Two-Dimensional Contact Mechanics And Fretting Analysis Of Functionally Graded Materials

Functionally graded materials (FGMs) possess properties that vary gradually with location within the material. Used as coatings and interfacial zones they tend to reduce stress concentration resulting from material property mismatch, increase the bonding strength, improve the surface properties and provide protection against adverse thermal and chemical environment. Thus the concept provides the materials scientists and engineers with an important tool to design new materials for some special applications, for example, in aerospace, automobile, biomedicine, nuclear energy, gas turbine engine and many other fields. Recent researches indicate that FGM used as coatings can improve the resistance to contact deformation and damage that cannot be realized in conventional homogeneous materials. Therefore, the contact mechanics of FGM becomes a significant research topic. In the present work, the linear multi-layered model is used to simulate the FGM with arbitrarily varying material properties. The model is based on the fact that an arbitrary curve can be approached by a series of continuous but piecewise linear curves, the FGM is divided into several sub-layers and in each sub-layers the shear modulus is assumed to be linear function and is continuous at the sub-interfaces. With the model, the following problems are investigated:(1) Stress and displacement fields of a functionally graded coated half-plane subjected to normal and tangential concentrated line loads acting at the coating surface are obtained. For the problem under plane strain deformation, Young's modulus or shear modulus of the FGM may vary arbitrarily while Poisson's ratio is taken to be a constant; whereas for the problem under plane stress deformation, both Young's modulus and Poisson's ratio may vary arbitrarily along the thickness direction of the FGM coating.(2) With the above solution as the fundamental solution, the frictionless contact and sliding frictional contact of rigid punches with various shapes on a functionally graded coated half-plane are solved.(3) Fretting contact between a rigid cylindrical punch and a functionally graded coated half-plane is analyzed.(4) Fretting contact of two FGM coated elastic bodies is analyzed.By using the transfer matrix method and Fourier integral transform technique, the mixed boundary value problems mentioned above are reduced to a Cauchy singular integral equation or a set of such singular integral equations that can be numerically calculated to obtained the solutions of contact problems. In the present work, the material properties are first assumed to vary in an exponential form. The results are compared with these obtained by other methods. Then the FGM with other functional forms of material properties is considered. The results show:(1) The present model allows for arbitrary variation of the material properties. The model is very efficient in solving the contact problem of the FGM. Generally 4-6 sub-layers can yield sufficiently accurate results.(2) Dependence of force-indentation relations on the Yang's modulus or shear modulus gradients indicates that we can measure the gradient of the coating using the indentation-testing method.(3) Variation of Poisson's ratio has little effect on the distribution of contact stress and may be negligible.(4) Variation of friction coefficient has almost no effect on normal contact stresses and force-contact region relation, but rather significant effect on in-plane stresses. As friction coefficient increases, the maximum tensile stress increases sharply at the trailing end of the contact region.(5) The distribution of the surface contact stresses can be altered by adjusting the gradient of the coating. In particular, reducing the Yang's modulus or shear modulus of the coating surface can lead to decreasing of the maximum in-plane tensile stress at the edges of the contact region, and thus suppress the surface cracking and enhance the contact damage resistance under sliding and fretting conditions.(6) During fretting contact between two elastic bodies, the FGM should be coated on the harder one in order to lower the fretting contact stresses and resist the fretting contact damage.(7) In comparison with a homogeneous coating, an FGM coating has a slight effect on surface contact stresses, interfacial normal and tangential stresses; whereas it is significant for the interfacial tensile stress, and can eliminate the interfacial stress concentration induced by material mismatch.