被覆層－基質物体のインデンテーション法における三次元弾性理論解析

抄録

We consider an elastic contact problem for indentation test of layer-substrate body. An elastic layer assumed to be perfectly bonded to an elastic semi-infinite substrate. This problem called Boussinesq's problem which is axisymmetric mixed boundary value problem in elasticity theory. The elastic layer is smoothly indented by a flat-ended cylindrical and spherical indenter. The analytical solutions are obtained by solving an infinite system of simultaneous equations using the method of expressing a normal contact stress at the upper surface of the elastic layer as an appropriate series. Convergence can be achieved using less than 10 terms of the series. The accuracy of values of present numerical results is verified by comparing the dimensionless axial load of present results with results of some previous literatures. Additionally, this paper presents not only distribution of the dimensionless normal contact stress under cylindrical and spherical indenters but also distribution of the dimensionless normal displacement at the upper surface of the elastic layer. Numerical results are given for several combinations of the ratio of shear modulus, Poisson's ratio of elastic layer and substrate and the thickness of elastic layer. These results may establish the foundation for indentation test of layer-substrate composite and provide guideline for design of mechanical property of layered materials.