The performance of flexible/stretchable electronics may be significantly reduced by the interfacial delamination due to the large mismatch at the interface between stiff films and soft substrates. Based on the theory of viscoelasticity, a cracked composite beam model is proposed in this paper to analyze the delamination of an elastic thin film from a viscoelastic substrate. The time-varying neutral plane of the composite beam is derived analytically, and then the energy release rate of the interfacial crack is obtained from the Griffith's theory. Further, three different states of the crack propagation under constant external loadings are predicted, which has potential applications on the structural design of inorganic flexible/stretchable electronics.
Issue Section:
Research Papers
References
1.
Ko
, H. C.
, Stoykovich
, M. P.
, Song
, J.
, Malyarchuk
, V.
, Choi
, W. M.
, Yu
, C.-J.
, Geddes
, J. B.
, III, Xiao
, J.
, Wang
, S.
, Huang
, Y.
, and Rogers
, J. A.
, 2008
, “A Hemispherical Electronic Eye Camera Based on Compressible Silicon Optoelectronics
,” Nature
, 454
(7205
), pp. 748
–753
.2.
Song
, Y. M.
, Xie
, Y.
, Malyarchuk
, V.
, Xiao
, J.
, Jung
, I.
, Choi
, K.-J.
, Liu
, Z.
, Park
, H.
, Lu
, C.
, Kim
, R.-H.
, Li
, R.
, Crozier
, K. B.
, Huang
, Y.
, and Rogers
, J. A.
, 2013
, “Digital Cameras With Designs Inspired by the Arthropod Eye
,” Nature
, 497
(7447
), pp. 95
–99
.3.
Chen
, Y.
, Lu
, B.
, Chen
, Y.
, and Feng
, X.
, 2015
, “Breathable and Stretchable Temperature Sensors Inspired by Skin
,” Sci. Rep.
, 5
, p. 11505
.4.
Kim
, D.-H.
, Lu
, N.
, Ma
, R.
, Kim
, Y.-S.
, Kim
, R.-H.
, Wang
, S.
, Wu
, J.
, Won
, S. M.
, Tao
, H.
, Islam
, A.
, Yu
, K. J.
, Kim
, T.-I.
, Chowdhury
, R.
, Ying
, M.
, Xu
, L.
, Li
, M.
, Chung
, H.-J.
, Keum
, H.
, McCormick
, M.
, Liu
, P.
, Zhang
, Y.-W.
, Omenetto
, F. G.
, Huang
, Y.
, Coleman
, T.
, and Rogers
, J. A.
, 2011
, “Epidermal Electronics
,” Science
, 333
(6044
), pp. 838
–843
.5.
Cheng
, H. Y.
, and Wang
, S. D.
, 2013
, “Mechanics of Interfacial Delamination in Epidermal Electronics Systems
,” ASME J. Appl. Mech.
, 81
(4
), p. 044501
.6.
Liu
, Z.
, Cheng
, H.
, and Wu
, J.
, 2014
, “Mechanics of Solar Module on Structured Substrates
,” ASME J. Appl. Mech.
, 81
(6
), p. 064502
.7.
Shi
, X.
, Xu
, R.
, Li
, Y.
, Zhang
, Y.
, Ren
, Z.
, Gu
, J.
, Rogers
, J. A.
, and Huang
, Y.
, 2014
, “Mechanics Design for Stretchable, High Areal Coverage GaAs Solar Module on an Ultrathin Substrate
,” ASME J. Appl. Mech.
, 81
(12
), p. 124502
.8.
Shi
, Y.
, Dagdeviren
, C.
, Rogers
, J. A.
, Gao
, C. F.
, and Huang
, Y.
, 2015
, “An Analytic Model for Skin Modulus Measurement Via Conformal Piezoelectric Systems
,” ASME J. Appl. Mech.
, 82
(9
), p. 091007
.9.
Yuan
, J. H.
, Shi
, Y.
, Pharr
, M.
, Feng
, X.
, Rogers
, J. A.
, and Huang
, Y.
, 2016
, “A Mechanics Model for Sensors Imperfectly Bonded to the Skin for Determination of the Young's Moduli of Epidermis and Dermis
,” ASME J. Appl. Mech.
, 83
(9
), p. 084501
.10.
Lu
, B.
, Chen
, Y.
, Ou
, D.
, Chen
, H.
, Diao
, L.
, Zhang
, W.
, Zheng
, J.
, Ma
, W.
, Sun
, L.
, and Feng
, X.
, 2015
, “Ultra-Flexible Piezoelectric Devices Integrated With Heart to Harvest the Biomechanical Energy
,” Sci. Rep.
, 5
, p. 16065
.11.
Zhang
, Y. Y.
, Chen
, Y. S.
, Lu
, B. W.
, Lü
, C. F.
, and Feng
, X.
, 2016
, “Electromechanical Modeling of Energy Harvesting From the Motion of Left Ventricle in Closed Chest Environment
,” ASME J. Appl. Mech.
, 83
(6
), p. 061007
.12.
Khang
, D. Y.
, Jiang
, H. Q.
, Huang
, Y.
, and Rogers
, J. A.
, 2006
, “A Stretchable Form of Single-Crystal Silicon for High-Performance Electronics on Rubber Substrates
,” Science
, 311
(5758
), pp. 208
–212
.13.
Kim
, D. H.
, Lu
, N. S.
