The buckling solutions for a stressed thin film deposited on a semi-infinite rigid substrate have been determined in the framework of the Föppl–von Karman’s theory of thin plates and the perturbed bifurcation theory when pressures are applied onto the lower and upper free surfaces of the buckled film. It is found that the equilibrium solutions of the film are modified compared with the classical case of the Euler column, as well as the critical stress above which the film buckles.

1.
Hutchinson
,
J. W.
, and
Suo
,
Z.
, 1991, “
Mixed Mode Cracking in Layered Materials
,”
Adv. Appl. Mech.
0065-2156,
29
, pp.
63
191
.
2.
Audoly
,
B.
, 1999, “
Stability of Straight Delamination Blisters
,”
Phys. Rev. Lett.
0031-9007,
83
, pp.
4124
4127
.
3.
Foppl
,
A.
, 1907,
Vorlesungen uber Technishe Mechanik
, Vol.
5
,
Springer Wien
,
New York
, pp.
132
144
.
4.
Karman
,
T. V.
, 1910,
Encyklopadie der Mathematischen Wissenschaften
, Vol.
IV
,
Liepzig
,
New York
, pp.
311
385
.
5.
Timoshenko
,
S.
, 1940,
Theory of Plates and Shells
,
McGraw-Hill
,
New York
.
6.
Langhaar
,
H. L.
, 1962,
Energy Methods in Applied Mechanics
,
Wiley
,
New York
.
7.
Moon
,
M. W.
,
Jensen
,
H. M.
,
Hutchinson
,
J. W.
,
Oh
,
K. H.
, and
Evans
,
A. G.
, 2002, “
The Characterization of Telephone Cord Buckling of Compressed Thin Films on Substrates
,”
J. Mech. Phys. Solids
0022-5096,
50
, pp.
2355
2377
.
8.
Gioia
,
G.
, and
Ortiz
,
M.
, 1997, “
Delamination of Compressed Thin Films
,”
Adv. Appl. Mech.
0065-2156,
33
, pp.
119
192
.
9.
Audoly
,
B.
,
Roman
,
B.
, and
Pocheau
,
A.
, 2002, “
Secondary Buckling Patterns of a Thin Plate Under In-Plane Compression
,”
Eur. Phys. J. B
1434-6028,
27
, pp.
7
10
.
10.
Paumier
,
F.
,
Gaboriaud
,
R.
, and
Coupeau
,
C.
, 2003, “
Buckling Phenomena in Y2O3 Thin Films on GaAs Substrates
,”
Appl. Phys. Lett.
0003-6951,
82
, pp.
2056
2058
.
11.
Crosby
,
K. M.
, and
Bradley
,
R. M.
, 1999, “
Pattern Formation During Delamination and Buckling of Thin Films
,”
Phys. Rev. E
1063-651X,
59
, pp.
R2542
R2545
.
12.
Murotani
,
T.
,
Hirose
,
H.
,
Sasaki
,
T.
, and
Okazaki
,
K.
, 2000, “
Study on Stress Measurement of PVD-Coating Layers
,”
Thin Solid Films
0040-6090,
377–378
, pp.
617
620
.
13.
Wang
,
J. S.
, and
Evans
,
A.
, 1998, “
Measurement and Analysis of Buckling and Buckle Propagation in Compressed Oxide Layers on Superalloy Substrates
,”
Acta Mater.
1359-6454,
46
, pp.
4993
5005
.
14.
Zhang
,
X. C.
,
Xuang
,
F. Z.
,
Zhang
,
Y. K.
, and
Tu
,
S. T.
, 2008, “
Multiple Film Cracking in Film/Substrate System With Mismatch Strain and Applied Strain
,”
J. Appl. Phys.
0021-8979,
104
, p.
063520
.
15.
Thouless
,
M. D.
,
Hutchinson
,
J. W.
, and
Liniger
,
E. G.
, 1992, “
Plane-Strain, Buckling-Driven Delamination of Thin Films: Model Experiments and Mode-II Fracture
,”
Acta Metall. Mater.
0956-7151,
40
, pp.
2639
2649
.
16.
Parry
,
G.
,
Coupeau
,
C.
