Non-Fourier Heat Conduction of a Functionally Graded Cylinder Containing a Cylindrical Crack

The present work investigates the problem of a cylindrical crack in a functionally graded cylinder under thermal impact by using the non-Fourier heat conduction model. The theoretical derivation is performed by methods of Fourier integral transform, Laplace transform, and Cauchy singular integral equation. The concept of heat flux intensity factor is introduced to investigate the heat concentration degree around the crack tip quantitatively. The temperature field and the heat flux intensity factor in the time domain are obtained by transforming the corresponding quantities from the Laplace domain numerically. The effects of heat conduction model, functionally graded parameter, and thermal resistance of crack on the temperature distribution and heat flux intensity factor are studied. This work is beneficial for the thermal design of functionally graded cylinder containing a cylindrical crack.

An Analytical Solution for Microannulus Cracks Developed Around a Wellbore

In situations like blowout or hydraulic fracturing, excessive fluid pressure may cause leaking in the casing in shallower parts of the formation. The resulting high pressure may form a cylindrical crack around the wellbore. An analytical solution for stress distribution and displacement along a cylindrical crack formed between the casing and the formation is provided in this paper. The crack is assumed to be opened by uniform fluid pressure exerted on both sides of the crack. This solution has a wide range of applications from failure analysis of fibers in manufacturing composite materials to wellbore integrity in petroleum and subsurface engineering problems.

The Torsional Dislocation Loop and Mode III Cylindrical Crack

ABSTRACTThe elastic fields of a torsional dislocation loop in a homogeneous material are first derived. The solution is based on torsional symmetry. The stress and displacement solutions are then extended to the case of a torsional loop in a bi-material. A main utility of basic dislocation solutions is in fracture mechanics. In particular, circular loop solutions can be used in the modeling of both cylindrical and penny-shaped cracks. In the present study we use them to model a Mode III cylindrical crack via the application of a “distributed-dislocation technique”. Stress intensity factors at the crack tips are presented. The influences of crack radius and material pair on the stress intensity factor of interfacial cracks are investigated.

Thermal Stresses in an Infinite Elastic Pipe Weakened by a Finite Cylindrical Crack

Axially symmetric thermal stresses in the vicinity of a finite cylindrical crack in an elastic pipe are calculated. The surfaces of the crack are assumed to be insulated. The outer surface of the pipe is heated so as to maintain a constant temperature Td, and the inner surface of the pipe is cooled so as to maintain a constant temperature Tb. Expressions developed by Sharma are used to solve the problem. Stress intensity factors are defined and calculated numerically for several configurations of the pipe.