Matched Asymptotic Expansions of Unbalanced Adhesive Joints
Publication: Journal of Engineering Mechanics
Volume 139, Issue 10
Abstract
A matched asymptotic expansion analysis is used to determine the dependence of shear stress boundary layer thickness on adhesive properties in unbalanced single-lap joints. A uniformly accurate expansion of shear stress, in a small and positive dimensionless parameter , is shown to contain a pair of adhesive edge boundary layers and an outer zone where the stress is slowly varying between the two layers. An overlap constraint is also found, and if it can be satisfied for , then there is sufficient overlap and a single boundary layer of width the order of at either adhesive end. The analytic results are presented in a generic format allowing their application and/or extension to similar problems. All results are numerically verified using a finite difference approximation.
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References
Banks-Sills, L., and Salganik, R. (1994). “An asymptotic approach applied to a longitudinal crack in an adhesive layer.” Int. J. Fract., 68(1), 55–73.
Barenblatt, G. I. (1996). Scaling, self-similarity, and intermediate asymptotics, Cambridge University Press, New York.
Bender, C. M., and Orzsag, S. A. (1978). Advanced mathematical methods for scientists and engineers, McGraw Hill, New York.
Gilibert, Y., and Rigolot, A. (1988). “Determination of stress distribution in double lap joints, matched asymptotic expansions and conformal mapping.” Adhesively Bonded Joints: Testing, Analysis, and Design, ASTM STP 981, ASTM, West Conshohoken, PA, 145–159.
Gustafson, P. A., Bizard, A., and Waas, A. M. (2007). “Dimensionless parameters in symmetric double lap joints: An orthotropic solution for thermomechanical loading.” Int. J. Solids and Structures, 44(17), 5774–5795.
Hassan, E., Kalamkarov, A. L., and Georgiades, A. (2009). “An asymptotic homogenization model for smart 3D grid-reinforced composite structures with generally orthotropic constituents.” Smart Mater. Struct., 18(7).
Kevorkian, J., and Cole, J. D. (1975). Perturbation methods in applied mathematics, Springer, New York.
Klarbring, A., and Movchan, A. (1998). “Asymptotic modelling of adhesive joints.” Mech. Mater., 28(1–4), 137–145.
Li, G. (2000). “Deformations of balanced and unbalanced adhesively bonded single-lap joints.” Ph.D. thesis, Univ. of New Brunswick, Fredericton, NB, Canada.
Shahin, K., Kember, G., and Taheri, F. (2008). “An asymptotic solution for evaluation of stresses in balanced and unbalanced adhesively bonded joints.” Mech. Adv. Mater. Struct., 15(2), 88–103.
Van Dyke, M. (1975). Perturbation methods in fluid mechanics, Parabolic Press, Stanford, CA.
Yuceoglu, U., and Updike, D. P. (1980). “Stress analysis of bonded plates and joints.” J. Engrg. Mech. Div., 106(1), 37–56.
Information & Authors
Information
Published In
Journal of Engineering Mechanics
Volume 139 • Issue 10 • October 2013
Pages: 1387 - 1394
Copyright
© 2013 American Society of Civil Engineers.
History
Received: Jun 22, 2012
Accepted: Nov 20, 2012
Published online: Nov 22, 2012
Published in print: Oct 1, 2013
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