,
Colin
,
J.
,
Cimetière
,
A.
, and
Grilhé
,
J.
, 2004, “
Buckling and Post-Buckling of Stressed Straight-Sided Wrinkles: Experimental AFM Observations of Bubbles Formation and Finite Element Simulations
,”
Acta Mater.
1359-6454,
52
, pp.
3959
3966
.
17.
Parry
,
G.
,
Cimetière
,
A.
,
Coupeau
,
C.
,
Colin
,
J.
, and
Grilhé
,
J.
, 2006, “
Stability Diagram of Unilateral Buckling Patterns of Strip-Delaminated Films
,”
Phys. Rev. E
1063-651X,
74
, p.
066601
.
18.
Parry
,
G.
,
Colin
,
J.
,
Coupeau
,
C.
,
Foucher
,
F.
,
Cimetière
,
A.
, and
Grilhé
,
J.
, 2005, “
Effect of Substrate Compliance on the Global Unilateral Post-Buckling of Coatings: AFM Observations and Finite Element Calculations
,”
Acta Mater.
1359-6454,
53
, pp.
441
447
.
19.
Foucher
,
F.
,
Coupeau
,
C.
,
Colin
,
J.
,
Cimetière
,
A.
, and
Grilhé
,
J.
, 2006, “
How Does Crystalline Substrate Plasticity Modify Thin Film Buckling?
Phys. Rev. Lett.
0031-9007,
97
, p.
096101
.
20.
Dundurs
,
J.
, 1967, “
Dependence of Stress on Poisson’s Ratio in Plane Elasticity
,”
Int. J. Solids Struct.
0020-7683,
3
, pp.
1013
1021
.
21.
Moon
,
M. W.
,
Lee
,
K. R.
,
Oh
,
K. H.
, and
Hutchinson
,
J. W.
, 2004, “
Buckle Delamination on Patterned Substrates
,”
Acta Mater.
1359-6454,
52
, pp.
3151
3159
.
22.
Colin
,
J.
,
Coupeau
,
C.
, and
Grilhé
,
J.
, 2007, “
Plastic Folding of Buckling Structures
,”
Phys. Rev. Lett.
0031-9007,
99
, p.
046101
.
23.
Ziebart
,
V.
,
Paul
,
O.
,
Munch
,
U.
,
Schwizer
,
J.
, and
Baltes
,
H.
, 1998, “
Mechanical Properties of Thin Films From the Load Deflection of Long Clamped Plates
,”
J. Microelectromech. Syst.
1057-7157,
7
(
3
), pp.
320
328
.
24.
Gu
,
B.
,
Liu
,
H.
,
Mai
,
Y. W.
,
Feng
,
X. Q.
, and
Yu
,
S. W.
, 2009, “
Fracture Mechanics Analysis on Smart-Cut Technology. Part I: Effect of Stiffening Wafer and Defect Interaction
,”
Acta Mech. Sin.
0459-1879,
25
, pp.
73
81
.
25.
Gu
,
B.
,
Liu
,
H.
,
Mai
,
Y. W.
,
Feng
,
X. Q.
, and
Yu
,
S. W.
, 2009, “
Fracture Mechanics Analysis on Smart-Cut Technology. Part II: Effect of Bonding Flaws
,”
Acta Mech. Sin.
0459-1879,
25
, pp.
197
203
.
26.
Rubel
,
M.
, 2008, “
Structure Materials in Fusion Reactors: Issues Related to Tritium, Radioactivity and Radiation-Induced Effects
,”
Fusion Sci. Technol.
1536-1055,
53
(
2
), pp.
459
467
.
27.
Freund
,
L. B.
, and
Suresh
,
S.
, 2003,
Thin Film Materials: Stress, Defect Formation and Surface Evolution
,
Cambridge University Press
,
Cambridge, UK
, pp.
355
366
.
28.
Iooss
,
G.
, and
Joseph
,
D. D.
, 1980,
Elementary Stability and Bifurcation Theory
,
Springer-Verlag
,
New York
.
29.
Coupeau
,
C.
, 2009,
Thin Solid Films
0040-6090, submitted.
You do not currently have access to this content.