Abstract: The quite new analysis of near crack line field for a Mode Ⅲ crack in an elastic perfectly-plastic material has been given in this paper.In the plastic region near the crack line,the particular solutions of the plastic stress and displacement fields have not been nsed to match with the elastic dominant fields (i.e.the elastic K-dominant fields),but the general solutions of the plastic fields have been taken to match with the exact elastic fields at the elastic-plastic boundary.The roughly qualitative assumptions of the small scale yielding theory have not been taken in this paper.No other qualitative assumptions have been attached.The solutions of this paper are sufficiently precise near the crack line.

Key words: elastic perfectly-plastic material, Mode Ⅲ crack, near crack line fields, elastic-plastic boundary, matching condition

摘要： 本文对理想弹塑性Ⅲ型静止裂纹的裂纹线附近的应力和变形场进行了全新的分析。在裂纹线附近的塑性区内,本文不再将以前一直认为正确的塑性应力,变形场的特解与裂纹尖端弹性奇异K场匹配,而是通过求得塑性区应力、位移场在裂纹线附近的通解,使之与弹性场的精确解在裂纹线附近的弹塑性边界上匹配。本文的分析完全放弃了小范围屈服理论的所有近似假定,并且不再附加任何其它的近似假定。本文所得结果在裂纹线附近是足够精确的。

关键词: 理想弹塑性材料, Ⅲ型裂纹, 裂纹线场, 弹塑性边界, 匹配条件