Analysis of graded coatings for resistance to contact deformation and damage based on a new multi-layer model

• A new multi-layer model is built to simulate the FGMs.
• The contact pressure and the relation of force–indentation are calculated.
• The variation of Poisson׳s ratio has no significant effect on the contact pressure.
• The contact pressure can be altered by adjusting the gradient index.

The contact-damage resistance of functionally graded materials coating is considered in this paper. We build a new multi-layer computational model to simulate the functionally graded materials with arbitrary spatial variation of material properties with no limit to Poisson׳s ratio. In this model, the graded coating is divided into several sub-layers with the elastic modulus varying as exponential function and Poisson׳s ratio is a constant, according to a curve can be approached by a series of continuous but piecewise exponential function. The axisymmetric contact problem is formulated in terms of a singular integral equation by using the transfer matrix and the Hankel integral transform technique. It is assumed that the shear modulus of graded coating varies as the power law forms along the thickness and that the graded coating is indented by a rigid spherical indenter. The effect of the variation of Poisson׳s ratio, the gradient index and the value of Poisson׳s ratio on the contact stress, contact radius and penetration depth are calculated by solving an equation numerically.