Contact and crack problems at the bonded double layers resting on an elastic half plane

In this paper, the symmetric contact problem of two bonded layers resting on an elastic half plane with a rigid punch and the same problem in the case of having a vertical crack at the bottom layer are solved with using the Theory of Elasticity and the Integral Transformation technique.In the first chapter, the literature studies on contact and crack problems are presented. By utilizing the Fourier Integral Transformation techniques to fundamental equations of theory of elasticity, general equations of stresses and displacements of layers and elastic half plane are obtained for both uncracked and cracked situation.In the second chapter, the considered problems are introduced and investigated. Firstly, the case of contact without a crack is investigated. The problem is reduced two singular integral equations where the contact stressses are the unknown functions under the punch and between the bottom layer and an elastic half plane after the boundary conditions are satisfied. Solving this integral equations by Gauss-Chebyshev integration formulation, the contact stresses are obtained. Depending on the contact stresses, the normal stresses are determined. Secondly, the same problem is investigated for having the internal or edge crack and the stresses intensity factors belonging to crack are calculated.In the third chapter, numerical implementations are performed. The contact lenghts, stress and dispacement components and the stress intensity factors are obtained according to different parameters of load, material and geometry. The Results are presented in tables and graphics.In the fourth chapter the results of this study is compared with related contact and crack problems in litherature.In the fifth chapter the conclusions are written. The recommendations are given in the sixth chapter.