自由孔口应力集中及深切口应力奇性的有限变形分析

本文运用增量分析方法,得到了含椭圆孔及抛物线孔的无限弹性平板的有限变形应力表达式.新的应力表达式是载荷、孔口形状及材料性质的函数.特别还分析了深切口根部的应力奇性,发现它可以与线性断裂力学的应力强度因子相联系,但应力奇性改变为αln 1/√ρ,ρ为切口根部的曲率半径,α为与材料有关的常数.新的结果还解释了平面应力和平面应变问题的区别.

FINITE DEFORMATION ANALYSIS FOR STRESS CONCENTRATION AROUND A FREE NOTCH AND STRESS SINGULARITY AROUND A DEEP NOTCH

The expressions of stresses in finite deformation of an elliptic or parabolic notch in infinite elastic plane has been obtained by incremental analysis. Such expressions are functions of loads, notch shape and material behavior. The stress singularity for a deep notch has especially been discussed, and it is found that this singularity could be related with the stress intensity factor in linear fracture mechanics, but the order of this singularity has been changed from 1/√ρ to α ln 1/√ρ, ρ being the curvature radiu of the notch root, α a material constant. The new result here explains the difference between the cases of plane strain and plane stress.