有限宽中心裂纹板在裂纹面受一对偏心反平面集中力的弹塑性分析

ELASTIC-PLASTIC ANALYSIS OF A FINITE PLATE WITH CENTRAL CRACK LOADED BY A PAIR OF ECCENTRIC FORCES

有限宽裂纹板的弹塑性分析是弹塑性断裂力学中最困难的问题之一。本文对有限宽裂纹板在裂纹面任意点受一对反平面集中力的情形采用裂纹线场分析方法，将各场量在裂纹线附近展开，利用平衡方程和屈服准则进行弹塑性分析，这种分析不需要作小范围屈服的假定。通过裂纹线上的弹塑性应力场在弹塑性边界上进行匹配得出荷载与裂纹线上塑性区长度之间的关系，进而分析得出荷载的不同位置和板宽所对应的临界荷载。

The elastic-plastic analysis for a cracked plate with finite dimensions is one of the most difficult problems in fracture mechanics. In this paper, the improved near crack line field analysis method is used to analyze a centrally cracked plate with finite dimensions loaded by a pair of antiplane eccentric point forces in an elastic-perfectly plastic material. The assumptions of the small scale yielding theory are abandoned and no other assumptions are made. By matching the general solutions of the plastic fields with the reasonable elastic fields at the elastic-plastic boundary, analytical solutions of the near crack line elastic-plastic fields and the the of the plastic zone which are sufficiently precise near the crack line are obtained. The critical load for different positions of the point forces on the crack surface and for different widths of the cracked plate is evaluated.