弹塑性Ⅰ型裂纹端三维应力应变场的结构分析

ANALYSIS OF THE STRESS AND STRAIN STRUCTURES FOR MODE I 3-D CRACK IN ELASTIC-PLASTIC STATE

本文从分析弹塑性力学的基本方程人手,探讨了幂硬化材料I型裂纹端三维应力应变场的结构,结果表明,按其应力特征,裂纹端沿厚度方向可划分为三个区域:ZⅠ,ZⅡ和ZⅢ,在区域ZⅠ,垂直于Z轴(厚度方向)的平面内应力分量可首先用平面应变条件下的基本方程求解,在区域ZⅢ,这些分量可首先用平面应力条件下的基本方程求解.本文定义区域ZⅡ为弹塑性Ⅰ型裂纹的过渡层,指出,过渡层是弹塑性Ⅰ型裂纹三维应力应变场的特性所在.对揭示其本质有特殊重要的意义.本文选择裂纹端张开位移(CTOD)作为描述局部解幅值系数的参数,并探讨了三维变形状态下,CTOD的分布规律.

In this paper, the stress and strain structures of Mode Ⅰ 3-D crack in power hardening material are studied by means of analysing the fundamental equations of elastic-plastic mechanics. It is shown that three regions, ZⅠ, ZⅡ and ZⅢ can be divided in the thickness direction according to the stress characteristic. In region ZⅠ, the stress components in the plane perpendicular to z axis (thickness direction) can first be solved by using the fundamental equations in plane strain state; in region ZⅢ, they can first by solved by using the equations in plane stress state. The region ZⅡ is defined as a transition layer is a characteristic of Mode Ⅰ 3-D crack in elastic-plastic state, and it is significant to the research on 3-D fracture. The crack tip opening displacement CTOD is chosen to describe the amplitude coefficient of local stress field, and the distribution of CTOD in 3-D state is investigated.