The Contact Problem Of Graded Material Interlayer Under A Rigid Cylindrical Indenter

This paper investigated the three-dimensional frictionless ax-symmetriccontact problem of a functionally graded material. Firstly, constructing amathematical model to simulate the structure consisting of a surface coating, afunctionally graded layer and a substrate; Secondly, by using integral transformtechnique, the contact problem was converted to a singular integral equation.The surface displacement field for three layer structure was gained by solvingthe equation; Finally, the normal contact pressure field on the homogeneoussurface and the longitudinal stress distribution at interface under a rigidcylindrical flat indenter were obtained by using the numerical methods. In thispaper, the homogeneous coating and substrate had different mechanicalproperties, which shear modulus have been given. Meanwhile, the FGMinterlayer was inhomogeneous with its elastic shear modulus changingexponentially along the thickness direction. In addition, the thickness of thecoating and interlayer were given quantities, and Poisson’s ratio was constant.This paper discussed the influence of the shear modulus ratio on the surfacenormal contact pressure distribution and the longitudinal stress distribution atinterface. The effect of the thickness and the Poisson’s ratio on the distributionsof the surface normal contact stress was also considered. The results showedthat:(1)The shear modulus ratio played a significant role in the distribution ofthe normal contact pressure. With the increment of the shear modulus ratio, inthe center of the contact region, the normal contact pressure showed adecreasing trend, while showing an increasing trend at the edge of the contactregion. At the same time, the larger contact radius, the more obvious thetendency was. Under the same conditions, the smaller shear modulus ratio couldeffectively reduce the normal contact stress around the boundary of contactregion, which was significant to inhibit the contact deformation and damage.(2)The shear modulus ratio had an important effect on the distribution of normal stress and the shear stress at interface. With the shear modulus ratioincreased, the interfacial normal stress and the shear stress decreased. However,the contact radius changed the margin of the tendency. By applying a biggershear modulus, which could effectively reduce the maximum of the interfacialnormal stress when passed through the center of the contact region. That is tosay, the study played a non-negligible role in guiding the actual application.(3)The thickness played a significant role in the distribution of surfacenormal contact stress. While the thickness increased, the surface normal contactstress decreased. Meantime, the thicker the coating was, the milder the influenceto the surface normal contact stress. In contrast, the thinner homogeneouscoating had a greater influence to the distribution of the surface normal contactstress. In addition, the Poisson’s ratio almost had no effect on the distribution ofthe surface normal contact stress. Through with the Poisson’s ratio increased,the surface normal contact stress decreased microscopically.Through the study in this paper, it was significant to explore the method tosuppress the contact deformation and contact damage. In addition, it had aguiding significance to achieve material optimized design requirements.