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Research Papers

A Coupled Shear Stress-Diffusion Model for Adhesively Bonded Single Lap Joints

[+] Author and Article Information
Sayed A. Nassar

Fellow ASME
Fastening and Joining Research Institute (FAJRI),
Department of Mechanical Engineering,
Oakland University,
Rochester, MI 48309
e-mail: nassar@oakland.edu

Emad Mazhari

Fastening and Joining Research Institute (FAJRI),
Department of Mechanical Engineering,
Oakland University,
Rochester, MI 48309
e-mail: mazhari.e@gmail.com

1Corresponding author.

Contributed by the Applied Mechanics Division of ASME for publication in the JOURNAL OF APPLIED MECHANICS. Manuscript received April 22, 2016; final manuscript received June 29, 2016; published online August 3, 2016. Assoc. Editor: Daining Fang.

J. Appl. Mech 83(10), 101006 (Aug 03, 2016) (7 pages) Paper No: JAM-16-1201; doi: 10.1115/1.4034043 History: Received April 22, 2016; Revised June 29, 2016

In this study, a coupled shear stress-diffusion model is developed for the analysis of adhesively bonded single lap joints (SLJs) by applying Fickian diffusion model to the adhesive layer. Differential equations of equilibrium are formulated in terms of adhesive material properties that are time and location dependent. By invoking a Volkersen approach on the equilibrium equations, a shear stress differential equation is formulated and numerically solved. Several scenarios are considered for investigating the effect of diffusion on shear stress distribution in adhesively bonded SLJs. Detailed discussion of the results is presented.

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References

Figures

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Fig. 1

(a) One-dimensional diffusion model and (b) normalized concentration variation along the overlap length, L = 12.7 mm, D = 2 × 10−7 (mm2/s)

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Fig. 2

Stress–strain curve of the adhesive

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Fig. 3

Upper and lower of elements along with internal stresses, selected from SLJ's bonding area

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Fig. 6

Shear modulus linear variation along the overlap for Eq.(22)

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Fig. 7

Shear modulus exponential variation along the overlap for Eq. (23)

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Fig. 8

Convergence of shear stress solution versus time

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Fig. 9

Shear stress distribution along the overlap-linear scenario

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Fig. 10

Shear stress distribution along the overlap-Exp. scenario

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Fig. 11

Model prediction of edge and central values of shear stress

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Fig. 12

Model prediction of maximum values of shear stress

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Fig. 4

Minimum required numbers of diffusion terms versus diffusing time for Eq. (22)

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Fig. 5

Minimum required numbers of diffusion and exponential terms versus diffusing time for Eq. (23)

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