Research Papers

Edge Debonding in Peeling of a Thin Flexible Plate From an Elastomer Layer: A Cohesive Zone Model Analysis

[+] Author and Article Information
Bikramjit Mukherjee

Department of Biomedical Engineering
and Mechanics, M/C 0219,
Virginia Polytechnic Institute
and State University,
Blacksburg, VA 24061

Romesh C. Batra

Fellow ASME
Department of Biomedical Engineering
and Mechanics, M/C 0219,
Virginia Polytechnic Institute
and State University,
Blacksburg, VA 24061
e-mail: rbatra@vt.edu

David A. Dillard

Fellow ASME
Department of Biomedical Engineering and Mechanics, M/C 0219,
Virginia Polytechnic Institute
and State University,
Blacksburg, VA 24061
e-mail: dillard@vt.edu

1Present address: Dow Chemical Company, Freeport, TX 77541.

2Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received October 7, 2016; final manuscript received October 10, 2016; published online November 7, 2016. Assoc. Editor: Kyung-Suk Kim.

J. Appl. Mech 84(2), 021003 (Nov 07, 2016) (10 pages) Paper No: JAM-16-1492; doi: 10.1115/1.4034988 History: Received October 07, 2016; Revised October 10, 2016

A cohesive zone modeling (CZM) approach with a bilinear traction-separation relation is used to study the peeling of a thin overhanging plate from the edge of an incompressible elastomeric layer bonded firmly to a stationary rigid base. The deformations are approximated as plane strain and the materials are assumed to be linearly elastic, homogeneous, and isotropic. Furthermore, governing equations for the elastomer deformations are simplified using the lubrication theory approximations, and those of the plate with the Kirchhoff–Love theory. It is found that the peeling is governed by a single nondimensional number defined in terms of the interfacial strength, the interface fracture energy, the plate bending rigidity, the elastomer shear modulus, and the elastomeric layer thickness. An increase in this nondimensional number monotonically increases the CZ size ahead of the debond tip, and the pull-off force transitions from a fracture energy to strength dominated regime. This finding is supported by the results of the boundary value problem numerically studied using the finite element method. Results reported herein could guide elastomeric adhesive design for load capacity and may help ascertain test configurations for extracting the strength and the fracture energy of an interface from test data.

