三维弹塑性缺口问题的应变等效法

通过对三维应力约束下含中心圆孔的双向拉伸板进行弹塑性理论分析,提出线弹性等效应变解与弹塑性等效应变解之间存在的内在关系,弹塑性等效应变解可以由线弹性解通过简单的变理代换得到。利用二维和三维弹塑性有限元分析证实,在一般制品几何情况下,本文提出的应变等效法比著名的Neuber法和等效应变能密度法具有更高的精度和适应能力,并且可经给出弹塑性全场解,对不同缺口形状,不同材料,不同载荷情况具有通用性,可以作为有限元法的补充,为结构的细节设计和寿命分析提供了高效的工程方法。

A Equivalent Strain Method for Three-Dimensional Elastic-Plastic Notch Problems

A theoretical study is carried out for a typical notch problem, a plate having a circular hole under biaxial tension and triaxial stress constraint in strain hardening materials, in order to reveal the natural characters of the notch fields. A very simple relationship is found between the whole elastic and the whole elastic-plastic fields:the elastoplastic equivalent strain ahead of the notch can be obtained from the corresponding elastic solution just by a simple variable replacement. With this relationship, a strain equivalent rule is proposed. Two- and three-dimensional finite element analyses are conducted to validate the proposed rule and good agreements are achieved for general notch problems. Validation against theoretical and numerical results also shows that the method is more accurate and stable than Neuber's rule and the equivalent strain energy density assumption.