In a bilayer structure consisting of a stiff film bonded to a soft substrate, the stress in the film is much larger when the rigidity of the film is much higher than that of the substrate so that film cracking is a common phenomenon in bilayer structures such as flexible electronics and biological tissues. In this paper, a theoretical model is developed to analyze the normal stress distribution in the structure to explain the mechanism of the formation of periodic crack patterns. The effects of geometrical and material parameters are systematically discussed. The analytical result agrees well with finite element analysis, and the prediction of spacing between cracks agrees with experiments from the literature.
Issue Section:
Research Papers
References
1.
Zhang
, P.
, and Parnell
, W. J.
, 2017
, “Band Gap Formation and Tunability in Stretchable Serpentine Interconnects
,” ASME J. Appl. Mech.
, 84
(9
), p. 091007
.2.
Yang
, S.
, Qiao
, S.
, and Lu
, N.
, 2017
, “Elasticity Solutions to Nonbuckling Serpentine Ribbons
,” ASME J. Appl. Mech.
, 84
(2
), p. 021004
.3.
Xie
, Z.
, Ji
, B.
, and Huo
, Q.
, 2018
, “Mechanics Design of Stretchable Near Field Communication Antenna With Serpentine Wires
,” ASME J. Appl. Mech.
, 85
(4
), p. 045001
.4.
Ma
, Q.
, and Zhang
, Y.
, 2016
, “Mechanics of Fractal-Inspired Horseshoe Microstructures for Applications in Stretchable Electronics
,” ASME J. Appl. Mech.
, 83
(11
), p. 111008
.5.
Meng
, X.
, Liu
, B.
, Wang
, Y.
, Zhang
, T.
, and Xiao
, J.
, 2016
, “Third-Order Polynomials Model for Analyzing Multilayer Hard/Soft Materials in Flexible Electronics
,” ASME J. Appl. Mech.
, 83
(8
), p. 081011
.6.
Raayai-Ardakani
, S.
, Luis Yague
, J.
, Gleason
, K. K.
, and Boyce
, M. C.
, 2016
, “Mechanics of Graded Wrinkling
,” ASME J. Appl. Mech.
, 83
(12
), p. 121011
.7.
Kurguzov
, V. D.
, and Demeshkin
, A. G.
, 2016
, “Experimental and Theoretical Study of the Buckling of Narrow Thin Plates on an Elastic Foundation Under Compression
,” J. Appl. Mech. Tech. Phys.
, 57
(3
), pp. 494
–500
.8.
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
.9.
Wang
, A.
, Avila
, R.
, and Ma
, Y.
, 2017
, “Mechanics Design for Buckling of Thin Ribbons on an Elastomeric Substrate Without Material Failure
,” ASME J. Appl. Mech.
, 84
(9
), p. 094501
.10.
Zhao
, R.
, and Zhao
, X.
, 2017
, “Multimodal Surface Instabilities in Curved Film-Substrate Structures
,” ASME J. Appl. Mech.
, 84
(8
), p. 081001
.11.
Wang
, B.
, and Wang
, S.
, 2016
, “Adhesion-Governed Buckling of Thin-Film Electronics on Soft Tissues
,” Theor. Appl. Mech. Lett.
, 6
(1
), pp. 6
–10
.12.
Li
, Y.
, Zhang
, J.
, Xing
, Y.
, and Song
, J.
, 2017
, “Thermomechanical Analysis of Epidermal Electronic Devices Integrated With Human Skin
,” ASME J. Appl. Mech.
, 84
(11
), p. 111004
.13.
Choi
, S.
, Lee
, H.
, Ghaffari
, R.
, Hyeon
, T.
, and Kim
, D.-H.
, 2016
, “Recent Advances in Flexible and Stretchable Bio-Electronic Devices Integrated With Nanomaterials
,” Adv. Mater.
, 28
(22
), pp. 4203
–4218
.14.
Wang
, L.
