Akademik Veri Yönetim Sistemi
ZAMM-ZEITSCHRIFT FUR ANGEWANDTE MATHEMATIK UND MECHANIK, cilt.105, sa.7, 2025 (SCI-Expanded, Scopus)
In this study, partial closure of the crack in the functionally graded (FG) layer under the effect of a single load from the upper and lower surfaces has been investigated with the help of elasticity theory. In the study, firstly, the stress and displacement expressions of the FG layer have been obtained by using the basic equations of elasticity theory and Fourier integral transforms. By applying the boundary conditions determined for the problem to the stress and displacement expressions, an equation system consisting of four equations with four unknowns has been obtained, and as a result of the solution of this equation system, the coefficients in the stress and displacement expressions have been obtained depending on an unknown slope function. The solution of the problem has been reduced to a singular integral equation by writing these coefficients in the boundary condition not used in obtaining the coefficients. Then, this non-dimensionalized integral equation has been converted into an algebraic equation system by Gauss-Chebyshev integration formulation, and the stress intensity factor at the crack tip has been determined depending on the unknown crack tip slope. The stress intensity factor has been calculated and investigated for different values of the layer thickness to crack closure length ratio, crack initiation and closure length ratio, load intensity factor, stiffness parameter, and Kolosov constant.