This paper provides full asymptotic crack-tip field solutions for an antiplane (mode-III) stationary crack in a functionally graded material. We use the complex variable approach and an asymptotic scaling factor to provide an efficient procedure for solving standard and perturbed Laplace equations associated with antiplane fracture in a graded material. We present the out-of-plane displacement and the shear stress solutions for a crack in exponentially and linearly graded materials by considering the gradation of the shear modulus either parallel or perpendicular to the crack. We discuss the characteristics of the asymptotic solutions for a graded material in comparison with the homogeneous solutions. We address the effects of the mode-III stress intensity factor and the antiplane T-stress onto crack-tip field solutions. Finally, engineering significance of the present work is discussed.
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e-mail: jhkim@engr.uconn.edu
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January 2011
Research Papers
Higher-Order Terms for the Mode-III Stationary Crack-Tip Fields in a Functionally Graded Material
Linhui Zhang,
Linhui Zhang
Department of Civil and Environmental Engineering,
University of Connecticut
, 261 Glenbrook Road, Unit 2037, Storrs, CT 06269
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Jeong-Ho Kim
Jeong-Ho Kim
Department of Civil and Environmental Engineering,
e-mail: jhkim@engr.uconn.edu
University of Connecticut
, 261 Glenbrook Road, Unit 2037, Storrs, CT 06269
Search for other works by this author on:
Linhui Zhang
Department of Civil and Environmental Engineering,
University of Connecticut
, 261 Glenbrook Road, Unit 2037, Storrs, CT 06269
Jeong-Ho Kim
Department of Civil and Environmental Engineering,
University of Connecticut
, 261 Glenbrook Road, Unit 2037, Storrs, CT 06269e-mail: jhkim@engr.uconn.edu
J. Appl. Mech. Jan 2011, 78(1): 011005 (10 pages)
Published Online: October 12, 2010
Article history
Received:
June 11, 2009
Revised:
July 28, 2010
Posted:
August 2, 2010
Published:
October 12, 2010
Online:
October 12, 2010
Citation
Zhang, L., and Kim, J. (October 12, 2010). "Higher-Order Terms for the Mode-III Stationary Crack-Tip Fields in a Functionally Graded Material." ASME. J. Appl. Mech. January 2011; 78(1): 011005. https://doi.org/10.1115/1.4002289
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