General Forms of Elastic-Plastic Matching Equations for Mode-Ⅲ Cracks Near the Crack Line

YI Zhi-jian; ZHAO Chao-hua; YANG Qing-guo; PENG Kai; HUANG Zong-ming

doi:10.3879/j.issn.1000-0887.2009.05.002

Volume 30 Issue 5

Turn off MathJax

Article Contents

Article Navigation > Applied Mathematics and Mechanics > 2009 > 30(5): 515-524

YI Zhi-jian, ZHAO Chao-hua, YANG Qing-guo, PENG Kai, HUANG Zong-ming. General Forms of Elastic-Plastic Matching Equations for Mode-Ⅲ Cracks Near the Crack Line[J]. Applied Mathematics and Mechanics, 2009, 30(5): 515-524. doi: 10.3879/j.issn.1000-0887.2009.05.002

Citation:

PDF( 411 KB)

General Forms of Elastic-Plastic Matching Equations for Mode-Ⅲ Cracks Near the Crack Line

doi: 10.3879/j.issn.1000-0887.2009.05.002

1.
School of Civil Engineering, Chongqing University, Chongqing 400044, P. R. China;

Received Date: 2009-02-23
Rev Recd Date: 2009-04-01
Publish Date: 2009-05-15

Abstract

Abstract

To address mode-Ⅲ crack problems under elastic-perfectly plastic condition, the matching procedures of the crack line analysis method was summarized and refined to give the general forms and formulation steps of plastic field, elastic-plastic boundary and elastic-plastic matching equations near the crack line. The work unified the different-condition mode-Ⅲ crack problems as determining 4 integral constants through 4 matching equations. An example was demonstrated to verify the correctness, conciseness and generality of the procedure.
- mode-Ⅲ crack,
- elastic-perfectly plastic material,
- crack line analysis method,
- crack line,
- plastic zone

FullText(HTML)

References(23)

References

[1]	YI Zhi-jian. The most recent solutions of near crack line fields for mode Ⅲ cracks[J].Engineering Fracture Mechanics,1994,47(1):147-155. doi: 10.1016/0013-7944(94)90245-3
[2]	易志坚,王士杰,王向坚.Ⅱ型平面应力裂纹线场的弹塑性精确解[J]. 应用数学和力学,1995, 16(10):909-916.
[3]	YI Zhi-jian, WANG Xiang-jian, WANG Shi-jie. Elastic-plastic crack line fields for a growing crack in a center cracked plate with finite dimensions[J].International Journal of Fracture,1995,73(2):R27-R31.
[4]	易志坚,王士杰.理想弹塑性Ⅰ型平面应力裂纹线场的精确解[J].应用数学和力学,1996, 17(4):335-342.
[5]	YI Zhi-jian, WANG Shi-jie, WU Heng-li. Precise elastic-plastic analysis of crack line field for mode Ⅱ plane strain crack[J].International Journal of Fracture,1996,80(4):353-363. doi: 10.1007/BF00018512
[6]	YI Zhi-jian, WANG Shi-jie, WANG Xiang-jian. Precise solutions of elastic-plastic crack line fields for cracked plate loaded by anti-plane point forces[J].Engineering Fracture Mechanics,1997,57(1):75-83. doi: 10.1016/S0013-7944(97)00003-9
[7]	易志坚,严波.Ⅰ型平面应力裂纹弹塑性场在裂纹线附近匹配方程的一般形式[J]. 应用数学和力学, 2001,22(10):1058-1066.
[8]	王成,吴承平. 偏心裂纹板在裂纹面受两对反平面点力的弹塑性解析解[J]. 应用数学和力学,2003, 24(7):691-698.
[9]	王成,张录坤. 有限宽板裂纹在裂纹面受两对反平面集中力时裂纹线场的弹塑性分析[J].应用数学和力学,1998,19(6):513-520.
[10]	张培源,张晓敏,严波，等.裂尖曲率对裂纹前缘塑性区的影响[J]. 应用力学学报, 2004,21(4):93-96.
[11]	WANG Jian-hua, ZHOU Xiao-ping. Near crack line elastic-plastic analysis for a infinite plate loaded by two pairs of point tensile forces[J].Mechanics Research Communication,2004,31(4):415-420. doi: 10.1016/j.mechrescom.2003.10.006
[12]	周小平,张永兴,朱可善.偏心裂纹板在裂纹面受一对集中拉应力作用时弹塑性解析解[J].固体力学学报, 2005,26(3):267-272.
[13]	王成,易志坚.断续节理在Ⅱ型受载下的弹塑性分析[J].岩石力学与工程学报,1998,17(2):153-158.
[14]	王成, 邓安福.岩体节理内压致裂解析研究[J].岩石力学与工程学报, 2002, 21(5):640-643.
[15]	王成. 层状岩体边坡锚固的断裂力学原理[J].岩石力学与工程学报, 2005, 24(11):1900-1904.
[16]	WANG Qi-zhi. The crack-line (plane) stress field method for estimating SIFs—a review[J].Engineering Fracture Mechanics,1996,55（4）:593-603. doi: 10.1016/S0013-7944(96)00032-X
[17]	WANG Qi-zhi. Simple formulae for the stress concentration factor for two- and three-dimensional holes in finite domains[J].Journal of Strain Analysis, 2002,37(3):259-264. doi: 10.1243/0309324021515014
[18]	YI Zhi-jian. The new and analytical solution for model III crack in an elastic-perfectly plastic material[J].Engineering Fracture Mechanics, 1992,42(5):833-840. doi: 10.1016/0013-7944(92)90064-L
[19]	WANG Qi-zhi. The crack-line stress field method for analysing SIFs of strips illustrated with an eccentrically cracked tension strip[J].International Journal of Fracture,1993,59(2):R39-R43.
[20]	Chen D L, Weiss B, Stickler R. A new approach for the determination of stress intensity factors for finite width plate[J].Engineering Fracture Mechanics,1994, 48(4):561-571. doi: 10.1016/0013-7944(94)90212-7
[21]	Hult J A., McClintock F A. Elastic-plastic stress and strain distribution around sharp notches under repeated shear[A].In：Proceedings of the 9th International Congress on Applied Mechanics[C]. Vol 8.University of Brussels, 1957, 51-58.
[22]	Hutchinson J W.A Course on Nonlinear Fracture Mechanics[M].University of Denmark, 1979.
[23]	Achenbach J D, Li Z L. Plane stress crack line fields for crack growth in an elastic-perfectly plastic material[J].Engineering Fracture Mechanics,1984,20(3):534-544.