Abstract
In general, materials can resist deformation in a solid-like or viscous-like manner. Solid-like materials store energy under deformation, and upon removal of stress, returns to its original state. Viscous materials dissipate energy during deformation and upon removal of stress, remains in its deformed state. Materials with combined solid-like and viscous-like properties are said to be viscoelastic. Nanoindentation can be used to quantitatively determine the viscoelastic properties of materials. In one method, a small oscillatory force or displacement is imparted to the indenter. The resulting load and displacement signals provide a method whereby the elastic and viscous components of the specimen response can be calculated. In another method, the load or displacement is held at a fixed value and the change in displacement (creep) or load (relaxation) recorded over a period of time. Application of an appropriate mechanical model can yield values for the elastic and viscous properties of the specimen.
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Notes
- 1.
Strictly speaking, time-dependent plasticity is one where the deformation rate is fixed by the mechanical configuration of the specimen. It is a special case of the more general term of viscoplasticity.
References
A. Kulkarni and B. Bhushan, “Nano/picoindentation measurements on a single-crystal aluminium using modified atomic force microscopy,” Mat. Lett. 29, 1996, pp. 221–227.
S. Akita, H. Nishijima, T. Kishida and Y. Nakayama, “Nanoindentation of polycarbonate using a carbon nanotube tip,” Jpn. J. Appl. Phys. 39, 2000, pp. 7086–7089.
S.A. Syed Asif, R.J. Colton, and K.J. Wahl, “Nanoscale surface mechanical property measurements: Force modulation techniques applied to nanoindentation,” in Interfacial properties on the submicron scale, J. Frommer and R. Overney, eds. ACS Books, Washington, DC, 2001, pp. 189–215.
S.A. Syed Asif, K.J. Wahl, and R.J. Colton, ‘The influence of oxide and adsorbates on the nanomechanical response of silicon surfaces,” J. Mater. Res. 15 2, 2000, pp. 546–553.
B.N. Lucas, W.C. Oliver, and J.E. Swindeman, “The dynamics of frequency specific, depth sensing indentation testing,” Mat. Res. Soc. Symp. Proc. 522, 1998, pp. 3–14.
J.-L. Loubet, B.N. Lucas, and W.C. Oliver, in NIST Special Publication 896, Conference Proceedings: International Workshop on Instrumented Indentation, eds. D.T. Smith (NIST) 1995, pp. 31–34.
N.A. Burnham, S.P. Baker, and H.M. Pollock, “A model for mechanical properties of nanoprobes,” J. Mater. Res. 15 9, 2000, pp. 2006–2014.
A.F. Bower, N.A. Fleck, A. Needleman, and N. Ogbonna, “Indentation of a power law creeping solid,” Proc. R. Soc. A441, 1993, pp. 97–124.
J. Menčík, G. Rauchs, J. Bardon, and A. Riche, “Determination of elastic modulus and hardness of viscoelastic-plastic materials by instrumented indentation under harmonic load,” J. Mater. Res. 20 10, 2005 pp. 2660–2669.
W.B. Li and R. Warren, “A model for nano-indentation creep,” Acta Metall. Mater. 41 10, 1993, pp. 3065–3069.
P.M. Sargent and M.F. Ashby, “Indentation creep,” Mat. Sci. and Tech. 8, 1992, pp. 594–601.
R. Hill, B. Storåkers, A.B. Zdunek, “A theoretical study of the Brinell hardness test,” Proc. R. Soc. A423, 1989, pp. 301–330.
T.R.G. Kutty, C. Ganguly and D.H. Sastry, “Development of creep curves from hot indentation hardness data,” Scripta Materialia, 34 12, 1996, pp. 1833–1838.
R. Hill, “Similarity analysis of creep indentation tests,” Proc. R. Soc. A436, 1992, pp. 617–630.
B. Storåkers and P.-L. Larsson, “On Brinell and Boussinesq indentation of creeping solids,” J. Mech. Phys. Solids, 42 2, 1994, pp. 307–332.
M. Sakai, “Time-dependent viscoelastic relation between load and penetration for an axisummetric indenter,” Phil. Mag. A 82 10, 2002, pp. 1841–1849.
S.Dj. Mesarovic and N.A. Fleck, “Spherical indentation of elastic-plastic solids,” Proc. R. Soc. A455, 1999, pp. 2707–2728.
J.R.M. Radok, “Viscoelastic stress analysis,” Q. Appl. Math. 15, 1957, pp. 198–202.
