双Ⅰ-型裂纹断裂动力学问题的非局部理论解

周振功; 王彪

双Ⅰ-型裂纹断裂动力学问题的非局部理论解

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(19725209);黑龙江省自然科学基金;黑龙江省博士后基金资助项目;哈尔滨工业大学科学研究基金(HIT2

详细信息

作者简介:
周振功(1963- ),河南人,男,教授,博士.

中图分类号: O345.21
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- 被引次数: 0
出版历程
- 收稿日期: 1999-12-14
- 修回日期: 2001-02-13
- 刊出日期: 2001-07-15

Investigation of the Scattering of Harmonic Elastic Waves by Two Collinear Symmetric Cracks Using the Non-Local Theory

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

摘要

摘要: 研究了非局部理论中双Ⅰ-型裂纹弹性波散射的动力学问题,并利用富里叶变换使本问题的求解转换为三重积分方程的求解,进而采用新方法和利用一维非局部积分核代替二维非局部积分核来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断裂静力学问题的结果准确和更加合理,克服了艾林根研究断裂静力学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下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 /
- 三重积分方程
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.
- the non-local theory /
- Schmidt's method /
- the triple-integral equation

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参考文献(22)

[1]	Edelen D G B.Non-local field theory[A].In:Dringen 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 Pysics[C] Vol 4.New York:Academic Press,1976,205-267.
[3]	Green A E,Rivilin R S.Multipolar continuum mechanics:functional theory Ⅰ[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 Plysics 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].Engineering Fracture Mechanics,1979,12(3):211-219.
[8]	Morse P M,Feshbach H.Methods of Theoretical Physics[M].Vol 1.New York:McGraw-Hill,1958.
[9]	ZHOU Zhen-gong,HAN Jie-cai,DU Shan-yi.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.
[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 Griffith cracks situated in an infinitely 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 Engineering 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 Engineering 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.