INVESTIGATION OF THE SCATTERING OF HARMONIC ELASTIC WAVES BY TWO COLLINEAR SYMMETRIC CRACKS USING THE NON-LOCAL THEORY

Applied Mathematics and Mechanics (English Edition) ›› 2001, Vol. 22 ›› Issue (7): 766-775.

• Articles • Previous Articles Next Articles

INVESTIGATION OF THE SCATTERING OF HARMONIC ELASTIC WAVES BY TWO COLLINEAR SYMMETRIC CRACKS USING THE NON-LOCAL THEORY

ZHOU Zhen-gong, WANG Biao

Center for Composite Materials, Harbin Institute of Technology, Harbin 150001, P. R. China

Received:1999-12-14 Revised:2001-02-13 Online:2001-07-18 Published:2001-07-18
Supported by:
the National Foundation for Excellent Young Investigations(19725209);the Post Doctoral Science Foundation of Heilongjiang Province;the Natural Science Foundation of Heilongjiang Province

Abstract

Abstract: The scattering of harmonic waves by two collinear symmetric cracks is studied using the non-local theory. A one-dimensional non-local kernel was used to replace a two-dimensional one for the dynamic problem to obtain the stress occurring at the crack tips. The Fourier transform was applied and a mixed boundary value problem was formulated. Then a set of triple integral equations was solved by using Schmidt’s method. This method is more exact and more reasonable than Eringen’s for solving this problem. Contrary to the classical elasticity solution, it is found that no stress singularity is present at the crack tip. The non-local dynamic elastic solutions yield a finite hoop stress at the crack tip, thus allowing for a fracture criterion based on the maximum dynamic stress hypothesis. The finite hoop stress at the crack tip depends on the crack length, the lattice parameter and the circular frequency of incident wave.

2010 MSC Number:

O345.21

ZHOU Zhen-gong;WANG Biao . INVESTIGATION OF THE SCATTERING OF HARMONIC ELASTIC WAVES BY TWO COLLINEAR SYMMETRIC CRACKS USING THE NON-LOCAL THEORY. Applied Mathematics and Mechanics (English Edition), 2001, 22(7): 766-775.

TrendMD

References

[1] Edelen D G B.Non-local f ield theory[A].In:Eringen A C,Ed.Continuum Physics[C].Vol 4.New York:Academic Press,1976,75-294.
[2] Eringen A C.Non-local polar field theory[A].In:Eringen A C Ed.Continuum Physics[C].Vol 4.New York:Academic Press,1976,205-267.
[3] Green A E,Rivilin R S.M ultipolar continuum mechanics:functional theory[J].Proceedings of the Royal Society London,Series A,1965,(284):303.
[4] 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(4):339.
[5] Eringen A C,Kim B S.Stress concentration at the tip of crack[J].Mechanics Research Communications,1974,1(2):233.
[6] Eringen A C.Linear crack subject to shear[J].International Journal of Fracture,1978,14(3):367-379.
[7] Eringen A C.Linear crack subject to anti-plane shear[J].En gineering Fracture Mechanics,1979,12(3):211-219.
[8] M orse P M,Feshbach H.Methods of Theoretical Physics[M].Vol 1.New York:M cGraw-Hill,1958.
[9] ZHOU Zhen-gong,HAN Jie-cai,DU Shan-yi.Investigation of the scattering of harmonic elastic waves by a f inite crack using the non-local theory[J].Mechanics Research Communications,1998,25(5):519-528.
[10] ZHOU Zhen-gong,DU Shan-yi,HAN Jie-cai.Non-local theory solution for in-plane shear of through crack[J].Theoretical and Applied Fracture Mechanics,1998,30(3):185-194.
[11] ZHOU Zhen-gong,WANG Biao,DU Shan-yi.Scattering of harmonic anti-plane shear waves by a finite crack by using the non-local thoery[J].International Journal of Fracture,1998,91(1):13-22.
[12] ZHOU Zhen-gong,HAN Jie-cai,DU Shan-yi.Investigation of a crack subjected to anti-plane shear by using the non-local theory[J].International Journal of Solids and Structure,1999,36(26):3891-3901.
[13] ZHOU Zhen-gong,BAI Ya-ying,ZHANG Xian-wen.Scattering of harmonic shear waves by a finite crack by using the non-local theory[J].International Journal of Engineering Science,1999,37(5):609-620.
[14] Eringen A C.On differential of non-local elasticity and solutions of screw dislocation and surface waves[J].Journal of Applied Physics,1983,54(4):4703-4710.
[15] Srivastava K N,Palaiya R M,Karaulia D S.Interaction of shear waves with two coplanar Griff ithcracks situated in an inf initely long elastic strip[J].International Journal of Fracture,1983,23(4):3-14.
[16] Nowinski J L.On non-local aspects of the propagation of love waves[J].International Journal of Engineerin g Science,1984,22(5):383-392.
[17] Nowinski J L.On non-local theory of wave propagation in elastic plates[J].ASME Journal Applied Mechanics,1984,51(4):608-613.
[18] Gradshteyn I S,Ryzhik I M.Table of Integral Series and Products[M].New York:Academic Press,1980.
[19] Amemiya A,Taguchi T.Numerical Analysis and Fortran[M].Tokyo:Maruzen,1969.
[20] Itou S.Three dimensional waves propagation in a cracked elastic solid[J].ASME Journal of Applied Mechanics,1978,45(2):807-811.
[21] Itou S.Three dimensional problem of a running crack[J].International Journal of Engin eering Science,1979,17(2):59-71.
[22] Eringen A C.Interaction of a dislocation with a crack[J].Journal of Applied Physics,1983,54(5):6811-6817.

INVESTIGATION OF THE SCATTERING OF HARMONIC ELASTIC WAVES BY TWO COLLINEAR SYMMETRIC CRACKS USING THE NON-LOCAL THEORY

PDF

Knowledge

Abstract

Cite this article

share this article

References

Related Articles 1

Recommended Articles

Metrics

Comments