圆柱型功能梯度双材料界面周期裂纹问题研究  

Study on Circular Interfacial Crack Problem of Cylindrical Isotropic Functional Gradient

作　　者：赵志耀 张雪霞[1] 赵文彬[1] ZHAO Zhi-yao;ZHANG Xue-xia;ZHAO Wen-bin(School of Applied Science,Taiyuan University of Science and Technology,Taiyuan 030024,China)

机构地区：[1]太原科技大学应用科学学院

出　　处：《太原科技大学学报》2020年第1期50-54,共5页Journal of Taiyuan University of Science and Technology

基　　金：国家自然科学基金(51574171);山西省自然科学基金(201601D102003);太原科技大学研究生科技创新项目(20151037)

摘　　要：研究了反平面剪切载荷作用下圆柱型功能梯度双材料界面周期裂纹尖端场的力学问题。建立圆柱型功能梯度双材料的控制方程和弧形界面周期裂纹边界条件,将力学问题转变为偏微分方程组的边值问题。利用分离变量和待定系数的方法,设定一个具有待定系数的特殊位移函数,借助于边界条件,获得满足边界条件的偏微分方程的解。引入位错密度函数以及奇异积分方程,从而推导出应力强度因子的计算公式。The mechanics of the interface periodic crack tip field of cylindrical functionally gradient double materials under antiplane shear loading is studied. The control equation of cylindrical functionally gradient double materials and the boundary conditions of circular interfacial periodic cracks were established,and the mechanical problem was transformed into the boundary value problem of partial differential equations. The special displacement function with undetermined coefficients is set,and the solution of partial differential equations satisfying the boundary is obtained using the method of separating variables and undetermined coefficients. The density function of dislocation is introduced,the singular integral equation is derived,and the formula of stress intensity factor is obtained.

关 键 词：圆柱型 功能梯度双材料 弧形界面周期裂纹 分离变量法 应力强度因子 

分 类 号：O157.5[理学—数学]