Nanoindentation is widely used to characterize the mechanical and interfacial properties of thin film systems. However, the effects of substrate compliance on the indentation response of compliant substrate systems are not well understood. This paper investigates the effects of the large compliance mismatch between the film and the substrate and of the film thickness for model systems using nanoindentation tests, finite element simulations, and an analytical model based on a classical plate-bending solution. The results showed that for displacements less than the film thickness and for ratio of the substrate to film modulus less than 100. The indentation force-displacement response exhibits a linear relationship that can be predicted accurately by the linear plate-bending model. The effective stiffness depends linearly on the film thickness and also on the substrate and film moduli. For larger displacements, the indentation response exhibits the scaling relationship of the nonlinear plate-bending model.

1.
Cadogan
,
D. P.
, and
Shook
,
L. S.
, 2005, “
Manufacturing and Performance Assessments of Several Applications of Electrotextiles and Large-Area Flexible Circuits
,”
Materials Research Society Symposium Proceedings
, Vol.
736
, pp.
D1.5.1
D1.5.12
.
2.
Khang
,
D.
,
Jiang
,
H.
,
Huang
,
Y.
, and
Rogers
,
J. A.
, 2006, “
A Stretchable Form of Single-Crystal Silicon for High-Performance Electronics on Rubber Substrates
,”
Science
0036-8075,
311
, pp.
208
212
.
3.
Kennedy
,
M. S.
,
Moody
,
N. R.
, and
Bahr
,
D. F.
, 2005, “
Investigation of Indentation Methods for Properties Determination in Hard Film-Soft Substrate Systems
,”
Materials Research Society Symposium Proceedings
, Vol.
841
, pp.
R12.7.1
R12.7.6
.
4.
Li
,
X.
, and
Bhushan
,
B.
, 2002, “
A Review of Nanoindentation Continuous Stiffness Measurement Technique and Its Application
,”
Mater. Charact.
1044-5803,
48
, pp.
11
36
.
5.
Page
,
T. F.
, and
Hainsworth
,
S. V.
, 1993, “
Using Nanoindentation Techniques for the Characterization of Coated Systems: A Critque
,”
Surf. Coat. Technol.
0257-8972,
61
, pp.
201
208
.
6.
Ramsey
,
P. M.
,
Chandler
,
H. W.
, and
Page
,
T. F.
, 1991, “
Modelling the Contact Response of Coated Systems
,”
Surf. Coat. Technol.
0257-8972,
49
, pp.
504
509
.
7.
McGurk
,
M. R.
,
Chandler
,
H. W.
,
Twigg
,
P. C.
, and
Page
,
T. F.
, 1994, “
Modelling the Hardness Response of Coated Systems: The Plate Bending Approach
,”
Surf. Coat. Technol.
0257-8972,
68-69
, pp.
576
581
.
8.
Gerberich
,
W. W.
,
Strojny
,
A.
,
Yoder
,
K.
, and
Cheng
,
L.
, 1999, “
Hard Protective Overlayers on Viscoelastic-Plastic Substrates
,”
J. Mater. Res.
0884-2914,
14
, pp.
2210
2218
.
9.
Bahr
,
D. F.
,
Woodcock
,
C. L.
,
Pang
,
M.
,
Weaver
,
K. D.
, and
Moody
,
N. R.
, 2003, “
Indentation Induced Film Fracture in Hard Film-Soft Substrate Systems
,”
Int. J. Fract.
0376-9429,
119
, pp.
339
349
.
10.
Yoo
,
Y.
,
Lee
,
W.
, and
Shin
,
H.
, 2004, “
Spherical Nano-Indentation of a Hard Thin Film/Soft Substrate Layered System: I. Critical Indentation Depth
,”
Modell. Simul. Mater. Sci. Eng.
0965-0393,
12
, pp.
59
67
.
11.
Yoo
,
Y.
,
Lee
,
W.
, and
Shin
,
H.
, 2004, “
Spherical Nano-Indentation of a Hard Thin Film/Soft Substrate Layered System: II. Evolution of Stress and Strain Fields
,”
Modell. Simul. Mater. Sci. Eng.
0965-0393,
12
, pp.
69
78
.
12.
Ni
,
W.
, and
Cheng
,
Y.
, 2005, “
Modeling Conical Indentation in Homogeneous Materials and in Hard Films on Soft Substrates
,”
J. Mater. Sci.
0022-2461,
20
, pp.
521
528
.
13.
Vanimisetti
,
S. K.
, and
Narasimhan
,
R.
, 2006, “
A Numerical Analysis of Spherical Indentation Response of Thin Hard Films on Soft Substrates
,”
Int. J. Solids Struct.
0020-7683,
43
, pp.
6180
6193
.
14.
Timoshenko
,
S.
, and
Woinowsky-Krieger
,
S.
, 1959,
Theory of Plates and Shells
,
2nd ed.
,
McGraw-Hill
,
New York
.
15.
Mesarovic
,
S. Dj.
, and
Fleck
,
N. A.
, 1999, “
Spherical Indentation of Elastic-Plastic Solids
,”
Proc. R. Soc. London, Ser. A
0950-1207,
455
, pp.
2707
2728
.
16.
Holzapfel
,
G. A.
, 2000,
Nonlinear Solid Mechanics: A Continuum Approach for Engineers
,
Wiley
,
Chichester, UK
.
You do not currently have access to this content.