E.H. Lee and J.R.M. Radok, “The contact problem for viscoelastic solids,” Trans. ASME Series E, J.App.Mech. 27, 1960, pp. 438–444.
K.L. Johnson, Contact Mechanics, Cambridge University Press, 1985.
L. Cheng, X. Xia, W. Yu, L.E. Scriven, and W.W. Gerberich, “Flat-punch indentation of a viscoelastic material,” J. Polymer Sci. 38, 2000, pp. 10–22.
T.C.T. Ting, “The contact stresses between a rigid indenter and a viscoelastic half-space,” Trans. ASME, J. App. Mech. 33, 1966, pp. 845–854.
M. Sakai and S. Shimizu, “Indentation rheometry for glass-forming materials,” J. Non-Crystalline Solids, 282, 2001, pp. 236–247.
S. Shimizu, Y. Yanagimoto and M. Sakai, “Pyramidal indentation load-depth curve of viscoelastic materials,” J. Mater. Res. 14 10, 1999, pp. 4075–4085.
X. Xia, A. Strojny, L.E. Scriven, W.W. Gerberich, A. Tsou, and C.C. Anderson, “Constitutive property evaluation of polymeric coatings using nanomechancial methods,” Mat. Res. Symp. Proc. 522, 1998, 199–204.
K.B. Yoder, S. Ahuja, K.T. Dihn, D.A. Crowson, S.G. Corcoran, L. Cheng, and W.W. Gerberich, “Nanoindentation of viscoelastic materials: Mechanical properties of polymer coatings an aluminum sheets,” Mat. Res. Symp. 522, 1998, pp. 205–210.
G. Feng and A.H.W. Ngan, “Effects of creep and thermal drift on modulus measurement using depth-sensing indentation,” J. Mater. Res. 17 3, 2002, pp. 660–668.
A.H.W. Ngan and B. Tang, “Viscoelastic effects during unloading in depth-sensing indentation,” J. Mater. Res. 17 10, 2002, pp. 2604–2610.
L. Cheng, L.E. Scriven, and W.W. Gerberich, “Viscoelastic analysis of micro- and nanoindentation,” Mat. Res. Symp. Proc. 522, 1998, pp. 193–198.
M.L. Oyen and R.F. Cook, “Load-displacement behavior during sharp indentation of viscous-elastic-plastic materials,” J. Mater. Res. 18 1, 2003, pp. 139–150.
A. Strojny and W.W. Gerberich, “Experimental analysis of viscoelastic behavior in nanoindentation,” Mat. Res. Soc. Symp. Proc. 522, 1998, pp. 159–164.
S.A. Syed Asif and J.B. Pethica, “Nano-scale indentation creep testing at non-ambient temperatures,” J.Adhesion, 67, 1998, pp. 153–165.
T. Chudoba and F. Richter, “Investigation of creep behavior under load during indentation experiments and its influence on hardness and modulus results,” Surf. Coat. Tech. 148, 2001, pp. 191–198.
M. Oyen, “Spherical indentation creep following ramp loading,” J. Mater. Res. 20 8, 2005, pp. 2094–2100.
C.Y. Zhang, Y.W Zhang, K.Y. Zeng and L. Shen, “Nanoindentation of polymers with a sharp indenter,” J. Mater. Res. 20 6, 2005, pp. 1597–1605.
M. Sakai, Phil. Mag. A 86 2006, pp. 5607.
Y.P. Cao, D. Ma and D. Raabe, “The use of flat punch indentation to determine the viscoelastic properties in the time and frequency domains of a soft layer bonded to a rigid substrate,’ Acta Biomater. 5, 2009, pp. 240–248.
Y.P. Cao, “Determination of the creep exponent of a power-law creep solid using indentation tests,” Mech Time-Depend Mater 11, 2007, pp. 159–172.
D. François, A. Pineau, and A. Zaoui, Mechanical Behaviour of Materials, Kluwer Academic Publishers, The Netherlands,1998.
Y.P. Cao, X.Y. Ji, and X.Q. Feng, “Geometry independence of the normalized relaxation functions of viscoelastic materials in indentation,” Phil. Mag. 90 12, 2010, pp. 1639–1655
B.J. Briscoe, L. Fiori and E. Pelillo, “Nano-indentation of polymeric surfaces,” J. Phys. D. Appl. Phys. 31, 1998, pp. 2395–2405.
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Fischer-Cripps, A.C. (2011). Time-dependent Nanoindentation. In: Nanoindentation. Mechanical Engineering Series. Springer, New York, NY. https://doi.org/10.1007/978-1-4419-9872-9_7
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