, Qiao
, S.
, Ameri
, S. K.
, Jeong
, H.
, and Lu
, N.
, 2017
, “A Thin Elastic Membrane Conformed to a Soft and Rough Substrate Subjected to Stretching/Compression
,” ASME J. Appl. Mech.
, 84
(11
), p. 111003
.15.
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
.16.
Okuyama
, T.
, Kobayashi
, K.
, Otsuki
, M.
, and Tanaka
, M.
, 2016
, “Measurement of Finger Joint Angle Using a Flexible Polymer Sensor
,” Int. J. Appl. Electromagn. Mech.
, 52
(3–4
), pp. 951
–957
.17.
Wang
, J. H.
, and Chen
, C. Q.
, 2017
, “Effects of Thickness on the Responses of Piezoresponse Force Microscopy for Piezoelectric Film/Substrate Systems
,” ASME J. Appl. Mech.
, 84
(12
), p. 121004
.18.
Gates
, B. D.
, 2009
, “Flexible Electronics
,” Science
, 323
(5921
), pp. 1566
–1567
.19.
Feng
, X.
, Cheng
, H.
, 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
.20.
Wang
, L.
, and Lu
, N.
, 2016
, “Conformability of a Thin Elastic Membrane Laminated on a Soft Substrate With Slightly Wavy Surface
,” ASME J. Appl. Mech.
, 83
(4
), p. 041007
.21.
Feng
, X.
, Huang
, Y.
, and Rosakis
, A. J.
, 2008
, “Stresses in a Multilayer Thin Film/Substrate System Subjected to Nonuniform Temperature
,” ASME J. Appl. Mech.
, 75
(2
), p. 021022
.22.
Liu
, Y.
, Li
, M.
, Liu
, J.
, and Chen
, X.
, 2017
, “Mechanism of Surface Wrinkle Modulation for a Stiff Film on Compliant Substrate
,” ASME J. Appl. Mech.
, 84
(5
), p. 051011
.23.
Zhang
, M.
, Liu
, H.
, Cao
, P.
, Chen
, B.
, Hu
, J.
, Chen
, Y.
, Pan
, B.
, Fan
, J. A.
, Li
, R.
, Zhang
, L.
, and Su
, Y.
, 2017
, “Strain-Limiting Substrates Based on Nonbuckling, Prestrain-Free Mechanics for Robust Stretchable Electronics
,” ASME J. Appl. Mech.
, 84
(12
), p. 121010
.24.
Chen
, P.
, Chen
, S.
, and Yao
, Y.
, 2016
, “Nonslipping Contact Between a Mismatch Film and a Finite-Thickness Graded Substrate
,” ASME J. Appl. Mech.
, 83
(2
), p. 021007
.25.
Guo
, G.
, and Zhu
, Y.
, 2015
, “Cohesive-Shear-Lag Modeling of Interfacial Stress Transfer Between a Monolayer Graphene and a Polymer Substrate
,” ASME J. Appl. Mech.
, 82
(3
), p. 031005
.26.
Huang
, Y.
, Yuan
, J.
, Zhang
, Y.
, and Feng
, X.
, 2016
, “Interfacial Delamination of Inorganic Films on Viscoelastic Substrates
,” ASME J. Appl. Mech.
, 83
(10
), p. 101005
.27.
Li
, J.
, An
, Y.
, Huang
, R.
, Jiang
, H.
, and Xie
, T.
, 2012
, “Unique Aspects of a Shape Memory Polymer as the Substrate for Surface Wrinkling
,” ACS Appl. Mater. Inter.
, 4
(2
), pp. 598
–603
.28.
Xia
, Z. C.
, and Hutchinson
, J. W.
, 2000
, “Crack Patterns in Thin Films
,” J. Mech. Phys. Solids
, 48
(6–7
), pp. 1107
–1131
.29.
Yin
, H. M.
, Paulino
, G. H.
