An analytical solution of contact problem of indentation for multi-layered material

Abstract

We considered the axisymmetric contact problem of multi-elastic layer with different elastic constants bonded on elastic semi-infinite substrate indented by a rigid flat-ended cylindrical indenter. In this study, the information of each elastic layers can be sorted by using transfer matrix method and dual integral equations were reduced to an infinite system of simultaneous equations by expressing a normal contact stress at the surface elastic layer as an appropriate series. Numerical results were obtained to demonstrate the effects of the elastic constants of each elastic layers and semi-infinite elastic substrate on the radial distribution of normal contact stress and normal displacement of free surface of elastic layer, stress singularity factor at the edge of cylindrical indenter, and applied load of rigid indenter which needed to penetrate to a constant depth into multi-layered materials. The present results of applied load were good agreement with the results of the previous other studies. Numerical results were given for several combinations of the shear modulus of each elastic layers and substrate, and Poisson's ratio of both each elastic layers and substrate was fixed as 0.3 throughout present study. These results give us great contribution to the establishment of the indentation tests on composite materials as well as the guideline for design of appropriate mechanical properties of layered materials.