Analysis of bonded finite wedges with an interfacial crack under antiplane shear loading

Abstract

Antiplane shear deformation of bonded finite wedges with an interface crack is studied in this article. The traction-free condition is imposed on the circular segment of the wedge. Boundary conditions on the radial edges are considered as traction—traction. In order to solve this problem a novel mathematical technique has been employed. This technique consists of the use of some recently proposed finite complex transforms, which have complex analogies to the standard finite Mellin transforms of the first and second kinds. However, for the problem of bonded wedges with an interfacial crack, first it is necessary to express the traction-free condition of the crack faces in the form of a singular integral equation, which is done in this article by describing an exact analytical method. The resultant singular integral equations are then solved numerically and the obtained results including the stress intensity factors at the crack tips are plotted. Comparison of the results in the special cases shows a complete agreement with those cited in the literature.

Keywords

antiplane shear deformation isotropic elastic wedge stress singularity stress intensity factor

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References

Tranter

C. J.

, ‘The use of the Mellin transform in finding the stress distribution in an infinite wedge’ Q. J. Mech. Appl. Math. 1 (1948): 125–130.

Williams

M. L.

, ‘Stress singularities resulting from various boundary conditions in angular corners of plates in extension’ J. Appl. Mech. 19 (1952): 526–528.

Bogy

D. B.

, ‘The plane solution for anisotropic elastic wedges under normal and shear loading’ J. Appl. Mech. 39 (1972): 1103–1109.

Kuo

M. C.

Bogy

D. B.

, ‘Plane solutions for the displacement and traction-displacement problems for anisotropic elastic wedges’ J. Appl. Mech. 41 (1974a): 197–202.

Kuo

M. C.

Bogy

D. B.

, ‘Plane solutions for traction problems on orthotropic unsymmetrical wedges and symmetrically twinned wedges’ J. Appl. Mech. 41 (1974b): 203–208.

C. C.

Hour

B. L.

, ‘Analysis of dissimilar anisotropic wedges subjected to antiplane shear deformation’ Int. J. Solids Struct. 25 (1989): 1295–1309.

Kargarnovin

M. H.

Shahani

A. R.

Fariborz

S. J.

, ‘Analysis of an isotropic finite wedge under antiplane deformation’ Int. J. Solids Struct. 34 (1997): 113–128.

Shahani

A. R.

, ‘Analysis of an anisotropic finite wedge under antiplane deformation’ J. Elast. 56 (1999): 17–32.

Erdogan

Gupta

G. D.

, ‘Bonded wedges with an interface crack under antiplane shear loading’ Int. J. Fract. 11 (1975): 583–593.

10.

Shahani

A. R.

Adibnazari

, ‘Analysis of perfectly bonded wedges and bonded wedges with an interfacial crack under antiplane shear loading’ Int. J. Solids Struct. 37 (2000): 2639–2650.

11.

Shahani

A. R.

, ‘Mode III stress intensity factors for edge-cracked circular shafts, bonded wedges, bonded half planes and DCB's’ Int. J. Solids Struct. 40 (2003): 6567–6576.

12.

Faal

R. T.

Fotuhi

A. R.

Fariborz

S. J.

Daghyani

H. R.

, ‘Antiplane stress analysis of an isotropic wedge with multiple cracks’ Int. J. Solids Struct. 41 (2004): 4535–4550.

13.

Lin

R. L.

C. C.

, ‘Theoretical full-field analysis of dissimilar isotropic composite annular wedges under anti-plane deformations’ Int. J. Solids Struct. 41 (2004): 6041–6080.

14.

Shahani

A. R.

, ‘Some problems in the antiplane shear deformation of bi-material wedges’ Int. J. Solids Struct. 42 (2005): 3093–3113.

15.

Shahani

A. R.

, ‘Mode III stress intensity factors in an interfacial crack in dissimilar bonded materials’ Arch. Appl. Mech. 75 (2006): 405–411.

16.

Faal

R. T.

Fariborz

S. J.

Daghyani

H. R.

, ‘Stress analysis of a finite wedge weakened by cavities’ Int. J. Mech. Sci. 49 (2007): 75–85.

17.

Shahani

A. R.

, ‘On the antiplane shear deformation of finite wedges’ Appl. Math. Model. 31 (2007): 141–151.

18.

Muskhelishvili

I. N.

, Singular integral equations (Groningen, The Netherlands: P. Noordhoff 1953).

19.

Erdogan

Gupta

G. D.

, ‘On the numerical solution of singular integral equations’ Q. Appl. Math. 29 (1972): 525–534.

20.

Shahani

A. R.

, ‘A note on the paper ‘Analysis of perfectly bonded wedges and bonded wedges with an interfacial crack under antiplane shear loading’ Int. J. Solids Struct. 38 (2001): 5041–5043.