Investigation of a Griffith Crack Subject to Uniform Tension Using the Non-Local Theory by a New Method

Zhou Zhengong; Wang Biao

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(10): 1025-1032

Zhou Zhengong, Wang Biao. Investigation of a Griffith Crack Subject to Uniform Tension Using the Non-Local Theory by a New Method[J]. Applied Mathematics and Mechanics, 1999, 20(10): 1025-1032.

Citation:

Zhou Zhengong, Wang Biao. Investigation of a Griffith Crack Subject to Uniform Tension Using the Non-Local Theory by a New Method[J]. Applied Mathematics and Mechanics, 1999, 20(10): 1025-1032.

Citation:

Zhou Zhengong, Wang Biao. Investigation of a Griffith Crack Subject to Uniform Tension Using the Non-Local Theory by a New Method[J]. Applied Mathematics and Mechanics, 1999, 20(10): 1025-1032.

PDF( 311 KB)

Investigation of a Griffith Crack Subject to Uniform Tension Using the Non-Local Theory by a New Method

P O Box 2147, Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, P R China

Received Date: 1998-07-02
Publish Date: 1999-10-15

Abstract

Abstract

Field equations of the non-local elasticity are solved to determine the state of stress in a plate with a Griffith crack subject to uniform tension. Then a set of dual-integral equations is solved using a new method, namely Schmidt's method. This method is more exact and more reasonable than Eringen's one for solving this kind of problem. Contrary to the solution of classical elasticity, it is found that no stress singularity is present at the crack tip. The significance of this result is that the fracture criteria are unified at both the macroscopic and the microscopic scales. The finite hoop stress at the crack tip depends on the crack length.
- non-local theory,
- Schmidt's method,
- dual-integral equation

FullText(HTML)

References(16)

References

[1]	Eringen A C,Speziale C G,Kim B S.Crack tip problem in non-local elasticity[J].Journal of Mechanics and Physics of Solids,1977,25(5):339.
[2]	Eringen A C.Linear crack subject to shear[J].International Journal of Fracture,1978,14(4):367～379.
[3]	Eringen A C.Linear crack subject to antiplane shear[J].Engineering Fracture Mechanics,1979,12(2):211～219.
[4]	Zhou Zhengong,Han Jiecai,Du Shangyi.Investigation of the scattering of harmonic elastic waves by a finite crack using the non-local theory[J].Mechanics Research Communications,1998,25(5):519～528.
[5]	Zhou Zhengong,Wang Biao,Du Shangyi.Scattering of the anti-plane shear waves by a finite crack by using the non-local theory[J].International Journal of Fracture,1998,91(4):13～22.
[6]	Nowinski J L.On non-local aspects of the propagation of Love waves[J].International Journal of Engineering Science,1984,22(4):383～392.
[7]	Nowinski J L.On non-local theory of wave propagation in elastic plates[J].ASME Journal Applied Mechanics,1984,51(3):608～613.
[8]	Eringen A C.Continuum mechanics at the atomic scale[J].Crystal Lattice Defects,1977,7(2):109～130.
[9]	Eringen A C.Non-local elasticity and waves[A].In:P Thoft-Christensen Ed.Continuum Mechanics Aspects of Geodynamics and Rock Fracture Mechanics[C].Holland:Dordrecht,1974,81～105.
[10]	Morse P M,Feshbach H.Methods of Theoretical Physics[M].Vol.1.New York:McGraw-Hill,1958.
[11]	Gradshteyn I S,Ryzhik I M.Table of Integral,Series and Products[M].New York:Academic Press,1980.
[12]	Erdelyi A.Tables of Integral Transforms[M].Vol.1.New York:McGraw-Hill,1954.
[13]	Amemiya A,Taguchi T.Numerical Analysis and Fortran[M].Tokyo:Maruzen,1969.
[14]	Itou S.Three dimensional waves propagation in a cracked elastic solid[J].ASME Journal of Applied Mechanics,1978,45(3):807～811.
[15]	Itou S.Three dimensional problem of a running crack[J].International Journal of Engineering Science,1979,17(4):59～71.
[16]	Eringen A C.Interaction of a dislocation with a crack[J].Journal of Applied Physics,1983,54(3):6811～6818.