The problem of a layered composite having a vertical crack at the bottom layer and loaded by means of a rigid stamp

SUMMARY In this study, the crack and the contact problem of a layered composite which consists of two layers having different heights and elastic constants and resting on two simple supports are investigated according to the theory of elasticity. The layered composite has a vertical crack at the bottom layer on the symmetry axis and is loaded by means of a rigid stamp. It is assumed that all surfaces are frictionless. This study consists of five main chapters. In the first chapter, the importance of subject, its content and the previous studies are mentioned. In addition, using the fundamental equations of theory of elasticity and integral transformation techniques, the general expressions of stresses and displacements for both cracked and uncracked layer cases are given. In the second chapter, the problem is introduced and the cases of the layered composite with and without a crack are individually examined. Firstly, the case of layered composite without a crack is considered. After the boundary conditions are satisfied, the problem is reduced to a singular integral equation where the contact pressure is the unknown function. The integral equation is numerically solved for various stamp profile and the contact stress distribution under the stamp is obtained. Depending on the contact stresses under the stamp, the normal stresses on the symmetry axis, initial separation load and its distance at the interface of two layers are determined. Secondly, the case of layered composite having a vertical crack at the bottom layer is considered and this case is separately examined for both edge and internal cracks by loading the normal stresses obtained from the previous case, i.e. uncracked case, with the same magnitude but in the opposite direction on the crack surfaces. By using the boundary conditions belonging to this case where there is not any external loading, the problem is examined to a singular integral equation again. As a result of numerically solving this equations, the stress intensity factors at the tips of the crack and the crack surface displacements for the edge and internal crack cases are calculated. In the third chapter, the numerical applications of the problem given in the previous chapter for various dimensionless quantities are done. By giving different numerical values to the layer thickness, radius of stamp profile, support width, contact area between stamp and layered composite (stamp width) and material constants ratios, the effect of these quantities on the contact stress, normal stress, initial separation load and initial separation distance, stress intensity factor at the tips of crack and crack surface displacements are examined and the results of these are discussed. In this chapter, the tables and graphics which are obtained from numerical applications are also given. In the fourth chapter, the conclusions drawn from this work and the recommendation are given. Keywords: Elasticity Theory, Layered Composite, Contact Mechanics, Fracture Mechanics, Contact Stress, Integral Transform Technique, Integral Equation, Initial Separation Load, Initial Separation Distance, Internal Crack, Edge Crack, Stress Intensity Factor VII