The Analysis of Crack Problems with Non-Local Elasticity

Zhao Minghao; Cheng Changjun; Liu Guoning; Shen Yapeng

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Article Navigation > Applied Mathematics and Mechanics > 1999 > 20(2): 135-143

Zhao Minghao, Cheng Changjun, Liu Guoning, Shen Yapeng. The Analysis of Crack Problems with Non-Local Elasticity[J]. Applied Mathematics and Mechanics, 1999, 20(2): 135-143.

Citation:

Zhao Minghao, Cheng Changjun, Liu Guoning, Shen Yapeng. The Analysis of Crack Problems with Non-Local Elasticity[J]. Applied Mathematics and Mechanics, 1999, 20(2): 135-143.

Citation:

Zhao Minghao, Cheng Changjun, Liu Guoning, Shen Yapeng. The Analysis of Crack Problems with Non-Local Elasticity[J]. Applied Mathematics and Mechanics, 1999, 20(2): 135-143.

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The Analysis of Crack Problems with Non-Local Elasticity

1.
Zhengzhou Research Institute of Mechanical Engineering, Zhengzhou 450052, P R China;
2.
Department of Mechanics, Shanghai University;Shanghai Institute of Applied Mathematics and Mechanics, Shanghai 200072, P R China;
3.
Xi'an Jiaotong University, Xi'an 710049, P R China

Received Date: 1997-10-06
Publish Date: 1999-02-15

Abstract

Abstract

In this paper,the displacement discontinuity fundamental solutions(DDFS)corresponding to the unit concentrated displacement discontinuity for plane problems of nonlocal elasticity are obtained.Based on the displacement discontinuity boundary integral equation(DDBIE)and boundary element method(BEM),a method of analysis of crack problems in non-local elasticity with generalized purpose is proposed.By using this method,several important problems in fracture mechanics such as edge crack are studied.The study of edge crack shows that the stress concentration factor(SCF) near the crack tip is not a constant but varies with the crack length.With this result the effect of crack length on the fracture toughness K_Ⅰc is studied.The results obtained in this paper are in accordance with the published ones.
- crack,
- boundary integral equation(BIM),
- boundary element method(BEM),
- non-local elasticity,fundamental solution,

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References(22)

References

[1]	Li Q F. A study about J_i and δ_i in three-point bend specimens with deep and shallow notches[J].Engrg Fracture Mech,1985,22(1):9～15
[2]	胡胜海,李庆芬,藩信吉.裂纹深度和形状对断裂韧度的影响[Z].见:第六届全国断裂学术会议文集[C].杭州:中国金属学会,中国力学学会,中国航空学会,中国机械工程学会,1991,262～265
[3]	Eringen A C, Edelen D G B. On nonlocal elasticity[J].Int J Engrg Sci,1992,10(3):223～248
[4]	Ilcewicz L, Narasimban M, Wilson J. An experimental verification of nonlocal fracture criterion[J].Engrg Fracture Mech,1981,14(4):801～808
[5]	Eringen A C, Spezial C G, Kim B S. Crack tip problem in nonlocal elastiity[J].J Mech Phy Solids,1977,25(5),339～355
[6]	Ramabraham B, Paraeswara Rao M. Line crack in an elastic plates subject to varying internal pressure in nonlocal elasticity [J].Indian J Pure Appl Math,1985,16(6):661～672
[7]	Eringen A C. Line crack subject to antiplane shear[J].Engrg Fracture Mech,1979,12(2):211～219
[8]	Eringen A C. On continuous distributions of dislocations in nonlocal elasticity[J].J Appl Phys,1984,56(10):2675～2680
[9]	Zhao Minghao, Liu Yuanjie, Cheng Changjun. Boundary-integral equations and the boundary-element method for three-dimensional fracture mechanics[J].Engineering Analysis with Boundary Elements,1994,13(4):333～338
[10]	Zhao Minghao, Cheng Changjun, Liu Yuanjie, et al. The analytical method of nonlocal elasticity and its application in fracture mechanics[J].Acta Mechanica Solida Sinica,1995,8(S. Issue):42～45
[11]	Sih G C. Mechanics of Fracture[M].Vol 1, Leyden, The Netherland:Noordhoff International Publishing,1973
[12]	Zhao Yishu. A strain energy criterion for mixed mode crack propagation[A].In: C Ouyang, M Sakata, C L Chow ed.Proceedings of International Conference on Fracture and Fracture Mechanics[C].Shanghai, P. R. China:Fudan University Press,1987,206～210
[13]	赵廷仕,赵诒枢,王元汉,等.复合型断裂准则的实验研究[J].华中工学院学报,1985,13(1):47～50
[14]	Shah R C. Fracture analysis[Z].ASTM STP560,1973,29
[15]	GB6394-86金属平均晶粒度测定方法,1986[S].见:中国国家标准汇编[S].70,北京:中国标准出版社,1990,716～737
[16]	Eringen A C. Interaction of a dislocation with a crack[J].J Appl Phys,1983,54(12):6811～6817
[17]	Eringen A C. Edge dislocation in nonlocal elasticity[J].Int J Engng Sci,1977,15(3):177～183
[18]	程品三.脆性断裂的非局部力学理论[J].力学学报,1992,23(3):329～338
[19]	虞吉林,郑哲敏.一种非局部弹塑性连续体模型与裂纹尖端附近的应力分布[J].力学学报,1984,16(5):485～494
[20]	王锐.非局部弹性力学中的裂纹题[J].中国科学(A辑),1989,34(10):1056～1064
[21]	高键,戴天民.用非局部弹性场研究圆盘裂纹问题[J].固体力学学报,1989,10(4):289～309
[22]	Crouch S L. Solution of plane elasticity problems by the displacement discontinuity method[J].Int J Num Meth Engng,1976,10(2):301～343