理想弹塑性I型平面应力裂纹线场的精确解  

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

作　　者：易志坚[1] 王士杰[1] 

机构地区：[1]重庆交通学院桥梁系

出　　处：《应用数学和力学》1996年第4期335-342,共8页Applied Mathematics and Mechanics

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σｙ，σｘｙ，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σｘ存在差别．The near crack line analysis method has been used in the present paper. Theclassical small scale yielding condit ions have been completely abandoned in theanalyses and one inappropriate matching condition used to be used at the elasticplastic boundary has been corrected.The reasonable solution of the plasticstresses near the crack line region has been established. By matching the plasticstresses with the exact elastic stresses at the elastic-plastic boundary, the plasticstresses,the length of the plastic zone and the unit normal v.ector of the elasticplastic boundary near the crack line region have been obtained for a mode I crackunder uniaxial tension,as well as a mode I crack under biaxial tension,which shows that for both conditions the plast ic stress components ay and a.y.the length of the plastic zone and the unit normal vector of the elastic-plasticboundary are quite the same while the plast ic stress a. is different.

关 键 词：I型 平面应力裂纹 线场 弹塑性 精确解 

分 类 号：O346.1[理学—固体力学]