Nonlinearly Viscoelastic Nanoindentation of PMMA Under a Spherical Tip

Experimental Mechanics

Volumn 53, Issue 5, 2013, Pages 731-742

  Kucuk, Y ^a   Mollamahmutoglu, C ^b   Wang, Y ^c   Lu, H ^b  

^a BARTIN UNIVERSITY   (Turkey)

^b The University of Texas at Dallas   (United States)

^c INTEL CORPORATION   (United States)

Author keywords

Finite element method; Nanoindentation; Nonlinear Burgers model; Nonlinear viscoelastic; PMMA; Polymer

Indexed keywords

BURGERS MODEL; FINITE ELEMENT SIMULATIONS; NANOINDENTATION LOAD-DISPLACEMENT CURVES; NONLINEAR VISCO-ELASTIC; PMMA; TIME DEPENDENT BEHAVIOR; VISCO-ELASTIC BEHAVIORS; VISCOELASTIC PROPERTIES;

ELASTIC MODULI; FINITE ELEMENT METHOD; INVERSE PROBLEMS; NANOINDENTATION; POLYMERS; STIFFNESS; UNLOADING; VISCOELASTICITY;

LOADING;

EID: 84877616536     PISSN: 00144851     EISSN: 17412765     Source Type: Journal    
DOI: 10.1007/s11340-012-9695-0     Document Type: Article

References (30)

1. Li X, Bhushan B (2002) A review of nanoindentation continuous stiffness measurement technique and its applications. Mater Charact 48: 11-36.
2. Oliver WC, Pharr GM (1992) An improved technique for determining hardness and elastic modulus using load and displacement sensing indentation experiments. J Mater Res 7: 1564-1583.
3. Doerner MF, Nix WD (1986) A method for interpreting the data from depth-sensing indentation instruments. J Mater Res 1: 601-609.
4. Cheng L, Xia X, Yu W, Scriven LE, Gerberich WW (2000) Flat-punch indentation of viscoelastic material. J Polym Sci B Polym Phys 38: 10-22.
5. Lu H, Wang B, Ma J, Huang G, Viswanathan H (2003) Measurement of creep compliance of solid polymers by nanoindentation. Mech Time Depend Mater 7: 189-207.
6. Huang G, Wang B, Lu H (2004) Measurements of viscoelastic functions in frequency-domain by nanoindentation. Mech Time Depend Mater 8: 345-364.
7. Zhou Z, Lu H (2010) On the measurements of viscoelastic functions of a sphere by nanoindentation. Mech Time Depend Mater 14: 1-24.
8. Odegard GM, Gates TS, Herring HM (2005) Characterization of viscoelastic properties of polymeric materials through nanoindentation. Exp Mech 45: 130-136.
9. VanLandingham MR, Chang NK, Drzal PL, White CC, Chang SH (2005) Viscoelastic characterization of polymers using instrumented indentation-1. quasi-static testing. J Polym Sci B Polym Phys 43: 1794-1811.
10. Cheng YT, Cheng CM (2005) General relationship between contact stiffness, contact depth, and mechanical properties for indentation in linear viscoelastic solids using axisymmetric indenters of arbitrary profiles. Appl Phys Lett 87 Art No 111914.
11. Cheng YT, Ni WY, Cheng CM (2006) Nonlinear analysis of oscillatory indentation in elastic and viscoelastic solids. Phys Rev Lett 97 Art No 075506.
12. Wei PJ, Shen WX, Lin JF (2008) Analysis and modeling for time-dependent behavior of polymers exhibited in nanoindentation tests. J Non-Cryst Solids 354(33): 3911-3918.
13. Oyen ML, Cook RF (2003) Load-displacement behavior during sharp indentation of viscous-elastic-plastic materials. J Mater Res 18(1): 139-150.
14. Liu CK, Lee S, Sung LP, Nguyen T (2006) Load-displacement relations for nanoindentation of viscoelastic materials. J Appl Phys 100: 033503.
15. Mencik J, He LH, Nemecek J (2011) Characterization of viscoelastic-plastic properties of solid polymers by instrumented indentation. Polym Test 30: 101-109.
16. Chen KS, Chen TC, Ou KS (2008) Development of semi-empirical formulation for extracting materials properties from nanoindentation measurements: residual stresses, substrate effect, and creep. Thin Solid Films 516: 1931-1940.
17. Jo C, Fu J, Naguib HE (2005) Constitutive modeling for mechanical behavior of PMMA microcellular foams. Polymer 46: 11896-11903.
18. Schiessel H, Metzler R, Blumen A, Nonnenmacher TF (1995) Generalized viscoelastic models: their fractional equations with solutions. J Phys A Math Gen 28: 6567-6584.
19. Hernandez-Jimenez A, Hernandez-Santiago J, Macias-Garcia A, Sanchez-Gonzalez J (2002) Relaxation modulus in PMMA and PTFE fitting by fractional Maxwell model. Polym Test 21(3): 325-331.
20. Schmidt A, Gaul L (2002) Finite element formulation of viscoelastic constitutive equations using fractional time derivatives. Nonlinear Dyn 29: 37-55.
21. Klompen ETJ, Govaert LE (1999) Nonlinear viscoelastic behaviour of thermorheologically complex materials: a modeling approach. Mech Time Depend Mater 3: 49-69.
22. Arzoumanidis GA, Liechti KM (2003) Linear viscoelastic property measurement and its significance for some nonlinear viscoelasticity models. Mech Time Depend Mater 7: 209-250.
23. Ovaert TC, Kim BR, Wang JJ (2003) Multi-parameter models of the viscoelastic/plastic mechanical properties of coatings via combined nanoindentation and non-linear finite element modeling. Prog Org Coat 47(3-4): 312-323.
24. Findley WN, Lai JS, Onaran K (1989) Creep and relaxation of nonlinear viscoelastic materials with an introduction to linear viscoelasticity. Dover Pub, New York, pp 57-64.
25. Marin J, Pao YH (1953) An analytical theory of the creep deformation of materials. J Appl Mech 20.
26. Richter H, Misawa EA, Lucca DA, Lu H (2001) Modeling nonlinear behavior in a piezoelectric actuator. Precis Eng 25(2): 128-137.
27. Shames IH, Cozzarelli FA (1997) Elastic and inelastic stress analysis. Taylor & Francis, Washington, pp 239-242.
28. Oyen ML (2005) Ultrastructural characterization of time-dependent, inhomogeneous materials and tissues. PhD Thesis, 84-85, University of Minnesota.
29. Liu Y, Varghese S, Ma J, Yoshino M, Lu H, Komanduri R (2008) Orientation effects in nanoindentation of single crystal copper. Int J Plast 24: 1990-2015.
30. Liu Y, Wang B, Yoshino M, Roy S, Lu H, Komanduri R (2005) Combined numerical simulation and nanoindentation for determining mechanical properties of single crystal copper at mesoscale. J Mech Phys Solids 53: 2718-2741.