This paper presents the nonlinear large deflection of the thin film and the effect of substrate deformation on the thin film deflection through the shaft-loaded blister test. The blister of thin film can be divided into two parts, namely, the annular contact brim and the central noncontact bulge. A two-coupled line spring model is developed to describe the deformation of the contact part, and Föppl–Hencky equations are employed to study the constitutive relation between the applied load and the central deflection. The analytical and numerical solutions for the constitutive relation between the applied load and the deflection of thin film with considering the deformation of substrate are derived.
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Research Papers
References
References
1.
Ju
, B. F.
, Ju
, Y.
, Masumi
, S. A.
, Liu
, K.-K.
, and Wan
, K.-T.
, 2005
, “A Systematic Method for Characterizing the Elastic Properties and Adhesion of a Thin Polymer Membrane
,” Int. J. Mech. Sci.
, 47
(3
), pp. 319
–332
.10.1016/j.ijmecsci.2005.02.0062.
Wang
, Y.
, Lin
, W.
, Feng
, Z.
, and Li
, X.-M.
, 2012
, “Characterization of Extensional Multi-Layer Microbeams in Pull-In Phenomenon and Vibrations
,” Int. J. Mech. Sci.
, 54
(1
), pp. 225
–233
.10.1016/j.ijmecsci.2011.10.0123.
Duan
, G.
, and Wan
, K. T.
, 2010
, “‘Pull-In’ of a Pre-Stressed Thin Film by an Electrostatic Potential: A 1-D Rectangular Bridge and a 2-D Circular Diaphragm
,” Int. J. Mech. Sci.
, 52
(9
), pp. 1158
–1166
.10.1016/j.ijmecsci.2010.04.0054.
Gecit
, M. R.
, 1987
, “Pull-Off Test for a Cracked Layer Bonded to a Rigid Foundation
,” Int. J. Eng. Sci.
, 25
(2
), pp. 213
–226
.10.1016/0020-7225(87)90007-35.
Gent
, A. N.
, and Hamed
, G. R.
, 1977
, “Peel Mechanics for an Elastic-Plastic Adherend
,” J. Appl. Polym. Sci.
, 21
(10
), pp. 2817
–2831
.10.1002/app.1977.0702110186.
Kahrobaiyan
, M. H.
, Asghari
, M.
, Rahaeifard
, M.
, and Ahmadian
, M. T.
, 2010
, “Investigation of the Size-Dependent Dynamic Characteristics of Atomic Force Microscope Microcantilevers Based on the Modified Couple Stress Theory
,” Int. J. Eng. Sci.
, 48
(12
), pp. 1985
–1994
.10.1016/j.ijengsci.2010.06.0037.
Randall
, N. X.
, Favaro
, G.
, and Frankel
, C. H.
, 2001
, “The Effect of Intrinsic Parameters on the Critical Load as Measured With the Scratch Test Method
,” Surf. Coat. Technol.
, 137
(2–3
), pp. 146
–151
.10.1016/S0257-8972(00)01097-58.
Ruffini
, A.
, Durinck
, J.
, Colin
, J.
, Coupeau
, C.
, and Grilhé
, J.
, 2013
, “Interface Step-Induced Thin-Film Delamination and Buckling
,” Acta Mater.
, 61
(12
), pp. 4429
–4438
.10.1016/j.actamat.2013.04.0129.
Williams
, M. L.
, 1969
, “The Continuum Interpretation for Fracture and Adhesion
,” J. Appl. Polym. Sci.
, 13
(1
), pp. 29
–40
.10.1002/app.1969.07013010510.
Dannenberg
, H.
, 1961
, “Measurement of Adhesion by a Blister Method
,” J. Appl. Polym. Sci.
, 5
(14
), pp. 125
–134
.10.1002/app.1961.07005140111.
Hencky
, H.
, 1915
, “On the Stress State in Circular Plates With Vanishing Bending Stiffness
,” Z. Math. Phys.
, 63
, pp. 311
–317
.12.
Föppl
, A.
