Pressure tubes pick up hydrogen while they are in service within CANDU reactors. Sufficiently high hydrogen concentration can lead to hydride precipitation during reactor shutdown/repair at flaws, resulting in the potential for eventual rupture of the pressure tubes by a process called Delayed Hydride Cracking (DHC). The threshold stress intensity factor (KIH) below which the cracks will not grow by delayed hydride cracking of Zr-2.5Nb micro pressure tubes (MPTs) has been determined using a load increasing mode (LIM) method at different temperatures. MPTs have been used to allow easy study of the impact of properties like texture and grain size on DHC. Previous studies on MPTs have focused on creep and effects of stress on hydride orientation; here the use of MPTs for DHC studies is confirmed for the first time. Micro pressure tube samples were hydrided to a target hydrogen content of 100 ppm using an electrolytic method. For DHC testing, 3 mm thick half ring samples were cut out from the tubes using Electrical Discharge Machining (EDM) with a notch at the center. A sharp notch with a root radius of 15 µm was introduced by broaching to facilitate crack initiation. The direct current potential drop method was used to monitor crack growth during the DHC tests. For the temperature range tested the threshold stress intensity factors for the micro pressure tube used were found to be 6.5-10.5 MPa.m1/2 with the value increasing with increasing temperature. The average DHC velocities obtained for the three different test temperatures 180, 230 and 250oC were 2.64, 10.87 and 8.45 x 10-8 m/s, respectively. The DHC data obtained from the MPTs are comparable to the data published in the literature for full sized CANDU pressure tubes. / Thesis (Master, Mechanical and Materials Engineering) -- Queen's University, 2009-04-24 12:55:36.917

Functionally graded materials processed by the thermal spray techniques such as electron beam physical vapor deposition and plasma spray forming are known to have an orthotropic structure with reduced mechanical properties. Debonding related failures in these types of material systems occur due to embedded cracks that are perpendicular to the direction of the material property gradation. These cracks are inherently under mixed-mode loading and fracture analysis requires the extraction of the modes I and II stress intensity factors. The present study aims at developing semi-analytical techniques to study embedded crack problems in graded orthotropic media under various boundary conditions. The cracks are assumed to be aligned parallel to one of the principal axes of orthotropy. The problems are formulated using the averaged constants of plane orthotropic elasticity and reduced to two coupled integral equations with Cauchy type dominant singularities. The equations are solved numerically by adopting an expansion - collocation technique. The main results of the analyses are the mixed mode stress intensity factors and the energy release rate as functions of the material nonhomogeneity and orthotropy parameters. The effects of the boundary conditions on the mentioned fracture parameters are also duly discussed.

This work considers a cracked semi-infinite cylinder and a finite cylinder. Material of the cylinder is linearly elastic and isotropic. One end of the cylinder is bonded to a fixed support while the other end is subject to axial tension. Solution for this problem can be obtained from the solution for an infinite cylinder having a penny-shaped rigid inclusion at z = 0 and two penny-shaped cracks at z = &plusmn / L. General expressions for this problem are obtained by solving Navier equations using Fourier and Hankel transforms. When the radius of the inclusion approaches the radius of the cylinder, the end at z = 0 becomes fixed and when the radius of the cracks approaches the radius of the cylinder, the ends at z = &plusmn / L become cut and subject to uniformly distributed tensile load. Formulation of the problem is reduced to a system of three singular integral equations. By using Gauss-Lobatto and Gauss-Jacobi integration formulas, these three singular integral equations are converted to a system of linear algebraic equations which is solved numerically.

The presence of notches or cracks causes stresses to amplify in nearby regions. This phenomenon is studied by estimating the Stress Concentration Factor (SCF) for notches, and the Stress Intensity Factor (SIF) for cracks. In the present work, a semi-analytical method under the framework of linear elasticity is developed to give an estimate of these factors, particularly for cracks and notches in finite domains. The solution technique consists of analytically deriving a characteristic equation based on the general solution and homogeneous boundary conditions, and then using the series form of the reduced solution involving the (possibly complex-valued) roots of this characteristic equation to satisfy the remaining non-homogeneous boundary conditions. This last step has to be carried out numerically using, say, a weighted residual method. In contrast to infinite domain problems where a fully analytical solution is often possible, the presence of more boundaries, and a variety in configurations, makes the solution of finite do-main problems much more challenging compared to infinite domain ones, and these challenges are addressed in this work. The method is demonstrated on several classical and new problems including the problems of a semi-circular edge notch in a semi-infinite and finite plate, an elliptical hole in a plate, an edge-crack in a finite plate etc.

