Partial closure of the crack in the functional graded elastic layer under the effect of a single load from two surfaces

Within the scope of this thesis, the partial closure of the crack in the functional graded layer under the effect of a singular load from under and upper surfaces was investigated with the help of elasticity theory. The shear modulus of the functionally graded layer is defined as depending on a function. In the study, the basic equations of elasticity theory and integral transformation techniques were used to obtain the stress and displacement expressions of the functionally graded layer. Then the problem is defined and the boundary conditions of the problem are determined. Applying the boundary conditions to the stress and displacement expressions, four equations with four unknowns were obtained as a result of solving this system of equations, the coefficients in the stress and displacement expressions were obtained depending on an unknown slope function. The solution of the problem is reduced to a singular integral equation by writing these coefficients in their places under the boundary condition that is not used to obtain the coefficients. Then, this dimensionalized integral equation was transformed into an algebraic equation system by the Gauss-Chebyshev integration formulation and the stress intensity factor at the crack end was determined depending on the slope at the crack end, which is unknown. The stress intensity factor, the ratio of layer thickness to crack closure length, the ratio of crack start and closure lengths, the load intensity factor, the stiffness parameter and the Kolosov constant were calculated and studied for different values.