带随机微缺陷椭圆孔口的应力分析

Analysis on stresses of elliptical hole with random micro-defect

利用复变函数方法,构造了保角变换函数,求解了带随机半圆形微缺陷的椭圆孔口应力场.通过分离保角变换函数,得到了微缺陷与宏观椭圆孔口应力场解析解的分离形式.研究结果表明,微缺陷主要对椭圆孔局部应力场产生影响,而对于远离微缺陷区域的应力场则影响较小.当椭圆形状固定时,微缺陷端部的应力集中系数仅与缺陷半径及微缺陷的位置有关;缺陷越小,应力集中系数越大,且此数值远大于无缺陷时椭圆孔口的应力集中系数,说明当孔边带有微缺陷时,尽管缺陷尺度远小于椭圆孔的尺度,但微缺陷对椭圆孔边缘应力集中的影响仍不容忽视.

The conformal mapping function is constructed and the stress field of an elliptical hole with a random semicircular micro-defect is solved by using the complex function method. The separation form of the analytical solution of the stress field for the small-scale defect and the circular hole can be obtained through splitting the conformal function. The results show that the micro-defect mainly affects on the local stress field around the elliptical hole,and the influence on the zone aw ay from the small-scale defect is small. When the ellipse shape is fixed,the stress concentration factor only depends on the curvature radius and the position of the defect. The smaller the defect,the greater the stress concentration factor. Moreover,the stress concentration factor of the micro-defect is much greater than that of an ellipse without micro-defects. This suggests that when there is a semicircular micro-defect on an elliptical hole edge,the influence of the micro-defect on stress concentration nearby the elliptical hole cannot be ignored even though the scale of the defect is far smaller than that of the ellipse.