, 1907
, “Vorlesungen über technische Mechanik: Bd. Die wichtigsten Lehren der höheren Elastizitätstheorie
,” BG Teubnerv.
, 5
, pp. 132
–144
.13.
Timoshenko
, S.
, Woinowsky-Krieger
, S.
, and Woinowsky
, S.
, 1959
, Theory of Plates and Shells
, McGraw-Hill
, New York
.14.
Sun
, J. Y.
, Hu
, J. L.
, He
, X. T.
, and Zheng
, Z.-L.
, 2010
, “A Theoretical Study of a Clamped Punch-Loaded Blister Configuration: The Quantitative Relation of Load and Deflection
,” Int. J. Mech. Sci.
, 52
(7
), pp. 928
–936
.10.1016/j.ijmecsci.2010.03.00915.
Jiang
, L. M.
, Zhou
, Y. C.
, Hao
, H. X.
, Liao
, Y.
, and Lu
, C.
, 2010
, “Characterization of the Interface Adhesion of Elastic-Plastic Thin Film/Rigid Substrate Systems Using a Pressurized Blister Test Numerical Model
,” Mech. Mater.
, 42
(10
), pp. 908
–915
.10.1016/j.mechmat.2010.07.00916.
Plaut
, R. H.
, White
, S. A.
, and Dillard
, D. A.
, 2003
, “Effect of Work of Adhesion on Contact of a Pressurized Blister With a Flat Surface
,” Int. J. Adhes. Adhes.
, 23
(3
), pp. 207
–214
.10.1016/S0143-7496(03)00013-717.
Wan
, K. T.
, and Lim
, S. C.
, 1998
, “The Bending to Stretching Transition of a Pressurized Blister Test
,” Int. J. Fract.
, 92
(4
), pp. L43
–L47
.10.1023/A:100761201614718.
Sun
, Z.
, Wan
, K.
, and Dillard
, D. A.
, 2004
, “A Theoretical and Numerical Study of Thin Film Delamination Using the Pull-Off Test
,” Int. J. Solids Struct.
, 41
(3–4
), pp. 717
–730
.10.1016/j.ijsolstr.2003.09.02719.
Lai
, Y.
, and Dillard
, D. A.
, 1994
, “A Study of the Fracture Efficiency Parameter of Blister Tests for Films and Coatings
,” J. Adhes. Sci. Technol.
, 8
(6
), pp. 663
–678
.10.1163/156856194X0041020.
Wan
, K. T.
, Guo
, S.
, and Dillard
, D. A.
, 2003
, “A Theoretical and Numerical Study of a Thin Clamped Circular Film Under an External Load in the Presence of a Tensile Residual Stress
,” Thin Solid Films
, 425
(1–2
), pp. 150
–162
.10.1016/S0040-6090(02)01103-321.
Wan
, K.
, and Liao
, K.
, 1999
, “Measuring Mechanical Properties of Thin Flexible Films by a Shaft-Loaded Blister Test
,” Thin Solid Films
, 352
(1–2
), pp. 167
–172
.10.1016/S0040-6090(99)00355-722.
Xu
, X. J.
, Shearwood
, C.
, and Liao
, K.
, 2003
, “A Shaft-Loaded Blister Test for Elastic Response and Delamination Behavior of Thin Film-Substrate System
,” Thin Solid Films
, 424
(1
), pp. 115
–119
.10.1016/S0040-6090(02)00909-423.
Malyshev
, B. M.
, and Salganik
, R. L.
, 1965
, “The Strength of Adhesive Joints Using the Theory of Cracks
,” Int. J. Fract. Mech.
, 1
(2
), pp. 114
–128
.10.1007/BF0018674924.
Jensen
, H. M.
, 1991
, “The Blister Test for Interface Toughness Measurement
,” Eng. Fract. Mech.
, 40
(3
), pp. 475
–486
.10.1016/0013-7944(91)90144-P25.
Nie
, P. L.
, Li
, Z. G.
, Huang
, J. A.
, and Chen
, Q.
