Mechanical modeling of thin films bonded to functionally graded materials

In this thesis, a compound structure consisting of thin film bonded to the coating offunctionally graded material (FGM) which resides on the homogeneous half plane isstudied by applying two dimensional linear elasticity theory under various loadingconditions. In these problems the loading consists of stresses caused by residualstresses resulting from film/coating processing and thermal or mechanical loadingsduring service life of the structure. The primary interest in this study is in examiningstress concentrations or strength of singularities near the film ends, which may causecrack initiation and propagation in the coating or along the interface. The underlyingcontact mechanics problem is formulated by assuming that the film is a ?membrane?and the FGM coating and homogeneous substrate are elastic continua. By using theelasticity solution for the FGM coating and the homogeneous substrate, andcontinuity of displacements at the interfaces, the governing integral equation for theproblem is found. This integral equation comes out to be singular and may bereduced to a linear algebraic system of equations by using the properties ofChebychev polinomials, and then solved for the unknown interfacial shear stressnumerically. The calculated results are the interfacial shear stress between the filmand the graded coating, strength of stress singularity at the end of the film and theaxial normal stress in the film. This study reveals that both mechanical andgeometrical parameters of the structure as well as loading type have a great effect onthe stress distribution and the strength of shear stress singularity at the film ends. Byadjusting these parameters and the type of the grading, it is possible to lower thestrength of shear stress singularity and the axial normal stress in the film that mayhave a bearing on the fatigue and fracture of the coating and damage or failure duringor after the production stage of the thin film.