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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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References

Figures

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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).

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Fig. 2

A bilinear TS relation

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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).

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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.

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Fig. 5

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

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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.

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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

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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.

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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

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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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