Am. Soc. For Metals, Cleveland, 147–166.Google Scholar
  38. Irwin, G.R. (1960). ASTM Bulletin, Jan., 29.Google Scholar
  39. Johnson, K. (1985). Contact Mechanics. Cambridge Univ. Press, U.K., 57.MATHGoogle Scholar
  40. Jungk, J.M., Boyce, B.L., Buchheit, T.E, Friedmann, T.A., Yang, D. and Gerberich, W.W. (2005). Indentation fracture toughness and acoustic energy release in diamond films, in preparation.Google Scholar
  41. Katz, Y., Keller, R.R., Huang, H. and Gerberich, W.W. (1993). A dislocation shielding model for the fracture of semibrittle crystals. Metallurgical Transactions A 24A, 343–350.Google Scholar
  42. Lane, M., Dauskardt, R.H., Krishna, N. and Hashim, I. (2000). Adhesion and reliability of copper interconnects with Ta and TaN barrier layers. Journal of Materials Research 15, 203–211.Google Scholar
  43. Li, J.C.M. (1986). Scripta Metallurgica 20, 1477.CrossRefGoogle Scholar
  44. Li, M., Chen, X.-F., Katz, Y. and Gerberich, W.W. (1990). Dislocation modeling and acoustic emission observation of alternating ductile/brittle events in Fe-3wt.%Si crystals. Acta Metallurgica et Materialia 38, 2435–2453.CrossRefGoogle Scholar
  45. Lin, J.H. and Thomson, R. (1986). Cleavage, dislocation emission, and shielding for cracks under general loading. Acta Metallurgica 34, 187–206.CrossRefGoogle Scholar
  46. Majzoub, R. and Chaudhri, M. (2000). High-speed photography of low-velocity impact cracking of solid spheres. Philosophical Magazine Letters 80, 387.CrossRefGoogle Scholar
  47. McElhaney, K.W., Vlassak, 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 13, 1300–1306.Google Scholar
  48. Michot, G. and George, A. (1982) In situ observation by x-ray synchrotron topography of the growth of plasticity deformed regions around crack tips in silicon under creep conditions. Scripta Metallurgica 16, 519–524.CrossRefGoogle Scholar
  49. Mook, W.M., Jungk, J.M., Cordill, M.J., Moody, N.R., Sun, Y., Xia, Y. and Gerberich, W.W. (2004). Geometry and surface state effects on the mechanical response of Au nanostructures. Zeischrift fur Metallkunde 95, 416–424.Google Scholar
  50. Mook, W.M., Perrey, C.R. Carter, C.B., Mukherjee, R., Girschick, S.L., McMurry, P.H. and Gerberich, W.W. (2005). Scale effects on nanoparticle modulus and fracture, Physical Review B, submitted.Google Scholar
  51. Moriarty, J.A., Belak, J.F., Rudd, R.E., Soderlind, P., Streitz, F.H. and Yang, L.H. (2002). Quantumbased atomistic simulation of materials properties in transition metals. Journal of Physics: Condensed Matter 14, 2825–2857.CrossRefGoogle Scholar
  52. Murnaghan, F. (1967). Finite Deformation in an Elastic Solid. Dover Publ., New York.Google Scholar
  53. Nix W.D., Gao H (1998). Indentation size effects in crystalline materials: a law for strain gradient plasticity. Journal of the Mechanics and Physics of Solids 46, 411–425.CrossRefGoogle Scholar
  54. Oliver, W.C. and Pharr, G.M. (1992). An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. Journal of Materials Research 1, 1564–1583.Google Scholar
  55. Orowan, E. (1950). Fatigue and Fracture of Metals. MIT Press, Cambridge, MA, 139.Google Scholar
  56. Parker, E.R. (1957). Brittle Behavior of Engineering Structures. National Academy of Sciences, National Research Council, J. Wiley, New York.Google Scholar
  57. Petch, N.J. (1953). Journal of the Iron and Steel Institute 173, 25.Google Scholar
