采用新方法研究非局部理论中Ⅰ-型裂纹的断裂问题

周振功; 王彪

采用新方法研究非局部理论中Ⅰ-型裂纹的断裂问题

周振功,
王彪

哈尔滨工业大学复合材料研究所, 哈尔滨 150001

基金项目: 国家优秀青年研究基金资助项目(19725209)

详细信息

作者简介:
周振功(1963~ ),男,教授.

中图分类号: O345.19
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- 被引次数: 0
出版历程
- 收稿日期: 1998-07-02
- 刊出日期: 1999-10-15

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

摘要

摘要: 采用新的方法研究非局部理论中Ⅰ-型裂纹的断裂问题,进而确定裂纹尖端的应力状态,这种方法就是Schmidt方法.所得结果比艾林根研究同样问题的结果准确和更加合理,克服了艾林根研究同样问题时遇到的数学困难.与经典弹性解相比,裂纹尖端不再出现物理意义上不合理的应力奇异性,并能够解释宏观裂纹与微观裂纹的力学问题.
- 非局部理论 /
- Schmidt方法 /
- 对偶积分方程
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

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参考文献(16)

[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.