The fractal-like finite element method (FFEM) is developed to compute stress intensity factors (SIFs) for isotropic homogeneous and bi-material V-notched plates. The method is semi-analytical, because analytical expressions of the displacement fields are used as global interpolation functions (GIFs) to carry out a transformation of the nodal displacements within a singular region to a small set of generalised coordinates. The concept of the GIFs in reducing the number of unknowns is similar to the concept of the local interpolation functions of a finite element. Therefore, the singularity at a notch-tip is modelled accurately in the FFEM using a few unknowns, leading to reduction of the computational cost.The analytical expressions of displacements and stresses around a notch tip are derived for different cases of notch problems: in-plane (modes I and II) conditions and out-of-plane (mode III) conditions for isotropic and bi-material notches. These expressions, which are eigenfunction series expansions, are then incorporated into the FFEM to carry out the transformation of the displacements of the singular nodes and to compute the notch SIFs directly without the need for post-processing. Different numerical examples of notch problems are presented and results are compared to available published results and solutions obtained by using other numerical methods.A strain energy approach (SEA) is also developed to extract the notch SIFs from finite element (FE) solutions. The approach is based on the strain energy of a control volume around the notch-tip. The strain energy may be computed using commercial FE packages, which are only capable of computing SIFs for crack problems and not for notch problems. Therefore, this approach is a strong tool for enabling analysts to compute notch SIFs using current commercial FE packages. This approach is developed for comparison of the FFEM results for notch problems where available published results are scarce especially for the bi-material notch cases.A very good agreement between the SEA results and the FFEM results is illustrated. In addition, the accuracy of the results of both procedures is shown to be very good compared to the available results in the literature. Therefore, the FFEM as a stand-alone procedure and the SEA as a post-processing technique, developed in this research, are proved to be very accurate and reliable numerical tools for computing the SIFs of a general notch in isotropic homogeneous and bi-material plates.

The thesis deals with the behaviour of a cracked rail wheel. The aim was to perform the strain analysis of intact wheel as well as the fracture analysis of the primary direct cracked wheel. Solution includes an analysis of operating conditions, assessment of the substantiality of articular components of load, stiffness of the wheel, a comprehensive analysis of fracture of the selected railway wheel profile and optimization of the wheel shape depending on the matching fracture properties.

The presented diploma thesis deals with a problem of the determination of the stress intensity factor of the finite length crack in the vicinity of the bi-material interface solved by the distributed dislocation technique. The work is divided into several parts. The first part is theoretical and includes basic concepts of the fracture mechanics, the crack behaviour at the bi-material interface, the formulation of the singular integral equation by virtue of the distributed dislocation technique, the Bueckner's principle, complex potentials and consequently the determination of the stress intensity factor. The second part is the theory application to the specific configuration of the crack of the finite length with respect to the bi-material interface and in the third part, there is carried out the solution of this problem for various configurations of the bi-material solved by the distributed dislocation technique and its comparison with the results obtained from the FE analysis.

A two-parameter fracture criterion (TPFC) is used to correlate and predict failure loads on cracked configurations made of ductile materials. The current study was conducted to validate the use of the fracture criterion on more brittle materials, using elastic-plastic finite-element analyses with the critical crack-tip-opening angle (CTOA) failure criterion. Forman generated fracture data on middle-crack tension, M(T), specimens made of thin-sheet 7075-T6 aluminum alloy, which is a quasi-brittle material. The fracture data included a wide range of specimen widths (2w) ranging from 3 to 24 inches. A two-dimensional (2D) finite-element analysis code (ZIP2D) with a ''plane-strain core" option was used to model the fracture process. Fracture simulations were conducted on M(T), single-edge-crack tension, SE(T), and single-edge-crack bend, SE(B), specimens. The results supported the TPFC equation for net-section stresses less than the material proportional limit. However, some discrepancies were observed among the numerical results of the three specimen types. Thus, more research is needed to improve the transferability of the TPFC from the M(T) specimen to both the SE(T) and SE(B) specimens.

This thesis investigates the feasibility and usability of the finite element method approach in the design of crack arresting devices. Current design and manufacturing practices are improving structures' susceptibility to fracture, in particular brittle fracture; however, cracks in structures are still observed within their lifespans due to severe unexpected service conditions, poor designs, or faulty manufacturing. Crack arrester systems can be added during service to prolong the longevity of structures with sub-critical or critical flaws. Fracture properties of different specific structures under specific services can be obtained experimentally, however, experiments are expensive and of high complexity. Alternatively, the finite element method can reduce these factors and provide reliable solutions. Finite element analysis conducted provides insight into the modeling process and the effectiveness of the simulation of fracture problems. Fracture mechanics technology in conjunction with the finite element method allows for the evaluation of the effectiveness of introducing crack arresters to a flawed structure. Additionally, the simulation of recorded crack arrester experiments alongside analytic methods are used to verify the finite element analysis results. The work in this thesis verifies the validity of using the finite element approach in designing crack arrester systems for flawed structures and suggests further investigation be done with variation in crack arrester types.

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