截面含切口圆柱体自由扭转的弹塑性分析

Elastic-plastic torque analysis of notched cross-section cylinder

对于截面含切口圆柱体的弹塑性自由扭转问题的分析,可按受力特点分为三个阶段:全弹性阶段、全塑性阶段和弹塑性阶段。每一阶段对应的分析方法不同,其中,在全弹性阶段可以采用有限差分法分析;在全塑性阶段可以按沙堆比拟的方法采用等倾曲面模拟;弹塑性阶段可以结合上述两种方法的结果和思路进行分析。利用差分法可以求出自由扭转截面内各离散点应力函数的数值解。本文推导了自由扭转的应力函数与J积分之间的关系,得出了自由扭转的应力函数与III型裂纹的J积分之间的关系式。数值计算结果验证了本文方法的有效性和精确性。

The research of elastic-plastic torque analysis of notched cross-section cylinder can be divided into three steps： elastic stage, plastic stage and elastic-plastic stage. Each stage will employ different analysis method, such as the finite difference method for the elastic stage, and the sand heap analogy method for the plastic stage. As to the elastic-plastic stage, the ideas and results of both above approaches will be utilized. Using difference method, numerical solutions of stress function Ф of the discrete points can be obtained. In this paper, the relationship between the stress function Ф and J-integral of the notch is studied. The J-integral of the III type crack can be calculated effectively, and be proved right by the numerical analysis.