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Kaelble, D. , 1959, “ Theory and Analysis of Peel Adhesion: Mechanisms and Mechanics,” Trans. Soc. Rheol., 3(1), pp. 161–180. [CrossRef]
Kaelble, D. , 1960, “ Theory and Analysis of Peel Adhesion: Bond Stresses and Distributions,” Trans. Soc. Rheol., 4(1), pp. 45–73. [CrossRef]
Bikerman, J. , 1957, “ Theory of Peeling Through a Hookean Solid,” J. Appl. Phys., 28(12), pp. 1484–1485. [CrossRef]
Spies, G. , 1953, “ The Peeling Test on Redux-Bonded Joints: A Theoretical Analysis of the Test Devised by Aero Research Limited,” Aircr. Eng. Aerosp. Technol., 25(3), pp. 64–70. [CrossRef]
Kaelble, D. , 1965, “ Peel Adhesion: Micro‐Fracture Mechanics of Interfacial Unbonding of Polymers,” Trans. Soc. Rheol., 9(2), pp. 135–163. [CrossRef]
Dillard, D. , 1989, “ Bending of Plates on Thin Elastomeric Foundations,” ASME J. Appl. Mech., 56(2), pp. 382–386. [CrossRef]
Lefebvre, D. R. , Dillard, D. A. , and Brinson, H. , 1988, “ The Development of a Modified Double-Cantilever-Beam Specimen for Measuring the Fracture Energy of Rubber to Metal Bonds,” Exp. Mech., 28(1), pp. 38–44. [CrossRef]
Ghatak, A. , Mahadevan, L. , and Chaudhury, M. K. , 2005, “ Measuring the Work of Adhesion Between a Soft Confined Film and a Flexible Plate,” Langmuir, 21(4), pp. 1277–1281. [CrossRef] [PubMed]
Bao, G. , and Suo, Z. , 1992, “ Remarks on Crack-Bridging Concepts,” ASME Appl. Mech. Rev., 45(8), pp. 355–366. [CrossRef]
Xu, X.-P. , and Needleman, A. , 1996, “ Numerical Simulations of Dynamic Crack Growth Along an Interface,” Int. J. Fract., 74(4), pp. 289–324. [CrossRef]
Geubelle, P. H. , and Baylor, J. S. , 1998, “ Impact-Induced Delamination of Composites: A 2D Simulation,” Compos. Part B: Eng., 29(5), pp. 589–602. [CrossRef]
Dugdale, D. , 1960, “ Yielding of Steel Sheets Containing Slits,” J. Mech. Phys. Solids, 8(2), pp. 100–104. [CrossRef]
Tang, T. , and Hui, C. Y. , 2005, “ Decohesion of a Rigid Punch From an Elastic Layer: Transition From “Flaw Sensitive” to “Flaw Insensitive” Regime,” J. Polym. Sci. Part B: Polym. Phys., 43(24), pp. 3628–3637. [CrossRef]
Williams, J. , and Hadavinia, H. , 2002, “ Analytical Solutions for Cohesive Zone Models,” J. Mech. Phys. Solids, 50(4), pp. 809–825. [CrossRef]
Georgiou, I. , Hadavinia, H. , Ivankovic, A. , Kinloch, A. , Tropsa, V. , and Williams, J. , 2003, “ Cohesive Zone Models and the Plastically Deforming Peel Test,” J. Adhes., 79(3), pp. 239–265. [CrossRef]
Blackman, B. , Hadavinia, H. , Kinloch, A. , and Williams, J. , 2003, “ The Use of a Cohesive Zone Model to Study the Fracture of Fibre Composites and Adhesively-Bonded Joints,” Int. J. Fract., 119(1), pp. 25–46. [CrossRef]
Ouyang, Z. , and Li, G. , 2009, “ Local Damage Evolution of Double Cantilever Beam Specimens During Crack Initiation Process: A Natural Boundary Condition Based Method,” ASME J. Appl. Mech., 76(5), p. 051003. [CrossRef]
Plaut, R. H. , and Ritchie, J. L. , 2004, “ Analytical Solutions for Peeling Using Beam-on-Foundation Model and Cohesive Zone,” J. Adhes., 80(4), pp. 313–331. [CrossRef]
Stigh, U. , 1988, “ Damage and Crack Growth Analysis of the Double Cantilever Beam Specimen,” Int. J. Fract., 37(1), pp. R13–R18. [CrossRef]
Biel, A. , and Stigh, U. , 2007, “ An Analysis of the Evaluation of the Fracture Energy Using the DCB-Specimen,” Arch. Mech., 59(4–5), pp. 311–327. http://am.ippt.pan.pl/am/article/view/v59p311
Dhong, C. , and Fréchette, J. , 2015, “ Coupled Effects of Applied Load and Surface Structure on the Viscous Forces During Peeling,” Soft Matter, 11(10), pp. 1901–1910. [CrossRef] [PubMed]
Timoshenko, S. , 1940, Theory of Plates and Shells, McGraw-Hill, New York.
Ripling, E. , Mostovoy, S. , and Patrick, R. , 1964, “ Measuring Fracture Toughness of Adhesive Joints,” Mater. Res. Stand., 4(3), pp. 129–134.
Maugis, D. , 1992, “ Adhesion of Spheres: the JKR-DMT Transition Using a Dugdale Model,” J. Colloid Interface Sci., 150(1), pp. 243–269. [CrossRef]
Reynolds, O. , 1886, “ On the Theory of Lubrication and Its Application to Mr. Beauchamp Tower's Experiments, Including an Experimental Determination of the Viscosity of Olive Oil,” Proc. R. Soc. London, 40(242–245), pp. 191–203. [CrossRef]
Wolfram, Research, 2014, Mathematica, Wolfram Research, Champaign, IL.
Mukherjee, B. , Batra, R. C. , and Dillard, D. A. , 2016, “ Effect of Confinement and Interfacial Adhesion on Peeling of a Flexible Plate From an Elastomeric Layer,” Int. J. Solids Struct. (in press).
Obreimoff, J. , 1930, “ The Splitting Strength of Mica,” Proc. R. Soc. London A, 127(805), pp. 290–297. [CrossRef]
Ha, K. , Baek, H. , and Park, K. , 2015, “ Convergence of Fracture Process Zone Size in Cohesive Zone Modeling,” Appl. Math. Model., 39(19), pp. 5828–5836. [CrossRef]
Ghatak, A. , 2006, “ Confinement-Induced Instability of Thin Elastic Film,” Phys. Rev. E, 73(4), p. 041601. [CrossRef]
Ghatak, A. , Chaudhury, M. K. , Shenoy, V. , and Sharma, A. , 2000, “ Meniscus Instability in a Thin Elastic Film,” Phys. Rev. Lett., 85(20), p. 4329. [CrossRef] [PubMed]
Ghatak, A. , and Chaudhury, M. K. , 2003, “ Adhesion-Induced Instability Patterns in Thin Confined Elastic Film,” Langmuir, 19(7), pp. 2621–2631. [CrossRef]
Li, S. , Wang, J. , and Thouless, M. , 2004, “ The Effects of Shear on Delamination in Layered Materials,” J. Mech. Phys. Solids, 52(1), pp. 193–214. [CrossRef]
Ghatak, A. , Mahadevan, L. , Chung, J. Y. , Chaudhury, M. K. , and Shenoy, V. , 2004, “ Peeling From a Biomimetically Patterned Thin Elastic Film,” Proc. R. Soc. London Ser. A, 460(2049), pp. 2725–2735. [CrossRef]


