On The Adhesive Contact Properties Of Functionally Graded Nanocoating–Substrate Structures

The preparation and performance analysis of gradient nanostructured materials are the international frontier research topics.Experimental researches recently have proved that the gradient nanocrystallization of the surface region of conventional coarse-grained metal materials can significantly improve the strength,hardness,wear resistance,corrosion resistance,fatigue,contact and film-base bonding properties while retaining good plasticity and toughness.Existing researches mainly focus on the experimental preparation of gradient nanostructures on metal surface using severe plastic deformation technology and the performance characterization,and lack systematic theoretical analysis of the mechanical properties and gradient control laws of gradient nanostructures.The contact mechanics model of functionally graded nano coatingsubsrtate structures that can consider the effects of adhesion and surface force provides a unique solution for the analysis and control of the mechanical properties of gradient nanostructuresOn this basis,the adhesive contact between a rigid cylinder and a coating-substrate system comprised by a functionally graded coating and an infinite homogeneous half-plane are investigated.The contact mechanical properties of the functionally graded nano coating-subsrtate structure with the adhesive and surface effects considered simultaneously are explored to clarify the possible competition mechanism between these two effects.Starting from the Flamant solution of plane strain states with the full version of Steigmann-Ogden surface elasticity taken into account,the Green function of the nano coating-ubstrate system are formulated to construct the dispalacement boundary condition with a circular rigid indenter applied.Three widely used classical adhesive models,namely Johnson-Kendall-Roberts(JKR),Maugis-Dugdale(MD)model and Lennard-Jones potential(LJ)method are subsequently coupled with to analyze the adhesive contact propoerties of the graded nano coating-substrate structure,respectively.Finally,the control mechanism and influence of adhesive parameters,surface effects parameter,the shear modulus gradation of graded coating and other system factors on the adhesive contact behaviors are performed and discussed in detail based on extensive numerical experiments.Be constrained by the difficulty of the theoretical calculation and the complexity of the problem,the shear modulus of the functionally graded coating is assumed to vary exponentially along the thickness direction and the effects of gravity and friction are also assumed to be negligible.In order to solve the adhesive contact problems,the basic equations of elasticity theory and the mixed boundary conditions will be reduced to a system of singular integral equations which is subsequently discretized into a set of nonlinear algebraic equations with respect to the unknown mechanical properties by the use of appropriate numerical quadratures.Effective iterative algorithms of Newton type are finally developed to determine those discretized unknowns with high accuracy.The following problems are consecutively investigated:(1)Firstly,non-classical boundary conditions suitable for two-dimensional flat surfaces are derived based on the Steigmann-Ogden surface elasticity theory.The linear equations used to solve unknown variables are constructed by using the explicit expressions of displacements and stress in functionally graded materials and homogeneous half-plane combined with boundary conditions.The displacement and stress solutions of the functionally graded nano coating-substrate structure under the application of distributed surface force are determined,and then the plane strain solutions to the non-classical Flamant problem are obtained according to the limit analysis.The Green function of the upper surface of the coating-substrate system are eventually established.(2)Secondly,using the basic solution of the non-classical Flamant problem of functionally graded coating-substrate system,the displacement boundary conditions induced by the action of the circular rigid indenter on the upper surfaace of graded coating are established through the definite integration of the unknown contact pressure.Coupled with the equation of static contact load equilibrium,the the non-classical contact pressure and contact half-length are determined simultaneously for the Hertz contact problem with the surface effects considered individually.Next,the JKR adhesive effect between the circular rigid indenter and the upper surface of the graded nano coating-substrate structure is additionally considered.The total energy consists of the elastic strain energy and the adhesive energy,and the minimum potential energy principle is employed to solve the adhesive contact pressure and half-length when the surface effect and the JKR adhesive effect are considered at the same time.(3)Thirdly,the JKR model which can only consider the adhesive force within the contact area is replaced by the MD adhesive model so as to extend the adhesive force to the contact area and an annular region outside the contact zone.According to the superposition principle,the total contact pressure is decomposed into Hertz contact pressure and constant adhesive force during the solution process.A system of integral equations consisting of displacement boundary conditions,the geometric relationship of the critical distance at the boundary of the adhesive force zone and the static balance equation of the contact load are established.Finally,the solutions of contact pressure and contact half-length are achieved with the aid of numerical quadrature formula and loop iterative algorithm.(4)Finally,the LJ potential function widely used in molecular dynamics simulations is used to describe the adhesion between the circular rigid indenter and the graded nano coatingsubstrate structure.This model overcomes the shortcomings of JKR and MD adhesive models that can only describe attractive forces,it can describe attractive and repulsive forces at the same time.Since LJ potential provides a long-range description of intermolecular forces,it is obviously much more realistic.Due to the existence of repulsive force,the method of solving the mechanical properties of the LJ adhesion contact is significantly different from the previous two models.The geometric relationship of the contact distance between the indenter and the upper surface of the graded coating must be established first,which is manifested as a nonlinear implicit integral equation.Once the distance is determined,the LJ adhesive force,contact load and maximum indentation depth of the indenter can be subsequently obtained.The surface effects and effect of three typical adhesive models are considered at the same time for the solutions to the adhesive contact problems of a rigid cylinder and a functionally graded coating-substrate system in ths paper.The surface residual stress,the surface tensile stiffness and the surface bending stiffness are considered simultaneously in the context of Steigmann-Ogden surface elasticity.The control mechanisms and influence of adhesive energy density,Tabor’s parameter,surface effect intensity parameters,the shear modulus of the graded coating and other geometric and mechanical parameters on the adhesive contact properties of functionally graded coating-substrate system are extracted based on detailed parameter research and analysis.The common mechanism between the surface effects and the adhesive effect is combed,and the competitive relationship between the two effects on the contact mechanical properties are also clarified.The connection and difference between these three typical adhesive models of JKR,MD and LJ are discussed in this paper.It is found that when the Tabor’s parameter is small,the adhesive contact pressures of LJ and MD model tend to the result of Hertz contact without consideration of the adhesive effect,and this trend becomes much more obvious when the surface effects are considered.Whereas,the adhesive contact behaviors of LJ and MD models approach to the JKR adhesive model with the increasing of Tabor’s parameter.Therefore,the JKR adhesive model can be regarded as the limit case of that two models.The results and conclusions of this paper can not only provide theoretical guidance for the analysis of the mechanical properties of the gradient nanostructures of coarse-grained metal materials,but also greatly enrich the research results in the field of functionally graded materials nanocontact mechanics.