有限厚双边U型切口板的三维弹塑性有限元分析  

Three dimensional elasto-plastic stress and strain fields near notch root of deep double edges U notched plate with finite thickness

作　　者：李振环[1] 王乘[1] 徐学军[1] 郭万林[2,3] 

机构地区：[1]华中科技大学力学系工程计算与仿真研究所 [2]西安交通大学机械结构强度与振动国家重点实验室 [3]南京航空航天大学飞机系,南京210016

出　　处：《计算力学学报》2002年第3期324-331,共8页Chinese Journal of Computational Mechanics

基　　金：国家自然科学基金 ( 10 10 2 0 0 6 )资助

摘　　要：针对单向拉伸载荷作用下的有限厚双边 U型切口板 ,本文对其切口根部的三维效应进行了详细的三维弹塑性大变形有限元分析 ,得到了不同于平面切口问题的新结果 :( 1 )在线弹性阶段 ,三维切口根部的应力集中因子 Kt高于二维情形 ,且 Kt在板厚 ( B)约为 8倍切口根部半径 (ρ)时达到峰值 ;进入塑性后 ,切口根部的 Kt随载荷水平的增加逐渐下降 ,并介于平面应力和平面应变情形之间 ;( 2 )切口前缘等效应变εe的最大值出现在约束最高的中面 ,且可比约束最低的自由表面处的应变值高一倍 ;( 3)薄板中 ,塑性区尺寸 xp 的最大值不是出现在约束较低的自由表面 ,而是出现在约束较高的中面 ,但随 B/ρ的增大逐渐向自由表面外推 ;( 4 )面内应力比 Tx在切口根部塑性区内的分布对板厚和载荷水平不敏感 ,可以用 Hill的滑移线解很好地近似。另外 ,对三维影响区内一些重要的三维约束参量进行了详细分析 ,总结了它们的三维分布规律。Based on three dimensional (3D) elasto-plastic finite element analyses, various aspects of 3D characters ahead of the notch root in the deep double edges U notched plates are been investigated. By comparison with the planar notch root fields, the characters of the 3D elasto-plastic stress strain fields near the notch front are revealed: (1) the thickness of the plate has the strong effects on the stress concentration factor Kt (SCF). In the elastic phase, the SCF is higher in finite thickness specimen than that in the plane stress and plane strain cases, and reaches its peak when the ratio of plate thickness to the notch root curvature radius B/ρ equals to 4 or so. However, in plastic phase, the SCF in finite thickness specimen falls into between two extreme plane stress and strain cases with the plastic deformation increasing. (2) Due to combined actions of the stress triaxiality and the opening stress, the distribution of the effective strain is different from usual intuition. The effective strainon the mid-plane, where the triaxial constraint is highest, is as twice high as the effective strain on the free surface, where the constraint is lowest. (3) In thinner plates, the plastic zone size x p/ρ reaches its peak on the mid-plane, but the peak of plastic zone size x p/ρ removes toward the free surface with the plate thickness B/ρ increasing. (4) The distributions of in-plane constraint T x on different layers of the finite thickness specimens are insensitive to the specimen thickness and load levels within the plastic zone, and can be well approximated by Hills Slipline solution. Added to these, the regularities of distribution of some important 3D-constraint parameters within the 3D-effect zone are also given out.

关 键 词：U型切口 有限厚板 弹塑性 三维效应 有限元 

分 类 号：O346.1[理学—固体力学]