Abstract
Indentation experiments on thin films are analyzed by using a rigorous solution to model elastic substrate effects. Two cases are discussed: elastic indentations where film and substrate are anisotropic and elastoplastic indentations where significant material pileup occurs. We demonstrate that the elastic modulus of a thin film can be accurately measured in both cases, even if there is significant elastic mismatch between film and substrate.
Similar content being viewed by others
References
W.C. Oliver, G.M. Pharr An improved technique for determining hardness and elastic-modulus using load and displacement sensing indentation experiments. J. Mater. Res. 7, (6) 1564 (1992)
W.C. Oliver, G.M. Pharr Measurement of hardness and elastic modulus by instrumented indentation: Advances in understanding and refinements to methodology. J. Mater. Res. 19, (1) 3 (2004)
A.C Fischer-Cripps Nanoindentation 2nd ed. (Springer, Verlag 2004)
G.M. Pharr Measurement of mechanical properties by ultra-low-load indentation. Mater. Sci. Eng., A 253, (1–2) 151 (1998)
N.X. Randall, C. Julia-Schmutz, J.M. Soro Combining scanning force microscopy with nanoindentation for more complete characterisation of bulk and coated materials. Surf. Coat. Technol. 108, (1–3) 489 (1998)
N.X. Randall Direct measurement of residual contact area and volume during the nanoindentation of coated materials as an alternative method of calculating hardness. Philos. Mag. A 82, (0) 1883 (2002)
Y.Y. Lim, M.M. Chaudhri, Y. Enomoto Accurate determination of the mechanical properties of thin aluminum films deposited on sapphire flats using nanoindentations. J. Mater. Res. 14, (6) 2314 (1999)
M. Sakai, N. Hakiri, T. Miyajima Instrumented indentation microscope: A powerful tool for the mechanical characterization in microscales. J. Mater. Res. 21, (9) 2298 (2006)
L. Fang, C.L. Muhlstein, J.G. Collins, A.L. Romasco, L.H. Friedman Continuous electrical in situ contact area measurement during instrumented indentation. J. Mater. Res. 23, (9) 2480 (2008)
H.J. Gao, C.H. Chiu, J. Lee Elastic contact versus indentation modeling of multilayered materials. Int. J. Solids Struct. 29, (20) 2471 (1992)
R. Saha, W.D. Nix Effects of the substrate on the determination of thin film mechanical properties by nanoindentation. Acta Mater. 50, (1) 23 (2002)
X. Chen, J.J. Vlassak Numerical study on the measurement of thin film mechanical properties by means of nanoindentation. J. Mater. Res. 16, (10) 2974 (2001)
J. Mencik, D. Munz, E. Quandt, E.R. Weppelmann, M.V. Swain Determination of elastic modulus of thin layers using nanoindentation. J. Mater. Res. 12, (9) 2475 (1997)
G.M. Pharr, W.C. Oliver Measurement of thin-film mechanical properties using nanoindentation. MRS Bull. 17, (7) 28 (1992)
R.B. King Elastic analysis of some punch problems for a layered medium. Int. J. Solids Struct. 23, (12) 1657 (1987)
H.Y. Yu, S.C. Sanday, B.B. Rath The effect of substrate on the elastic properties of films determined by the indentation test—Axisymmetrical Boussinesq problem. J. Mech. Phys. Solids 38, (6) 745 (1990)
S.M. Han, R. Saha, W.D. Nix Determining hardness of thin films in elastically mismatched film-on-substrate systems using nanoindentation. Acta Mater. 54, (6) 1571 (2006)
T.Y. Tsui, G.M. Pharr Substrate effects on nanoindentation mechanical property measurement of soft films on hard substrates. J. Mater. Res. 14, (1) 292 (1999)
