理想弹塑性I型平面应力裂纹线场的精确解

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

重庆交通学院桥梁系重庆 630074

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出版历程
- 收稿日期: 1995-05-25
- 修回日期: 1995-12-11
- 刊出日期: 1996-04-15

Exact Solutions of Near Crack Line Fields for Mode I Crack under Plane Stress Condition in an Elastic Perfectly Plastic Solid

Bridge and Structure Engineering Department, ChongqingJiaotong University, Chongqing 630074, P. R. China

摘要

摘要: 本文纠正了过去在裂纹弹塑性场匹配上存在的问题,采用线场分析方法,通过求得塑性区应力场的合理解答,使之与弹性精确场在裂纹线附近的弹塑性边界上匹配。本文就远场受单向拉伸及双向拉伸的理想弹塑性平面应力裂纹无限板,在完全放弃了小范围屈服条件的情况下求得了塑性区应力场、塑性区长度以及弹塑性边界的单位法向量在裂纹线附近足够精确的表达式。结果表明,无论单向拉伸和双向拉伸,塑性区应力分量σ_y,σ_xy,塑性区长度以及弹塑性边界的单位法向量在裂纹线附近的表达式完全相同,但塑性区沿X方向的正应力σ_x存在差别。
- I型平面应力裂纹 /
- 线场 /
- 塑性区 /
- 匹配条件
Abstract: The near crack line analysis method has been used in the present paper,The classical small scale yielding conditions have been completely abandoned in the analyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plastic stresses near the crack line region has been established.By matching the plastic stresses with the exact elastic stresses at the elastic-plastic boundary,the plastic stresses the length of the plastic zone and the unit normal vector of the elastic-plastic boundary near the crock line region have been obtained for a mode I crack under uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plastic stress componentsσ_y,and σ_xy.he length of the plastic zone and the unit normal vector of the elastic-plastic boundary are quite the same while the plastic stress σ_x is different.
- mode I plane stress crack /
- crack line field /
- plastic zone /
- elastic zone

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参考文献(6)

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[3]	Yi Zhijian,The most recent solutions of near crack line fields for mode Ⅲ cracks,Engineering Fracture Mechanics,47( 1994),147-155.
[4]	易志坚,理想弹塑性111型扩展裂纹的全新和精确分析,应用数学和力学,14(4)(1993),327-333.
[5]	易志坚、王士杰、王向坚,B型平面应力裂纹线场的弹塑性精确解,应用数学和力学,.16(10)(1995),909-916
[6]	J.A.Hult and F.A.McClintock,Elastic-plastic stress and strain distribution around sharp notches under repeated shear,Proc.9th Int.Congr.Appl.Mech.,8(1957),51-58.