无限大薄板椭圆孔口裂纹前缘应力研究  

Stress of Crack Front in Elliptical Hole of Infinite Sheet

作　　者：杨剑锋[1] 张秀凤[1] 陶干强[1] 朱忠华[1] 

机构地区：[1]南华大学核资源工程学院,湖南衡阳421001

出　　处：《南华大学学报（自然科学版）》2017年第2期47-50,55,共5页Journal of University of South China：Science and Technology

基　　金：国家自然科学基金项目(51574151)

摘　　要：带裂纹含孔口构件的研究一直是断裂力学与岩石力学等学科的重要课题.基于复变函数方法,利用保角变换将无限大多连域映射为单位圆,将问题的边界条件使用柯西积分简化.由于孔口是薄板应力变化剧烈的区域,在考虑孔口应力时,应用椭圆孔口分析结果探讨裂纹应力分布.以裂纹尖端点为新的极坐标原点建立坐标系,对裂纹前缘应力场计算公式进行了推导,得到了计算裂纹前缘应力场的二级渐进公式.研究中发现,原有一级渐进公式与精确解的相对误差较大,而本文推导出的二级渐进公式与精确解的相对误差较小.The study on structure with orifice and cracks is still a significant project in the field of fracture mechanics and rock mechanics. Based on the complex variable function method,the paper maps the infinite domain to a unit circle by conformal transformation and the boundary conditions of the problem is simplified by Cauchy integral. Severe stress of sheet usually occurs in the area near orifice.In consideration of orifice stress,analysis re-sults of elliptical hole is used to investigate stress distribution of crack.A polar coordinate is set up based on the cracktip as new origin. The stress field calculation formula of crack front is deduced and its progressive formula are obtained.Calculation results show that the relative error of two-step progressive formula is smaller than exact solution.

关 键 词：复变函数 裂纹前缘应力 应力分量 孔口应力 椭圆孔口 

分 类 号：O346[理学—固体力学] O174.5[理学—力学]