# Axisymmetric crack problem for a hollow cylinder imbedded in a dissimilar medium

2005-05-01
The analytical solution for the linear elastic problem of flat annular crack in a transversely isotropic hollow cylinder imbedded in a transversely isotropic medium is considered. The hollow cylinder is assumed to be perfectly bonded to the surrounding medium. This structure, which can represent a cylindrical coating-substrate system, is subjected to uniform crack surface pressure. Because of the geometry and the loading, the problem is axisymmetric. The z = 0 plane on which the crack lies, is also a plane of symmetry. The composite media consisting of the hollow cylinder and the surrounding medium extends to infinity in z and r directions. The mixed boundary value problem is formulated in terms of the unknown derivative of the crack surface displacement by using Fourier and Hankel transforms. By extending the crack to the inner surface and to the interface, the cases of surface crack and crack terminating at the interface are obtained. Asymptotic analyses are performed to derive the generalized Cauchy kernel and associated stress singularities. The resulting singular integral equation is solved numerically. Stress intensity factors for various crack configurations, crack opening displacements and stresses along the interface and on z = 0 plane are presented for sample material combinations and geometric parameters.
International Journal of Engineering Science

# Suggestions

 COMPRESSIBLE, HYPERELASTIC SPINNING TUBES SUBJECTED TO CIRCUMFERENTIAL SHEAR ERTEPINAR, A (Elsevier BV, 1991-01-01) The finite strain behavior of cylindrical tubes, made of a polynomial compressible material and subjected to the simultaneous action of constant spin and uniform external circumferential shear, is investigated using the theory of finite elasticity. The inner surface of the tube is assumed to be perfectly bonded to a rigid shaft. The governing quasi-linear system of two ordinary differential equations is solved using a shooting method. Numerical results are generated to analyze, qualitatively, the effects...
 Yielding of two-layer shrink-fitted composite tubes subject to radial pressure Eraslan, Ahmet Nedim (Springer Science and Business Media LLC, 2005-12-01) Yielding of two-layer shrink-fitted composite tubes with axially constrained ends subject to either internal or external pressure is investigated in detail. In the framework of small deformations, a state of plane strain and von Mises yield criterion, analytical expressions are obtained for critical values of the pressure leading to plastic flow. It is shown that, depending on material properties and tube dimensions, different modes of plastic deformation may occur. Yielding may commence at the inner tube o...
 Edge cracks in a transversely isotropic hollow cylinder Kadıoğlu, Fevzi Suat (Elsevier BV, 2005-09-01) The analytical solution for the linear elastic, axisymmetric problem of inner and outer edge cracks in a transversely isotropic infinitely long hollow cylinder is considered. The z = 0 plane on which the crack lies is a plane of symmetry. The loading is uniform crack surface pressure. The mixed boundary value problem is reduced to a singular integral equation where the unknown is the derivative of the crack surface displacement. An asymptotic analysis is done to derive the generalized Cauchy kernel associat...
 Damage diagnosis in frame structures with a dynamic response method Akgün, Müşerref Asuman; Ju, Fudong (Informa UK Limited, 1990-6) The dynamic response of planar frame structures composed of damped Bernoulli-Euler beams is computed, with and without a crack present in the structure. The inertance changes due to the crack are investigated in relation to the crack location, with the aim of developing a diagnosis method. The optimum excitation location and frequency and the optimum locations for response measurement are determined for best diagnosis results. The effects of crack location and severity and of damping are investigated. Dampi...
 DIRECTIONAL DEPENDENCE OF EXTRAORDINARY INFRARED OSCILLATOR PARAMETERS OF TLGAS2-TYPE LAYER CRYSTALS Hasanlı, Nızamı; TAGIROV, VI (Elsevier BV, 1983-01-01) The directional dispersion of IR-active modes of TlGaS2, TlGaSe2 and TlInS2 layersingle crystals has been investigated, depending on the angle between the phonon wave vector q and the optical c-axis. Owing to the possibility of preparation crystals with various orientations of reflecting surfaces with respect to the optical c-axis, it was of interest to check the applicability of the generalized Born and Huang theory of long-wave optical vibrations in uniaxial crystals to TlGaS2-type layer crystals.
Citation Formats
F. S. Kadıoğlu, “Axisymmetric crack problem for a hollow cylinder imbedded in a dissimilar medium,” International Journal of Engineering Science, pp. 617–638, 2005, Accessed: 00, 2020. [Online]. Available: https://hdl.handle.net/11511/36619.