Grahic Jump Location
Fig. 1

Sketch of (a) the problem studied, and (b) various zones near the debond tip B after it has moved in the x̃ direction by the distance a−a0. Also, schematically plotted are variations of the peel stress (normal traction) and the corresponding contact opening (displacement jump) along the x̃ -axis. (Color is available in the online version).

Grahic Jump Location
Fig. 2

A bilinear TS relation

Grahic Jump Location
Fig. 5

Nondimensional traction-free length as a function of the applied nondimensional displacement

Grahic Jump Location
Fig. 4

Comparisons of predicted peel stresses from present work with those predicted by the LEFM [8] solution and computed using the FEM [27]. The nondimensional input parameters are listed in the insets.

Grahic Jump Location
Fig. 3

For three values of the nondimensional applied displacement, ΔA, distributions of the nondimensional (a) plate deflection and (b) peel stress (T/Tc) on the global horizontal axis X̃=βx̃. For ΔA=4.0, the three regions around a debond are marked in (b).

Grahic Jump Location
Fig. 6

Nondimensional CZ size, the plate deflection at the debond tip, and the plate slope at the debond tip versus the nondimensional applied displacement. The dashed lines represent results prior to the initiation of debonding.

Grahic Jump Location
Fig. 9

For A0=2.83, the peak load (pull-off force) as a function of the nondimensional number ηs on a log–log scale

Grahic Jump Location
Fig. 7

(a) The CZ size at debond initiation versus ηs for three values of the initial overhang length A0 (solid lines) and versus A0 for two values of ηs (dashed lines) and (b) peel stress distribution at ΔA=4.0 and the size of the tensile region near the debond tip as a function of the debond length given by Ghatak et al.'s [8] solution

Grahic Jump Location
Fig. 8

Nondimensional load versus the applied nondimensional displacement for (a) ηs=1.4 and (b) ηs=2. The dotted line (oa) and the dashed line (ab) represent results, respectively, prior to the initiation of damage and between damage initiation and debonding initiation. The solids portion (bc) are for debond propagation.

Grahic Jump Location
Fig. 10

The dimensionless debond length as a function of ΔA from (a) Eq. (A10) and (b) Eq. (A12). Corresponding LEFM plots are included for comparison.



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