2D thermo-mechanical contact simulations in a functionally graded material: A multigrid-based approach

The development and selection of coatings or coating combinations is a complex and costly task. Numerical simulations provide a great help to analyze the behavior of coatings and layer interfaces under mechanical and thermal loading through the computation of stress and strain fields. They are also used to fine tune the geometrical configuration and define optimal thermo-mechanical properties related to the applied stress to enhance wear and crack resistance. Coating design has been based mainly on discrete layer models with abruptly changing properties at interface perfectly bonded to a substrate. These assumptions result in discontinuities in stress and temperature fields at the interface between successive layers. These models are based either on integral transform (classically Fourier transform) or finite element (FE) methods. The former cannot handle 3D thermo-mechanical problems. The latter demands huge calculation times, especially when considering thin layers with very small elements. The aim of this paper is to account for materials with continuously changing properties and to obtain an improved prediction of the resistance of such graded materials. This gradation may be linked to surface treatments like nitruration, thermal treatment, … or to the deposition of coatings inducing diffuse boundaries between those dissimilar materials. The proposed model aims at providing valuable description and understanding of the behavior and resistance of such graded material. It is based on a second order finite difference (FD) formulation of the continuous thermal and elasticity equations. It can handle any kind of depth dependence of the material properties. Multigrid techniques are implemented to accelerate the convergence, reduce CPU time and thus permit the use of fine grids to accurately describe the variation in the material properties. The first step of this project consists in implementing the above-cited numerical techniques in a 2D plane strain model.