圆柱型功能梯度双材料界面裂纹问题研究

Study of Interfacial Fracture in a Cylindrical Functionally-graded Bi-material

研究圆柱型功能梯度双材料在轴向剪切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,将力学问题转换成偏微分方程组的边值问题,建立数学模型。运用分离变量法,设定特殊包含待定系数的位移函数,借助边界条件和待定系数法,推导出奇异积分方程,从而得到满足边界的偏微分方程组的解。利用位移函数与应力、应变关系式,计算得到级数形式的圆柱型双材料界面裂纹尖端附近的应力以及位移的表达式。

The mechanical problem of the interfacial crack tip field on cylindrical functionally graded bi-material under the condition of axial shear force was studied. By using the governing equations and material boundary conditions of the arc-shaped interfacial crack tip,the paper changed the mechanical problem into the boundary value problem of partial differential equations and the mathematical model was established. By using the method of variable separation,the paper introduced the special displacement function with undeter mined coefficients. Based on the boundary conditions and undeter mined coefficient method,the singular integral equations were obtained,thereby,the solution of partial differential equations satisfying the boundary was got. The expressions of stress and displacement in the series form near the crack tip of a cylindrical bi-material were obtained using the relation between the stress function and the stress and displacement.