圆柱型各向同性双材料界面裂纹问题研究  

Study of the Interfacial Fracture in a Cylindrical Isotropic Bi-material

作　　者：王慧[1] 张雪霞[1] 赵文彬[1] 韩贵花 

机构地区：[1]太原科技大学应用科学学院,太原030024

出　　处：《太原科技大学学报》2017年第6期472-476,共5页Journal of Taiyuan University of Science and Technology

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

摘　　要：研究圆柱型各向同性双材料在径向应力条件下的界面裂纹尖端场的力学问题。利用弧形界面裂纹尖端的控制方程和材料边界条件,将力学问题化为偏微分方程组边值问题,建立了数学模型。运用分离变量法,设定特殊含待定系数的位移函数,借助边界条件和待定系数法,得到满足边界的偏微分方程组的解。利用应力函数与位移、应力的关系式,计算得到级数形式的圆柱型复合材料界面裂纹尖端附近的应力和位移的解析表达式。The mechanical problem of the interfacial crack tip field on cylindrical composite bi-material under the condition of radial stress is studied. By using the governing equations and material boundary conditions of the arcshaped interfacial crack tip,the mechanical problem is transformed into the boundary value problem of partial differential equations and the mathematical model is established. By using the method of variable separation,the special displacement function with undetermined coefficients is introduced. Based on the boundary conditions and undetermined coefficient method,we can get the solution of partial differential equations satisfying the boundary. The analytical expressions of stress and displacement in the series form near the crack tip of a cylindrical bi-material are obtained using the relation between the stress function and the stress and displacement.

关 键 词：圆柱型 各向同性双材料 弧形界面裂纹 分离变量法 无穷级数 

分 类 号：O157.5[理学—数学]