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Research Papers: Conduction

A Thermal Interface Crack Problem for Dissimilar Functionally Graded Isotropic Materials

[+] Author and Article Information
David L. Clements

School of Mathematics,
The University of Adelaide,
Adelaide SA 5005, Australia
e-mail: david.clements@adelaide.edu.au

1Corresponding author.

Contributed by the Heat Transfer Division of ASME for publication in the JOURNAL OF HEAT TRANSFER. Manuscript received August 29, 2014; final manuscript received May 18, 2015; published online July 14, 2015. Assoc. Editor: Amy Fleischer.

J. Heat Transfer 137(11), 111301 (Jul 14, 2015) (7 pages) Paper No: HT-14-1572; doi: 10.1115/1.4030883 History: Received August 29, 2014

The problem of determining the steady-state temperature and flux fields in a material containing a plane crack along the bonded interface of two dissimilar functionally graded isotropic materials is considered. The materials exhibit quadratic variation in the coefficients of heat conduction. At large distances from the crack, a uniform heat flux is prescribed. The crack is modeled as an insulated cut. Numerical values for the temperature and flux are obtained for some particular materials. The results demonstrate how the variation in the functional gradation of the thermal parameters in the bonded materials affects the temperature discontinuity across the crack faces and the heat flux flow around the crack tips.

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References

Chao, C. K. , and Chang, R. C. , 1972, “Thermal Interface Crack Problems in Dissimilar Anisotropic Media,” J. Appl. Phys., 72(7), pp. 2598–2604 . [CrossRef]
Shiah, Y. C. , Yang, R. B. , and Hwang, P. W. , 2005, “Heat Conduction in Dissimilar Anisotropic Media With Bonding Defects/Interface Cracks,” J. Mech., 21(1), pp. 15–23. [CrossRef]
Clements, D. L. , 1983, “A Thermoelastic Problem for a Crack Between Dissimilar Anisotropic Media,” Int. J. Solids Struct., 19(2), pp. 121–130. [CrossRef]
Clements, D. L. , 2013, “An Antiplane Crack Between Bonded Dissimilar Functionally Graded Isotropic Elastic Materials,” Q. J. Mech. Appl. Math., 66(3), pp. 333–349. [CrossRef]
Erdogan, F. , and Ozturk, M. , 1992, “Diffusion Problems in Bonded Nonhomogeneous Materials With an Interface Cut,” Int. J. Eng. Sci., 30(10), pp. 1507–1523. [CrossRef]
Mason, J. C. , and Handscomb, D. C. , 2002, Chebyshev Polynomials, CRC Press, Boca Raton, FL.
England, A. H. , 1971, Complex Variable Methods in Elasticity, Wiley, London.

Figures

Grahic Jump Location
Fig. 2

Crack temperature discontinuity t(x,0)/p0' for β'=0,λR=1, and various values of λL

Grahic Jump Location
Fig. 3

Crack temperature discontinuity t(x,0)/p0' for β'=10, λR= 1, and various values of λL

Grahic Jump Location
Fig. 4

Crack temperature discontinuity t(x,0)/p0' for β'=50, λR= 1, and various values of λL

Grahic Jump Location
Fig. 5

Temperature T(0,y)/p0'T0 for β'=0, λR= 1, and various values of λL

Grahic Jump Location
Fig. 6

Temperature T(0,y)/p0'T0 for β'=50, λR= 1, and various values of λL

Grahic Jump Location
Fig. 7

Temperature with crack T(0,y)/p0'T0 for β'=0, λR= 1, and various values of λL

Grahic Jump Location
Fig. 8

Temperature with crack T(0,y)/p0'T0 for β'=50, λR= 1, and various values of λL

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