被覆弾性層一弾性基質体の軸対称接触問題の解析解とその応用

Abstract

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. 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.