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Research Papers

Interface Cracks in Kirchhoff Anisotropic Thin Plates of Dissimilar Materials

[+] Author and Article Information
Xu Wang

School of Mechanical and Power Engineering,
East China University of Science and Technology,
130 Meilong Road,
Shanghai 200237, China

Peter Schiavone

Department of Mechanical Engineering,
University of Alberta,
4-9 Mechanical Engineering Building,
Edmonton, AB T6G 2G8,Canada

Manuscript received April 10, 2012; final manuscript received November 12, 2012; accepted manuscript posted November 19, 2012; published online May 23, 2013. Assoc. Editor: George Kardomateas.

J. Appl. Mech 80(4), 041025 (May 23, 2013) (4 pages) Paper No: JAM-12-1144; doi: 10.1115/1.4023020 History: Received April 10, 2012; Revised November 12, 2012; Accepted November 19, 2012

This paper investigates the problem of stretching and bending deformations of a Kirchhoff anisotropic thin plate composed of two dissimilar materials bonded along a straight interface containing a crack. Our analysis makes use of the Stroh octet formalism developed recently by Cheng and Reddy (Cheng and Reddy, 2002, “Octet Formalism for Kirchhoff Anisotropic Plates,” Proc. R. Soc. Lond., A458, pp. 1499–1517; Cheng and Reddy, 2003, “Green’s Functions for Infinite and Semi-Infinite Anisotropic Thin Plates,” ASME J. Appl. Mech., 70, pp. 260–267; Cheng and Reddy, 2004, “Laminated Anisotropic Thin Plate With an Elliptic Inhomogeneity,” Mech. Mater., 36, pp. 647–657; Cheng and Reddy, 2005, “Structure and Properties of the Fundamental Elastic Plate Matrix,” J. Appl. Math. Mech., 85, pp. 721–739) for Kirchhoff anisotropic plates. It is found that the interfacial crack-tip field consists of a pair of two-dimensional oscillatory singularities, which are explicitly determined. Two complex intensity factors are proposed to evaluate the two oscillatory singularities.

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References

Williams, M. L., 1959, “The Stresses Around a Fault or Crack in Dissimilar Media,” Bull. Seismol. Soc. America, 49, pp. 199–204.
Sih, G. C., and Rice, J.R., 1964, “The Bending of Plates of Dissimilar Materials With Cracks,” ASME J. Appl. Mech., 86, pp. 477–482. [CrossRef]
Cheng, Z. Q., and Reddy, J. N., 2002, “Octet Formalism for Kirchhoff Anisotropic Plates,” Proc. R. Soc. Lond., A458, pp. 1499–1517.
Cheng, Z. Q., and Reddy, J. N., 2003, “Green’s Functions for Infinite and Semi-Infinite Anisotropic Thin Plates,” ASME J. Appl. Mech., 70, pp. 260–267. [CrossRef]
Cheng, Z. Q., and Reddy, J. N., 2004, “Laminated Anisotropic Thin Plate With an Elliptic Inhomogeneity,” Mech. Mater., 36, pp. 647–657. [CrossRef]
Cheng, Z. Q., and Reddy, J. N., 2005, “Structure and Properties of the Fundamental Elastic Plate Matrix,” J. Appl. Math. Mech., 85, pp. 721–739.
Suo, Z., 1990, “Singularities, Interfaces and Cracks in Dissimilar Anisotropic Media,” Proc. R. Soc. Lond., A427, pp. 331–358.
Yang, W., Suo, Z., and Shih, C. F., 1991, “Mechanics of Dynamic Debonding,” Proc. R. Soc. Lond., A433, pp. 679–697.
Wang, X., and Schiavone, P., 2012, “Dislocations, Imperfect Interfaces and Interface Cracks in Anisotropic Elasticity for Quasicrystals,” Mathematics and Mechanics of Complex Systems (accepted).

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