| With the development of high and new technology industries,the research on the mechanical behavior of components at the micro-scale becomes more and more important.Adhesion effect,as an important phenomenon on the micro scale,is an important factor which affects contact behavior.Because functionally graded materials have the characteristic which requires the continuous changes in material properties,they are often used as coatings or interface layers to reduce stress concentration caused by material mismatch and to improve the performance of contact surfaces to resist contact damage and deformation in harsh external environments.At present,a large number of research results on the contact problems of functionally graded material coatings have been gained.However,these studies mainly focus on contact problems of graded coatings at the macroscopic scale,but the effect of adhesion on contact problems is not considered.This paper will consider the effect of adhesion on axisymmetric contact problems.Using two mathematical models to analyze the effects of adhesion parameters,material gradient parameters and coating thickness on the axisymmetric adhesive contact behavior of functionally graded materials.The main contents include:(1)A mathematical model for the axisymmetric adhesive contact of functionally graded materials coating under a spherical indenters was established.The exponential function model and the linear multi-layered model are used to simulate functionally graded materials coating.According to Maugis-Dugdale adhesion theory,Hankel integral transformation technology and transfer matrix method are used to transform the axisymmetric adhesive contact problem of functionally graded materials coating into a set of singular integral equations.(2)The Erdogan-Gupta numerical method is used to solve the controlling singular integral equations of axisymmetric adhesive contact problem.The relationship between normal load and contact radius,the relationship between normal load and maximum indentation,the surface stress distribution of the coating and the ratio of adhesion / contact region were obtained by giving different adhesion parameters,gradient parameters and coating thickness.(3)The effects of adhesion parameters,gradient parameters and coating thickness on the adhesive contact behavior of functionally graded materials coating were analyzed,and exploring ways to suppress contact deformation and damage by changing materialparameters.Based on the study of the axisymmetric adhesive contact of the functionally graded materials coating half-space under a spherical indenter,the following conclusions are obtained in this paper:(1)When the model in this paper is degraded to the case for a homogeneous material,the curve of normal load and contact radius is closer to the DMT model by choosing the smaller adhesion parameters.When adhesion parameters is larger,the curve of normal load and contact radius is closer to the JKR model.The conclusion shows that the results obtained by the present method in this paper are in good agreement with the results of classical theory.(2)When using the exponential function model to solve the axisymmetric adhesive contact problem,it can be found that the pull-off force between the indenter and the coating surface increases with the ratio of the shear modulus or the adhesion parameter decreases.For the softer coating(the ratio of the shear modulus is less than 1),the pull-off force between the indenter and the coating surface increases with the coating thickness decreases.For the harder coating(the ratio of the shear modulus is greater than 1),the trend of the corresponding pull-off force becomes more complicated.In addition,the results in this paper also show that the ratios of shear modulus,adhesion parameter,and coating thickness have important influence on the coating surface stress distribution and the contact region.Therefore,the contact behavior of the coating surface can be improved by changing the material parameters of the functionally graded materials coating.(3)Using a linear multi-layered model,this paper solves the contact problem when the shear modulus of functionally graded materials coating vary as a power-low function form.The research results show that the pull-off force increases with the gradient index increases when the ratio of shear modulus of functionally graded materials coating is greater than 1(hard coating).When the ratio of shear modulus of functionally graded materials coating is less than 1(soft coating),the pull-off force will be less affected by the gradient index.Otherwise,it can be found from the results obtained in this paper that the pressure increases and the tensile force decrease with the adhesion parameter increases to create the same indentation.The maximum compressive stress on the coating surface decreases with the adhesion parameters increases.The results in this paper presented the compressive stress on the coating surface decreases and the tensile stress increases with the adhesion parameters increase.When the coating is softer,the contact region is less affected by the gradient index.As the coating thickness increases,the compressive stress on the coatingsurface decreases and the tensile stress increases and the contact region decreases with the coating thickness increases.When the coating is harder,the gradient index has a greater effect on the contact region.Stress on the coating surface become more complex when the coating thickness changes.The contact region increases with the coating thickness increases.In this paper,the effects of adhesion parameters,gradient parameters and coating thickness on axisymmetric adhesive contact behavior are analyzed by considering the effects of adhesion effects and material non-uniformity on axisymmetric contact behavior.The results of this paper not only improve the theoretical study of the axisymmetric adhesive contact of functionally graded materials,but also provide a reference for using functionally graded materials coating to resist contact deformation and damage. |
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