Analysis of contact between transversely isotropic coated surfaces: development of stress and displacement relationships using FEM

The problem of an elastic cylinder in normal contact between transversely isotropic layered substrate surfaces is investigated using the finite element method (FEM). A two-dimensional finite element model is developed which accurately determines the normal stress, contact length, and approach distance of layered surfaces. Numerical results, which are initially verified using Hertzian theory, are obtained at 756 distinct conditions by varying coating material, coating thickness, normal load, cylinder radius, and cylinder material. The numerical results are normalized with respect to Hertzian contact theory and a dimensionless anisotropic coating material parameter, ζ, is introduced. Numerical expressions for the normalized maximum normal stress, contact length, and approach distance are subsequently determined by curve-fitting the results of the 756 simulations performed. The relevance of such expressions are ascertained and discussed by comparing predicted results to isotropic layer theory presented by Gupta and Walowit P.K. Gupta, J.A. Walowit. Contact stresses between an elastic cylinder and a layered elastic solid, ASME J. Lubrication Technol., Vol. 94 (1974) pp. 250–274.]