H. Li, J.J. Vlassak Determining the elastic modulus and hardness of an ultra-thin film on a substrate using nanoindentation. J. Mater. Res. 24, (3) 1114 (2009)
Y.F. Gao, H.T. Xu, W.C. Oliver, G.M. Pharr Effective elastic modulus of film-on-substrate systems under normal and tangential contact. J. Mech. Phys. Solids 56, (2) 402 (2008)
A.K. Bhattacharya, W.D. Nix Analysis of elastic and plastic-deformation associated with indentation testing of thin-films on substrates. Int. J. Solids Struct. 24, (12) 1287 (1988)
S.J. Bull Nano-indentation of coatings. J. Phys. D: Appl. Phys. 38, (24) R393 (2005)
A.C Fischer-Cripps Review of analysis and interpretation of nanoindentation test data. Surf. Coat. Technol. 200, (14–15) 4153 (2006)
I.N. Sneddon The relation between load and penetration in the axisymmetric Boussinesq problem for a punch of arbitrary profile. Int. J. Eng. Sci. 3, 47 (1965)
S.E. Elgendi Chebyshev solution of differential, integral and integro-differential equations. Comput. J. 12, (3) 282 (1969)
iMechanica, Harvard School of Engineering and Applied Sciences http://www.imechanica.org/node/4050
G.W. Pharr, W.C. Oliver, F.R. Brotzen On the generality of the relationship among contact stiffness, contact area, and elastic-modulus during indentation. J. Mater. Res. 7, (3) 613 (1992)
M. Sakai Substrate-affected indentation contact parameters of elastoplastic coating/substrate composites. J. Mater. Res. 24, (3) 831 (2009)
J.J. Vlassak, W.D. Nix Measuring the elastic properties of anisotropic materials by means of indentation experiments. J. Mech. Phys. Solids 42, (8) 1223 (1994)
J.J. Vlassak, W.D. Nix Indentation modulus of elastically anisotropic half-spaces. Philos. Mag. A 67, (5) 1045 (1993)
J.J. Vlassak, M. Ciavarella, J.R. Barber, X. Wan The indentation modulus of elastically anisotropic materials for indenters of arbitrary shape. J. Mech. Phys. Solids 51, (9) 1701 (2003)
J.J. Vlassak New experimental techniques and analysis methods for the study of the mechanical properties of materials in small volumes. Ph.D. Thesis Stanford University 1994
M. Dietiker Nanoindentation of single-crystalline gold thin films: Correlating hardness and the onset of plasticity. Acta Mater. 56, (15) 3887 (2008)
P.A. Gruber, C. Solenthaler, E. Arzt, R. Spolenak Strong single-crystalline Au films tested by a new synchrotron technique. Acta Mater. 56, (8) 1876 (2008)
G.M. Pharr, A. Bolshakov Understanding nanoindentation unloading curves. J. Mater. Res. 17, (10) 2660 (2002)
J. Nohava, N.X. Randall, N. Conte Novel ultra nanoindentation method with extremely low thermal drift: Principle and experimental results. J. Mater. Res. 24, (3) 873 (2009)
G. Feng, A.H.W. Ngan Effects of creep and thermal drift on modulus measurement using depth-sensing indentation. J. Mater. Res. 17, (3) 660 (2002)
K.W. McElhaney, J.J. Vlassak, W.D. Nix Determination of indenter tip geometry and indentation contact area for depth-sensing indentation experiments. J. Mater. Res. 13, (5) 1300 (1998)
W.A. Brantley Calculated elastic-constants for stress problems associated with semiconductor devices. J. Appl. Phys. 44, (1) 534 (1973)
Author information
Authors and Affiliations
Corresponding author
Rights and permissions
About this article
Cite this article
Li, H., Randall, N.X. & Vlassak, J.J. New methods of analyzing indentation experiments on very thin films. Journal of Materials Research 25, 728–734 (2010). https://doi.org/10.1557/JMR.2010.0095
Received:
Accepted:
Published:
Issue Date:
DOI: https://doi.org/10.1557/JMR.2010.0095