关键词: 椭圆孔口, 微裂纹, 尺度分离, 复变函数, 保角变换

Abstract: Abstract： In view of the problem of analysis of stress field near an elliptical hole with a random microcrack, which existed widely in practical projects, a theoretical model was proposed in this paper. According to local conformal properties of microcrack in smallscale, the approximate composite conformal mapping function was established. By splitting the microcrack and macrohole, different scale stress fields were obtained, which extended the application range of the complex function method. The research results show that the stress fields and stress intensity factor (SIF) near the microcrack can be obtained by constructing and scale separating composite conformal mapping function. On the condition that the infinite plane containing an ellipse hole with a random microcrack is under vertical uniform load, the bigger the ratio of long axis and short axis of ellipse hole is, the faster the KI is decreased around the edge of ellipse, and the greater the maximum is. When the ratio is sufficiently small, the microcrack position does not affect stress intensity factor of the microcrack.

Key words: Key words： elliptical hole, microcrack, scale separation, complex function, conformal mapping