The New Liner Multi-layered Model For The Contact Problem Of The Heterogeneous Medium

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 new 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, in the present work , using the reciprocal of the shear modulus (flexibility coefficient) simulate the FGM, 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.(2) With the above solution as the fundamental solution, the frictionless contact of rigid punches with various shapes on a functionally graded coated half-plane are solved.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: The present model allows for arbitrary variation of the material properties. The model is very efficient in solving the contact problem of the FGM. The results are compared with these obtained by other methods,we has the equation inferential reasoning process simple and saved many computing time. Generally 6 sub-layers can yield sufficiently accurate results.