, and Buttlar
, W. G.
, 2008
, “An Explicit Elastic Solution for a Brittle Film With Periodic Cracks
,” Int. J. Fract.
, 153
(1
), pp. 39
–52
.30.
Ambrico
, J. M.
, and Begley
, M. R.
, 2002
, “The Role of Initial Flaw Size, Elastic Compliance and Plasticity in Channel Cracking of Thin Films
,” Thin Solid Films
, 419
(1–2
), pp. 144
–153
.31.
Zhao
, Q.
, Wang
, W.
, Shao
, J.
, Li
, X.
, Tian
, H.
, Liu
, L.
, Mei
, X.
, Ding
, Y.
, and Lu
, B.
, 2016
, “Nanoscale Electrodes for Flexible Electronics by Swelling Controlled Cracking
,” Adv. Mater.
, 28
(30
), pp. 6337
–6344
.32.
Wan
, H. Y.
, Luo
, X. M.
, Li
, X.
, Liu
, W.
, and Zhang
, G. P.
, 2016
, “Nanotwin-Enhanced Fatigue Resistance of Ultrathin Ag Films for Flexible Electronics Applications
,” Mat. Sci. Eng., A
, 676
, pp. 421
–426
.33.
Lohmiller
, J.
, Woo
, N. C.
, and Spolenak
, R.
, 2010
, “Microstructure-Property Relationship in Highly Ductile Au-Cu Thin Films for Flexible Electronics
,” Mat. Sci. Eng., A.
, 527
(29–30
), pp. 7731
–7740
.34.
Kim
, C. I.
, Schiavone
, P.
, and Ru
, C. Q.
, 2010
, “The Effects of Surface Elasticity on an Elastic Solid With Mode-III Crack: Complete Solution
,” ASME J. Appl. Mech.
, 77
(2
), p. 021011
.35.
Arruda
, L.
, Bonadiman
, R.
, Costa
, J.
, and Reinikainen
, T.
, 2009
, “Cracking Phenomena on Flexible-Rigid Interfaces in PCBs Under Thermo Cycling Loading
,” Circuit World
, 35
(2
), pp. 18
–22
.36.
van der Sluis
, O.
, Engelen
, R. A. B.
, Timmermans
, P. H. M.
, and Zhang
, G. Q.
, 2009
, “Numerical Analysis of Delamination and Cracking Phenomena in Multi-Layered Flexible Electronics
,” Microelectron. Reliab.
, 49
(8
), pp. 853
–860
.37.
Steffensen
, S.
, and Jensen
, H. M.
, 2014
, “Energy Release Rate for Circular Crack Due to Indentation in a Brittle Film on a Ductile Substrate
,” Eur. J. Mech. A-Solid
, 43
, pp. 133
–141
.38.
Han
, Y.
, Liu
, Y.
, Wang
, W.
, Leng
, J.
, and Jin
, P.
, 2016
, “Controlled Wettability Based on Reversible Micro-Cracking on a Shape Memory Polymer Surface
,” Soft Matter
, 12
(10
), pp. 2708
–2714
.39.
Vellinga
, W. P.
, De Hosson
, J. T. M.
, and Bouten
, P. C. P.
, 2012
, “Effect of Relative Humidity on Crack Propagation in Barrier Films for Flexible Electronics
,” J. Appl. Phys.
, 112
(8
), p. 083520
.40.
Jia
, Z.
, Tucker
, M. B.
, and Li
, T.
, 2011
, “Failure Mechanics of Organic-Inorganic Multilayer Permeation Barriers in Flexible Electronics
,” Compos. Sci. Technol.
, 71
(3
), pp. 365
–372
.41.
Lin
, C. B.
, Lin
, C. C.
, Lee
, S.
, and Chou
, Y. T.
, 2008
, “The Effect of Dislocations on Crack Propagation in Wrinkled Gold Film Deposited on Polydimethylsiloxane
,” J. Appl. Phys.
