On The Sliding Frictional Nanocontact Of A Graded Coating Bonded To A Homogeneous Substrate

The development of modern industry continuously inspires the requirements for the comprehensive mechanical properties of metal materials.It is hoped that high-performance metal materials with both high yield strength and ductility can be obtained.In recent years,experimental studies have proved that the gradient nanostructure prepared on the surface of the coarse-grained metal can significantly improve the strength,hardness and wear resistance of the metal materials with the maintaining of good plasticity and toughness.Meanwhile,this preparation can form a gradient polycrystalline structure on the surface of the coarse-grained metal,that is,the grain size is gradient distribution along the thickness direction,and continuously increases from the nanoscale to the conventional coarse-grained grain size.The coarse-grained metal with a gradient nanostructure on the surface can be modeled as a functionally graded nanocoating/substrate system composed of a functionally graded nanofilm and a homogeneous substrate.However,existing studies mainly focus on the experimental preparation and performance characterization of such coating/substrate structure,and theoretical modeling and analysis are relatively lagging behind.Based on the above background,after introducing the surface mechanical effects at the nanoscale,this paper solves the nanocontact response of the graded coating/substrate system under the indentation of surface tractions and rigid punches.Furthermore,the main research method of this paper is theoretical modeling and semi-analytical analysis.Firstly,with the framework of the Steigmann-Ogden surface elasticity model,a nonclassical surface boundary conditions is established on the upper surface of the nanostructure,in which the surface residual stress,surface tensile stiffness and surface flexural stiffness are all taken into account at the nanoscale.The shear modulus of the graded coating is assumed to vary exponentially along the thickness direction.Using the elastic field solution of the classical functionally graded layer and the homogeneous half-plane,and combining the nonclassical boundary conditions,the analytical solution of displacements and stresses of the graded coating/substrate structure due to surface loadings can be solved,where the Coulomb friction law is satisfied between the tangential and the normal traction.Then,the infinite integral is discretized by the numerical quadrature method and the numerical solution can be obtained.After that,the plane strain solution of the graded coating/substrate system under concentrated loading is determined by limit analysis.Stress and displacement distributions of graded coating/substrate system along the surface and depth directions is analyzed in detail under the two working conditions,where both uniform and concentrated surface traction are considered.The results show that the surface effects,the inhomogeneity index of the graded layer and the frictional coefficient have significant influences on the stress and displacement distributions.Secondly,based on the displacement solution and displacement continuity condition on the contact surface of the graded coating/substrate structure,an integral equation is established to solve the contact properties.Then,the convergence speed of built-in infinite integral of integral equation is improved,which can greatly enhance the numerical solution accuracy and speed of integration.Subsequently,the Gauss-Chebyshev numerical quadratures are used to discrete and collocate the integral equation and indentation force equilibrium condition for the coating/substrate contact system under the loading of flat and cylindrical indenter.The algebraic equations about contact stress and contact boundaries are obtained and the iterative algorithm is further developed to solve the equation system.On the basis of the detailed parameter analysis,the couple effects of the surface parameters and the inhomogeneity index of the graded layer on the contact mechanical properties of the graded nanostructures is mainly studied under various working conditions.Finally,by further taking the frictional effects into consideration,the sliding frictional contact between the two indenters and the graded nanocoating is solved.The influence of friction on contact properties of the structure is discussed at the nanoscale.For the built-in infinite integral of the integral term related to frictional coefficient,mathematical transformations are also carried out to improve the accuracy of numerical integration.Then,the integral equations arised by the flat indenter and the cylindrical indenter are discretized and collocated by using the Gauss-Chebyshev and Gauss-Jacobi quadratures,and the corresponding iterative algorithm is developed to calculate the contact pressure and asymmetrical contact widths.Extensive studies show that surface parameters,inhomogeneity index of the graded layer and frictional coefficient have significant effects on the contact properties.The main goal of this paper is to investigate the contact problem between the graded coating/substrate system and the surface tractions or rigid indenters.Using the method of theoretical modeling and semi-analytical analysis,we focuse on the effects of shear modulus variation of the graded layer,frictional coefficient,surface residual stress,surface tensile stiffness,and surface flexural stiffness on the mechanical properties of the nanocontact structure.From uniform surface loading to concentrated loading,from surface tractions to the indentation of flat and cylindrical indenter,from frictionless contact to sliding frictional contact,the research difficulty increases step by step.The successful solution of these nanocontact problems is of great significance for expanding the research scope of contact mechanics,and also has certain engineering guiding value for further optimizing the gradient nanocrystallization process of traditional coarse-grained metal materials with synergistic development of strength and plasticity.