  58. Poirier, J.-P. (2000). Murnaghan’s integrated linear equation of state. In: Introduction to the Physics of the Earth’s Interior, 2nd Ed., Cambridge University Press, 65.Google Scholar
  59. Read, D.T. (1998). Piezo-actuated microtensile test apparatus. Journal of Testing & Evaluation 26, 255–259.Google Scholar
  60. Rice, J.R. (1969). A path independent integral and the approximate analysis of strain concentration by notches and cracks. Journal of Applied. Mechanics 35, 379–386.Google Scholar
  61. Rice, J.R. and Thomson, R. (1974). Ductile versus brittle behaviour of crystals. Philosophical Magazine 29, 74–97.Google Scholar
  62. Shipway, P.H. and Hutchings, I.M. (1993). Fracture of brittle spheres under compression and impact loading. I. Elastic stress distributions. Philosophical Magazine A67, 1389–1404.Google Scholar
  63. Suo, Z., Shih, F. and Varias, A. (1993). A theory for cleavage cracking in the presence of plastic flow. Acta Metallurgica et Materialia 41, 551–557.CrossRefGoogle Scholar
  64. Thomson, R. (1986). Dislocation emission from cracks in crystals or along crystal interfaces. Scripta Metallurgica 20, 1473.Google Scholar
  65. Tymiak, N.I., Kramer, D.E., Bahr, D.F., Wyrobek, T.J. and Gerberich, W.W. (2001). Plastic strain and strain gradients at very small indentation depths. Acta Materialia 49, 1021–1034.CrossRefGoogle Scholar
  66. Tymiak, N.I., Daugela, A., Wyrobek, T.J. and Warren, O.L. (2004). Acoustic emission monitoring of the earliest stages of contact-induced plasticity in sapphire. Acta Materialia 52, 553–563.CrossRefGoogle Scholar
  67. Van Swygenhoven, H. and Spaczer, M. (1989). Competing plastic deformation mechanisms in nanophase metals. Physical Review B 60, 22–25.CrossRefGoogle Scholar
  68. Van Vliet, K., Li, J., Zhu, T., Yip, S. amd Suresh, S. (2003). Quantifying the early stages of plasticity through nanoscale experiments and simulations. Physical Review B Physical Review B, 104–105.Google Scholar
  69. Vlassak, J.J. (2003). Channel cracking in thin films on substrate of finite thickness. International Journal of Fracture 119/ 120, 299–323.Google Scholar
  70. Volinsky, A.A., Moody, N.R. and Gerberich, W.W. (2002). Interfacial toughness measurements for thin films on substrates. Acta Materialia 50, 441–466.CrossRefGoogle Scholar
  71. Volinsky, A.A., Moody, N.R., Kottke, M.L. and Gerberich, W.W. (2002a). Fiducial mark and nanocrack zone formation during thin-film delaminating. Philosophical Magazine A 82, 3383–3391.CrossRefGoogle Scholar
  72. Wei, Y. and Hutchinson, J.W. (1997). Nonlinear delamination mechanics for thin films. Journal of the Mechanics and Physics of Solids 45, 1137–1159.CrossRefMathSciNetGoogle Scholar
  73. Yu, M.F., Lourie, O., Dyer, M.J., Moloni, K., Kelly, T.F. and Ruoff, R.S. (2000). Strength and breaking mechanism of multiwalled carbon nanotubes under tensile load. Science 287, 637–640.CrossRefGoogle Scholar

Copyright information

© Springer 2006

Authors and Affiliations

  • W. W. Gerberich
    • 1
  • W. M. Mook
    • 1
  • M. J. Cordill
    • 1
  • J. M. Jungk
    • 1
  • B. Boyce
    • 2
  • T. Friedmann
    • 2
  • N. R. Moody
    • 3
  • D. Yang
    • 4
  1. 1.Department of Chemical Engineering and Materials ScienceUniversity of MinnesotaMinneapolisUSA
  2. 2.Sandia National LaboratoriesAlbuquerqueUSA
  3. 3.Sandia National LaboratoriesLivermoreUSA
  4. 4.Hysiton, Inc.MinneapolisUSA

Personalised recommendations