Axi-Symmetric Contact Mechanics And Fretting Analysis Of Functionally Graded Materials

Functionally graded material(FGM)--a new kind of nonhomogeneous composites materials has predominant properties and can be used in many fields,so it has been the interest of scientists.In recent years,the experimental results which have been obtained by many reseachers indicate that FGM used as coatings can improve the resistance to contact deformation and damage,thus it is very important to study the contact problems of FGM coatings.The theoretical results which have been obtained localized on the two-dimension contact mechanics of FGM coatings.In this thesis the axisymmetric contact and fretting problems of FGM coatings are considered.The properties of non-nomogeneous may vary aribitarily along a certain spatial direction,which makes the solution of the contact problem very difficult in mathematics.In the present work, we adopt two methods to model the FGM:First,assume the elastic modulus of the FGM varies as the exponent functuion.Second,simulate the FGM with arbitrarily varying material modulus by the linear multi-layered model limited to Possion's ratio of 1/3.That is,the FGM is divided into a series of sub-layers,with linear variation of the shear modulus in each sub-layer.The shear modulus is taken to be continuous on the sub-interfaces and equal to their real values.With these two models,several axisymmetric contact problems are solved:1 ) The fundamental solutions of a functionally graded coated half-space under arbitrary axisymmetric loads are obtained by both exponential functiuon model and the linear multi-layered model.2) With the above fundamental solutions,the frictionless axisymmetric contact problem of the FGM coating indented by a rigid cylinder and spheical and conical punch are solved.3) With the above fundamental solutions,the Reissner-Sagoci problem of the FGM coated half-space is solved.4) With the above fundamental solutions,the finite friction contact problem of the FGM coated half-space which indented by a rigid spherical punch is solved.5) Based on the above analysis,fretting contact of two FGM coated elastic bodies under torsion is discussed.The Hankel integral transform technique and the transfer matrix method are applied to reduce the axisymmetric contact and fretting problems to a set of Cauchy singular integral equations that can be numerically caculated.The results obtained by these two methods are compared.The problems with other functional forms of the elatic modulus are caulated by using linear multi-layered model.The results show:1 ) The numerical results with the two models are in pretty agreement.Compared with the piecewise multi-layered(PWML) model,the linear multi-layered model can simulate FGM coatings with arbitrarily varying elatic modulus and involves no discontinuties of the materials properties at the sub-layers.The linear multi-layered model is more efficient in solving the axisymmetric contact problem of the FGM than thePWML model.2) The varying form of the elastic modulus can alter the contact tractions at the surface of FGMs.So control of the gradients of the elastic modulus offers the opportunities for the design of surfaces with resisitance to contact deformation and damage.The results also show that the relation between the load vs the indenter displacement is greatly effected by the gradient of the coating,so the results provide a way to measure the gradient of the coating using the indentation-testing method. Furthermore,the contact stress,surface displacement and torque can be changed by adjusting the gradient of the coating for Reissner-Sagoci problem.This is of interest to materials non-desreuctive testing.3) The varying forms of the elastic modulus can change the distribution of contact tractions and alter the stick/slip region and the position where the maximum contact shear tractions appearing in fretting problem.In particular,reducing the shear modulus or the gradient of the coating can lead to decreasing of the maximum shear tractions in finit frctional contact as well as the maximum circumferical shear traction in the fretting problem under torsion.Therefore,we can enhance the contact damage resistance under fretting conditions by adjusting the gradient of the coating.4) The varying of Possion's ratio has no significiant effect on the contact tractions in axisymmetric frictionless contact and the fretting problem under torsion,but it has influence on the shear tractons in the contact problem with finite friction.5) In the contact problem with finite frction,the friction coefficient has slight effect on the normal tractions but a significant effect on the distribution of shear tractions.The present investigation will be expected to perfect the theory and analytical methods for the axisymmetric contact and fretting problem of FGM coatings,and to provid a guidance for design considertations and applications of FGMs.