Analysis Of Two- Dimensional Adhesive Contact Problem For Functionally Graded Materials Coating

Functionally graded material（FGM）is a new composite material whose parameters continuously vary along the thickness direction.Used as coatings or interfacial zones,FGM tends to reduce stress concentration resulting from material mismatch,improve the performance of the contact surface and provide protection against a bad environment as a protective layer.Recent studies indicate that gradient coatings can be used to suppress contact damage and failure.Therefore,the contact research of FGM has attracted extensive attention.With the decrease of contact area,adhesion has an important influence on the contact behavior of coatings.Therefore,the adhesive contact of gradient material coatings is discussed in this thesis.In this thesis,two types of mathematical models are established to simulate FGMs.The first one is to assume that the elastic parameter of FGMs vary as the exponential function;the second is to simulate that FGMs with a multi-layered model.In this multi-layered model,the gradient material is assumed to divide into several sub-layers and elastic parameters in each layer vary as the exponential function.By consideration of Maugis-Dugdale adhesion theory,the transfer matrix method and Fourier integral transform technique are used to transfer the two-dimensional adhesive contact problem to the singular integral equation（s）with Cauchy Kernel.The stress distribution,indentation and the adhesion zone with the different gradient parameters and adhesion parameters were obtained by making use of numerical integration method.With the models,the following problems are investigated:1)The fundamental solution of contact problem for FGM coated half-plane subjected to concentrated line is obtained by using the exponential function model and the multi-layered model which require the elastic parameter in each sub-layer varying as a exponential function.2)The fundamental solution of the adhesive contact problem is obtained by the exponential function model.It is used to solve the adhesive contact problem of the functionally gradient coating half-plane indented by a cylindrical punch.The effects of shear modulus ratio and adhesion parameter on adhesive contact behavior were obtained.3)The fundamental solution of the adhesive contact problem is obtained by the multi-layered model which require the elastic parameter in each sub-layer varying as a exponential function.The solution is used to solve the adhesive contact problem with the shear modulus of coating varying as the power function.The effects of gradient parameters of functionally graded materials whose shear modulus varies as the power function on the adhesive contact behavior were given.Through the study of two-dimensional adhesive contact problem of functionally graded coated half plane indented by a cylindrical punch,the results are obtained as follows:1)When a homogeneous material is considered by using the present model,the curve of force vs.contact radius reach that obtained from the JKR Model when λ=5;when adhesion parameter λ=1.0,the result obtained from the present model is coincided with that obtained from Hertz model.The results show that the present method is good agree with the classical theoretical method.2)Based on the Maugis-Dugdale theory,the pull-off force increases and the surface stress at the contact center decreases with the increases of the adhesion parameter.When the elastic parameters of the gradient coating vary as the exponential function,the pull-off force increases and the surface stress at the contact center decreases while the shear modulus ratio μ₁/μ₂（μ₁mis the shear modulus of the coating at the upper surfaces and μ₂ is the shear modulus at the lower surface）decreases.3)The multi-layered model which require the elastic parameter in each sub-layer varying as a exponential function can be used to solve the adhesive contact problem of FGM coating whose material parameters vary as arbitrarily function.When the elastic parameters of the gradient coating vary as the power function,the pull-off force increases with the increase of the gradient index n.The stress at the contact center increases when the shear modulus ratio μ₀/μ_h＞1（corresponding to the stronger coating）,but the result is the opposite while the shear modulus ratio μ₀/μ_h＜1（corresponding to the softer coating）.This thesis tries to explore the method to alter the adhesive contact behavior of the surface of gradient coatings by using the theoretical analysis and numerical calculation.The results provide a theoretical basis for the improvement of the adhesive contact behavior and the design of gradient materials.