Analysis of a finite two-dimensional solid with an inclined crack and a rigid inclusion

• Main Author: Ozen, Metin
• Format: Dissertation
• Language: English
• Published: ProQuest Dissertations & Theses 01.01.1989
• Subjects: Materials science; Mechanical engineering; Mechanics; Metallurgy
• ISBN: 9798207106915

The stress field for a two-dimensional, finite solid with (i) a subsurface crack parallel to the contact surface and (ii) an inclined crack and a rigid inclusion, was derived. On the contact surface, a Hertzian load was applied to simulate a rolling/sliding contact. The crack tip stress intensity factors, normal and tangential displacement differences at the crack, contact surface normal displacement, and the normal derivatives of the thin "shell" surrounding the rigid inclusion were chosen as the unknowns. Finite two-dimensional Fourier transformation, in conjunction with the Green-Gauss theorem, was applied to the Navier's equations. The unknowns were expanded into regular Fourier series and Fourier series with square root singular terms. The collocation method was used to solve the system of integral equations resulting from the application of the boundary conditions. This operation lead to an infinite system of linear algebraic equations with respect to the Fourier coefficients of the unknown functions. The stress intensity factors at the crack tips, discontinuities of the displacements across the crack, and the displacement of the load edge were calculated for the subsurface crack case. These results showed very good agreement with the results from a finite element model. Numerical results from the inclined crack and inclusion case could not be presented due to numerical difficulties encountered during the solution phase.