, 104
(1
), p. 016106
.42.
Zhao
, Q.
, Topham
, N.
, Anderson
, J. M.
, Hiltner
, A.
, Lodoen
, G.
, and Payet
, C. R.
, 1991
, “Foreign-Body Giant Cells and Polyurethane Biostability: In Vivo Correlation of Cell Adhesion and Surface Cracking
,” J. Biomed. Mater. Res.
, 25
(2
), pp. 177
–183
.43.
Middleton
, J. D.
, 1969
, “The Effect of Temperature on Extensibility of Isolated Corneum and Its Relation to Skin Chapping
,” Brit. J. Dermatol.
, 81
(10
), pp. 717
–721
.44.
Gaul
, L. E.
, and Underwood
, G. B.
, 1952
, “Relation of Dew Point and Barometric Pressure to Chapping of Normal Skin
,” J. Invest. Dermatol.
, 19
(1
), pp. 9
–19
.45.
Sokoloff
, D. D.
, Remizowa
, M. V.
, Macfarlane
, T. D.
, Conran
, J. G.
, Yadav
, S. R.
, and Rudall
, P. J.
, 2013
, “Comparative Fruit Structure in Hydatellaceae (Nymphaeales) Reveals Specialized Pericarp Dehiscence in Some Early-Divergent Angiosperms With Ascidiate Carpels
,” Taxon
, 62
(1
), pp. 40
–61
.https://www.researchgate.net/publication/272823259_Comparative_fruit_structure_in_Hydatellaceae_Nymphaeales_reveals_specialized_pericarp_dehiscence_in_some_early-divergent_angiosperms_with_ascidiate_carpels46.
Lu
, J. J.
, Tan
, D. Y.
, Baskin
, C. C.
, and Baskin
, J. M.
, 2017
, “Delayed Dehiscence of the Pericarp: Role in Germination and Retention of Viability of Seeds of Two Cold Desert Annual Brassicaceae Species
,” Plant Biol.
, 19
(1
), pp. 14
–22
.47.
Aviles
, F.
, Llanes
, L.
, and Oliva
, A. I.
, 2009
, “Elasto-Plastic Properties of Gold Thin Films Deposited Onto Polymeric Substrates
,” J. Mater. Sci.
, 44
(10
), pp. 2590
–2598
.48.
McGuigan
, A. P.
, Briggs
, G. A. D.
, Burlakov
, V.
, Yanaka
, M.
, and Tsukahara
, Y.
, 2003
, “An Elastic-Plastic Shear Lag Model for Fracture of Layered Coatings
,” Thin Solid Films
, 424
(2
), pp. 219
–223
.49.
Gao
, X. L.
, and Li
, K.
, 2005
, “A Shear-Lag Model for Carbon Nanotube-Reinforced Polymer Composites
,” Int. J. Solids Struct.
, 42
(5–6
), pp. 1649
–1667
.50.
Okabe
, T.
, Takeda
, N.
, Kamoshida
, Y.
, Shimizu
, M.
, and Curtin
, W. A.
, 2001
, “A 3D Shear-Lag Model Considering Micro-Damage and Statistical Strength Prediction of Unidirectional Fiber-Reinforced Composites
,” Compos. Sci. Technol.
, 61
(12
), pp. 1773
–1787
.51.
Bhalla
, S.
, and Moharana
, S.
, 2013
, “A Refined Shear Lag Model for Adhesively Bonded Piezo-Impedance Transducers
,” J. Intel. Mat. Syst. Struct.
, 24
(1
), pp. 33
–48
.52.
Tobushi
, H.
, Okumura
, K.
, Hayashi
, S.
, and Ito
, N.
, 2001
, “Thermomechanical Constitutive Model of Shape Memory Polymer
,” Mech. Mater.
, 33
(10
), pp. 545
–554
.Copyright © 2018 by ASME
You do not currently have access to this content.