, Huang
, Y. G.
, and Rogers
, J. A.
, 2012
, “Materials for Stretchable Electronics in Bioinspired and Biointegrated Devices
,” Mrs Bull.
, 37
(3
), pp. 226
–235
.14.
Rogers
, J. A.
, and Huang
, Y. G.
, 2009
, “A Curvy, Stretchy Future for Electronics
,” Proc. Natl. Acad. Sci. U. S. A.
, 106
(27
), pp. 10875
–10876
.15.
Wang
, Y.
, Feng
, X.
, Lu
, B. W.
, and Wang
, G. F.
, 2013
, “Surface Effects on the Mechanical Behavior of Buckled Thin Film
,” ASME J. Appl. Mech.
, 80
(2
), p. 021002
.16.
Shi
, Y.
, Rogers
, J. A.
, Gao
, C. F.
, and Huang
, Y.
, 2014
, “Multiple Neutral Axes in Bending of a Multiple-Layer Beam With Extremely Different Elastic Properties
,” ASME J. Appl. Mech.
, 81
(11
), p. 114501
.17.
Meng
, X. H.
, Liu
, B. Y.
, Wang
, Y.
, Zhang
, T. H.
, and Xiao
, J. L.
, 2016
, “Third-Order Polynomials Model for Analyzing Multilayer Hard/Soft Materials in Flexible Electronics
,” ASME J. Appl. Mech.
, 83
(8
), p. 081011
.18.
Dai
, L. C.
, Feng
, X.
, Liu
, B.
, and Fang
, D. N.
, 2010
, “Interfacial Slippage of Inorganic Electronic Materials on Plastic Substrates
,” Appl. Phys. Lett.
, 97
(22
), p. 221903
.19.
Huang
, Y.
, Feng
, X.
, and Qu
, B. R.
, 2011
, “Slippage Toughness Measurement of Soft Interface Between Stiff Thin Films and Elastomeric Substrate
,” Rev. Sci. Instrum.
, 82
(10
), p. 104704
.20.
Park
, S. I.
, Ahn
, J. H.
, Feng
, X.
, Wang
, S. D.
, Huang
, Y. G.
, and Rogers
, J. A.
, 2008
, “Theoretical and Experimental Studies of Bending of Inorganic Electronic Materials on Plastic Substrates
,” Adv. Funct. Mater.
, 18
(18
), pp. 2673
–2684
.21.
Hutchinson
, J. W.
, and Suo
, Z.
, 1992
, “Mixed Mode Cracking in Layered Materials
,” Adv. Appl. Mech.
, 29
, pp. 63
–191
.22.
Chen
, H.
, Feng
, X.
, and Chen
, Y.
, 2014
, “Slip Zone Model for Interfacial Failures of Stiff Film/Soft Substrate Composite System in Flexible Electronics
,” Mech. Mater.
, 79
, pp. 35
–44
.23.
Chen
, H.
, Lu
, B. W.
, Lin
, Y.
, and Feng
, X.
, 2014
, “Interfacial Failure in Flexible Electronic Devices
,” IEEE Electron. Device Lett.
, 35
(1
), pp. 132
–134
.24.
Liu
, H. M.
, Liu
, Z. X.
, Xu
, Z. L.
, Yin
, Z. P.
, Huang
, Y. A.
, and Chen
, J. K.
, 2015
, “Competing Fracture of Thin-Chip Transferring From/Onto Prestrained Compliant Substrate
,” ASME J. Appl. Mech.
, 82
(10
), p. 101012
.25.
Christensen
, R. M.
, 1980
, “A Rate-Dependent Criterion for Crack Growth
,” Int. J. Fract.
, 16
(5
), pp. R233
–R237
.26.
Schapery
, R. A.
, 1975
, “A Theory of Crack Initiation and Growth in Viscoelastic Media
,” Int. J. Fract.
, 11
(1
), pp. 141
–159
.27.
Hui
, C. Y.
, Xu
, D. B.
, and Kramer
, E. J.
, 1992
, “A Fracture Model for a Weak Interface in a Viscoelastic Material (Small Scale Yielding Analysis)
,” J. Appl. Phys.
, 72
(8
), pp. 3294
–3304
.28.
Feng
, X.
, Cheng
, H. Y.
, Bowen
, A. M.
, Carlson
, A. W.
, Nuzzo
, R. G.
, and Rogers
, J. A.
, 2013
, “A Finite-Deformation Mechanics Theory for Kinetically Controlled Transfer Printing
,” ASME J. Appl. Mech.
, 80
(6
), p. 061023
.29.
Srinivas
, M. V.
, and Ravichandran
, G.
, 1994
, “Interfacial Crack Propagation in a Thin Viscoelastic Film Bonded to an Elastic Substrate
,” Int. J. Fract.
, 65
(1
), pp. 31
–47
.30.
Christensen
, R.
, 2012
, Theory of Viscoelasticity: An Introduction
, Academic Press
, New York
.31.
Huet
, C.
, 1992
, “Minimum Theorems for Viscoelasticity
,” Eur. J. Mech. A-Solids
, 11
(5
), pp. 653
–684
.32.
Griffith
, A. A.
, 1921
, “The Phenomena of Rupture and Flow in Solids
,” Philos. Trans. Ser. A
, 221
, pp. 163
–198
.Copyright © 2016 by ASME
You do not currently have access to this content.
