刘铁军^*

（  内蒙古工业大学理学院力学系；  ）

摘要： 本文将建立均匀材料涂层-功能梯度材料界面层-均匀材料基底的理论计算模型，研究三层结构上表面作用球形压头时的接触问题。假设涂层与基底为拥有不同弹性参数的均匀材料，通过弹性参数沿厚度方向按照指数函数形式变化的功能梯度材料界面层连接在一起。从弹性力学的轴对称问题基本方程出发，利用Hankel积分变换，得到三层结构模型接触问题的基本解。利用数值方法，得到涂层与界面层粘接处的应力分布。
关键词： 固体力学；功能梯度材料；界面应力；奇异积分方程

LIU Tiejun^*

（  Department of mechanics, school of science of Inner Mongolia University of Techonology；  ）

Abstract： In this paper, the computational model for coating-graded layer-substrate structure is constructed. By using the model, the contact problem of three layer structure subjected to a rigid spherical punch on its surface is considered. It is assumed that a graded interfacial layer with the shear modulus varying as exponential function along the thickness direction bonded the surface coating and substrate which are homogeneous materials with the different shear modulus coating. Based on the equilibrium equations for the axisymmetric problem, the fundamental solution for the three layer structure is obtained by using the Hankel integral transform technology. The stress components in the interface between the coating and graded layer are calculated by solving the equation numerically.

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