半平面双材料角界面应力奇异性分布规律的探究  

STUDY ON DISTRIBUTION OF SINGULAR INTERFACIAL STRESSES IN BIMATERIAL CORNERS OF EDGE-BONDED QUARTER-PLANES

作　　者：嵇醒[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092

出　　处：《固体力学学报》2011年第5期446-458,共13页Chinese Journal of Solid Mechanics

基　　金：国家自然科学基金项目(10672122)资助

摘　　要：论文对半平面双材料角受集中力问题的界面应力场作了深入的探究,特别着重于双材料角端点附近的界面应力的奇异性分布规律.论文通过对界面应力的严格解和渐近解[16]的比较,发现在双材料角界面端点邻近,严格解和渐近解的差是一个向端点衰减的微幅震荡分布的应力.这个向端点衰减的微幅震荡应力的起始点,称为转换点.自界面端点到转换点,严格解等于渐近解与微幅震荡衰减应力的叠加,称为渐近段.自转换点到无穷远,界面应力由严格解确定,是界面应力的基本段.在基本段内,渐近解单调变化并趋近于零,显著地偏离严格解.所以,转换点将界面应力曲线分成渐近段和基本段.文中讨论了渐近段界面剪应力奇异分布的特点,及半平面双材料角界面端点存在应力奇异性的条件.转换点的意义在于它是渐近段和基本段的过渡点.把转换点代入渐近段的渐近表达式,即可导出表征双材料角奇异性的界面剪应力强度因子与转换点的界面剪应力的关系式.这个关系式将有利于双材料角奇异性初始脱粘判据的研究和建立.The distribution of interfacial stresses in bimaterial corners of edge-bonded quarter-planes is investigated with a particular attention to the distribution of interfacial stresses in the vicinity of the interface tip of himaterial corners. It is found that,closely near the interface tip,the difference between the rigorous solution and the asymptotic solution of edge-bonded quarter-planes is an oscillation stress with tiny amplitude, and it quickly attenuates towards the tip. The starting position of the damping oscillation stress is defined as a transition point. Beyond the transition point, the asymptotic solution monotonically changes and approaches to zero, and it remarkably deviates from the rigorous solution. From the tip to the transition point, the rigorous solution just equals the sum of the asymptotic solution plus the damping oscillation stress. The segment from the tip to the transition point is called the asymptotic part. From the transition point to infinity,the asymptotic solution is no longer valid,and the interfacial stresses must be determined through the rigorous solution. The segment from the transition point to infinity is called the basic part. Therefore the curve of interfacial stress is divided into the asymptotic part and the basic part by the transition point. The transition point has a particular significance as it is the joining of the asymptotic part with the basic part. By substituting the transition point into the asymptotic expression, a relationship between the stress intensity factor in the asymptotic part and the interfacial stress at the transition point is deduced. It is believed that the the relationship between the stress intensity factor in the asymptotic part and the interfacial stress at the transition point will benefit to the development of a criterion of the interfacial initial debonding for bimaterial corners with stress singularity.

关 键 词：双材料角 应力奇异性 界面应力 应力强度因子 

分 类 号：O482.1[理学—固体物理] O343.4[理学—物理]