Ⅱ型平面应力裂纹线场的弹塑性精确解

The Exact Solutions of Elastic-Plastic Crack Line Field for Mode Ⅱ Plane Stress Crack

本文采用线场分析方法对理想弹塑性Ⅱ型平面应力裂纹裂纹线附近的应力场及弹塑性边界进行了精确分析。本文完全放弃了小范围屈服条件，探讨了弹塑性边界上弹塑性应力场匹配条件的正确提法，通过将裂纹线附近塑性区应力场的通解（而不是过去采用的特解）与弹性应力场的精确解（而不是通常的裂尖应力强度因子Ｋ场）在裂纹线附近的弹塑性边界上匹配，本文得出了塑性区应力场，塑性区长度及弹塑性边界的单位法向量在裂纹线附近的足够精确的表达式．

The near crack line field analysis method has been used to investigate into the exact elastic-plastic solutions of a mode Ⅱcrack under plane stress condition in an elastic- perfectly plastic solid. The assumptions of the usual small scale yielding theory have been completely abandoned and the correct formula-tions of matching conditions at the elastic- plastic boundary have been given. By matching the general solution of the plastic stress field (but not the special solution used to be adopte)with the exact elastic stress field (but not the crack tip K-dotninant field) at the elastic-plastic boundary near the crack line,the plastic stresses,the length of the plastic zone and the unit normal vector of the elastic-plastic boundary,which are sufficiently precise near the crack line region, have been given.