半无限平面裂纹构型横向应力的Green函数  

Green's Function for T-Stress of a Semi-Infinite Plane Crack

作　　者：崔元庆[1] 杨卫[2] 仲政[1] 

机构地区：[1]同济大学航空航天与力学学院,上海200092 [2]浙江大学校长办公室,杭州310058

出　　处：《应用数学和力学》2011年第8期912-919,共8页Applied Mathematics and Mechanics

基　　金：国家自然科学基金资助项目(10702071;11090334);中国博士后科学基金资助项目(201003281);上海博士后科学基金资助项目(10R21415800);上海市重点学科计划资助项目(B302);中德科学中心项目"Crack Growth in Ferroelectrics Driven by Cyclic Electric Loading"资助

摘　　要：针对各向同性弹性无限大板中半无限裂纹,用解析函数方法求解了裂尖处横向应力的Green函数.加载情况为一任意集中力作用于任意一内点处.用叠加法求解了复势,它给出该平面问题的弹性解.通过渐近分析抽取复势的非奇异部分.基于该非奇异部分,用一种直接方法求解了横向应力的Green函数.进一步,用叠加法得到了一对对称和反对称集中力加载时的Green函数.然后,用得到的Green函数来预测铁电材料双悬臂梁试验中畴变引起的横向应力.用力电联合加载引起的横向应力来判断试验中所观察到的稳定和不稳定裂纹扩展行为.预测结果和试验数据基本吻合.Green＇s function for the T-stress near a crack tip was addressed by an analytic function method for a semi-infinite crack lying in an elastical,isotropic,and infinite plate.The cracked plate was loaded by single inclined concentrated force at interior point.The complex potentials were obtained by a superposition principle,which provide the solutions to the plane problems of elasticity.The regular parts of the potentials were extracted by an asymptotic analysis.Based on the regular parts,Green＇s function for the T-stress was obtained in a straightforward manner.Furthermore,Green＇s functions were derived for a pair of symmetrically and anti-symmetrically concentrated forces by the superimposing method.Then Green＇s function was used to predict the domain-switch-induced T-stress in a ferroelectric double cantilever beam（DCB） test.The T-stress induced by the electromechanical loading was used to judge the stable and unstable crack growth behaviors observed in the test.The prediction results roughly agree with the experimental data.

关 键 词：GREEN函数 横向应力 复变函数 半无限裂纹 断裂力学 

分 类 号：O174.5[理学—数学] O343[理学—基础数学]