部分裂纹面受力情形下无限大板孔边双裂纹的张开位移研究

针对航空结构中常见的孔边裂纹问题,利用Muskhelishvili复变函数法和Cauchy积分理论推导了无限大板内圆孔边任意长度双裂纹在部分裂纹面受均布应力情形下的位移表达式,并计算了孔边裂纹对称和孔边裂纹不对称两种情况下的裂纹面张开位移。孔边双裂纹对称时,计算值与权函数方法的求解结果进行了对比,最大误差为16.21%。研究表明,应用复变函数法和Cauchy积分理论推导的裂纹面张开位移表达式,不仅适用于无限大板内孔边裂纹对称的情况,孔边裂纹不对称时同样适用,从而为圆孔边任意长度双裂纹的疲劳裂纹闭合分析和张开应力求解提供了研究基础。

RESEARCH OF OPENING DISPLACEMENTS FOR TWO CRACKS EMANATING FROM A CIRCULAR HOLE IN AN INFINITE PLATE UNDER PRESSURE ON PART OF CRACK SURFACE

The purpose of this paper is to research problems of cracks at a circular hole,which is a common crack configuration in aircraft structures.The Muskhelishvili complex function method and the Cauchy integral method are combined to develop crack surface displacement equation for two cracks with arbitrary length emanating from a circular hole in an infinite plate under pressure on part of crack surface,and calculate the crack-surface opening displacements for two cracks with arbitrary length emanating from a circular hole.When two cracks are symmetric,the calculated results were compared with the weight function method,the maximal relative error is 16.21%.The results show that the complex variable function method and the Cauchy integral method used to calculate crack surface opening displacements can be applied for two-symmetric(or asymmetric) cracks emanating from a circular hole in an infinite plate.The present study provides a research foundation for fatigue crack closure and crack opening stress analysis for double cracks with arbitrary length emanating from a circular hole.