, 2010
, “The Constitutive Relation of an Axisymmetric Detached Coating on a Rigid Substrate
,” Int. J. Mech. Sci.
, 52
(12
), pp. 1709
–1715
.10.1016/j.ijmecsci.2010.09.00426.
Sun
, J. Y.
, Hu
, J. L.
, He
, X. T.
, Zheng
, Z. L.
, and Geng
, H.-H.
, 2011
, “A Theoretical Study of Thin Film Delamination Using Clamped Punch-Loaded Blister Test: Energy Release Rate and Closed-Form Solution
,” J. Adhes. Sci. Technol.
, 25
(16
), pp. 2063
–2080
.10.1163/016942410X54486627.
Jin
, C. R.
, 2009
, “Theoretical Study of Mechanical Behavior of Thin Circular Film Adhered to a Flat Punch
,” Int. J. Mech. Sci.
, 51
(6
), pp. 481
–489
.10.1016/j.ijmecsci.2009.04.00328.
He
, X. T.
, Chen
, Q.
, Sun
, J. Y.
, and Zheng
, Z. L.
, 2012
, “Large-Deflection Axisymmetric Deformation of Circular Clamped Plates With Different Moduli in Tension and Compression
,” Int. J. Mech. Sci.
, 62
(1
), pp. 103
–110
.10.1016/j.ijmecsci.2012.06.00329.
Zhao
, M. H.
, Zheng
, W. L.
, and Fan
, C. Y.
, 2010
, “Mechanics of Shaft-Loaded Blister Test for Thin Film Suspended on Compliant Substrate
,” Int. J. Solids Struct.
, 47
(18–19
), pp. 2525
–2532
.10.1016/j.ijsolstr.2010.05.01130.
Zhao
, M.
, Zhou
, J.
, Yang
, F.
, Liu
, T.
, and Zhang
, T.-Y.
, 2007
, “Effects of Substrate Compliance on Circular Buckle Delamination of Thin Films
,” Eng. Fract. Mech.
, 74
(15
), pp. 2334
–2351
.10.1016/j.engfracmech.2006.11.00731.
Lu
, T. Q.
, Zhang
, W. X.
, and Wang
, T. J.
, 2011
, “The Surface Effect on the Strain Energy Release Rate of Buckling Delamination in Thin Film-Substrate Systems
,” Int. J. Eng. Sci.
, 49
(9
), pp. 967
–975
.10.1016/j.ijengsci.2011.05.00932.
Yu
, H. H.
, and Hutchinson
, J. W.
, 2002
, “Influence of Substrate Compliance on Buckling Delamination of Thin Films
,” Int. J. Fract.
, 113
(1
), pp. 39
–55
.10.1023/A:101379023235933.
Cotterell
, B.
, and Chen
, Z.
, 2000
, “Buckling and Cracking of Thin Films on Compliant Substrates Under Compression
,” Int. J. Fract.
, 104
(2
), pp. 169
–179
.10.1023/A:100762880062034.
Tarasovs
, S.
, and Andersons
, J.
, 2012
, “Competition Between the Buckling-Driven Delamination and Wrinkling in Compressed Thin Coatings
,” Microelectron. Reliab.
, 52
(1
), pp. 296
–299
.10.1016/j.microrel.2011.08.00735.
Schwerin
, 1929
, “Über Spannungen und Formänderungen kreisringförmiger Membranen
,” Z. Angew. Math. Mech. (J. Appl. Math. Mech.)
, 9
(6
), pp. 482
–483
.36.
Komaragiri
, U.
, Begley
, M. R.
, and Simmonds
, J. G.
, 2005
, “The Mechanical Response of Freestanding Circular Elastic Films Under Point and Pressure Loads
,” ASME J. Appl. Mech.
, 72
(2
), pp. 203
–212
.10.1115/1.182724637.
Lakes
, S. R.
, 1987
, “Foam Structures With a Negative Poisson's Ratio
,” Science
, 235
(4792
), pp. 1038
–1040
.10.1126/science.235.4792.1038Copyright © 2015 by ASME
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