Semi-circular specimens (SCB) under three point-bending which are commonly used for fracture testing of rocks were used here for fracture mechanics tests. A total of 65 specimens were tested by using Ankara andesite rock. Investigations including the effects of initial notch thickness, different loading span ratios (S/R), flattened loading end, and little dimensional variations when preparing the specimens were carried out. Stress intensity factors for specimens with different geometries were computed individually by using a 3D finite element program ABAQUS. Specimens with a preliminary notch thickness varying from 0.84 to 3.66 mm were tested under three point bending. For a second group of specimens loading span was changed and fracture toughness variation was studied. Another change in the specimen geometry was made by machining a flat loading end at the upper load application point. Fracture toughness values were computed using the stress intensity values computed from numerical modeling and failure loads from the experiments. It was found that up to 2 mm fracture toughness was not affected by variations in the thickness of preliminary notches. Fracture toughness was not affected by changing the loading span. For specimens with flat loading ends, fracture toughness was about 16% lower than the value found from regular SCB type specimens loaded at a point at the top by a steel roller. As a result of about 46 experiments average fracture toughness of Ankara G&ouml / lbasi andesite was found as 1.36 MPa .

Modified Ring specimens are of the shape of discs having a hole inside and flattened ends. These specimens are used for determination of Mode I fracture toughness. Finite element program, named ABAQUS, is used for numerical modeling for finding stress intensity factors. Varying disc geometries were used for the experiments and numerical modeling in which size of the flat ends, radius of the hole inside, and external radius of the specimen were varied. Experiments were done by using pink Ankara andesite. Effects of internal hole radius, external disc radius and size of the flat ends on both stress intensity factor and fracture toughness were studied. In order to compare the results, fracture tests with semi-circular specimens under three point bending (SCB) were also performed. From a similar previous study, fracture toughness values of gray andesite were recalculated and compared to the fracture toughness values of pink andesite for varying geometrical factors. Size effect studies were performed as well for varying diameter of core specimens.Fracture toughness values of andesite were found to increase with increasing specimen size. Fracture toughness of 100 mm specimens was determined as 1.11&plusmn / 0.07 MPa&amp / #8730 / m, whereas fracture toughness of 75 mm specimens was 0.96&plusmn / 0.08 MPa&amp / #8730 / m. 100 mm or larger diameter specimens were suggested for the fracture toughness determination with the modified ring tests.

The objective of this study is to model and analyze a three dimensional single riveted lap joint (with and without a crack). By using finite element method, stress and fracture analyses are carried out under both the residual stress field and external tensile loading. Using a two step simulation, riveting process and subsequent tensile loading of the lap joint are simulated to determine the residual and overall stress state. Residual stress state due to riveting is obtained by interference and clamping misfit method. By employing different interference and clamping misfit values, the effects of riveting process parameters on stress state are examined. Two cracks namely the semi elliptical surface crack at faying surfaces of plates and the quarter elliptical corner crack at rivet hole are the most widely observed crack types in riveted joints. Fracture analysis of cracked riveted joints is carried out by introducing these two crack types to the outer plate at a plane perpendicular to the loading. The mixed mode stress intensity factors (SIFs) and energy release rates (G) around the crack front are obtained by using displacement correlation technique (DCT). Effects riveting process parameters (interference and clamping ratios) and geometrical parameters (crack shape and size) on fracture parameters are studied. The stress intensity factor solutions presented herein could be useful for correlating fatigue crack growth rates, fracture toughness computation, and multiple site damage (MSD) analysis in aircraft bodies.

Fracture toughness is an important rock property for rock fracturing and fragmentation applications. Theory and practice of opening mode (mode I) and shearing mode (mode II) fracture toughness tests are still in a developing stage for the cylindrical rock cores. A new circular plate type test specimen is used for mode II fracture toughness testing on rock cores. This involves a straight edge notched circular plate type core disc geometry under three-point bending load / new method and its associated specimen geometry is referred as straight edge notched disc bend (SNDB) specimen under three-point bending. Mode II fracture toughness results of the tests with this new geometry were compared to the results of the tests commonly employed for mode II fracture toughness testing. Specimen geometries were modeled and mode II stress intensity factors were computed by finite element modeling using ABAQUS program. For comparison purposes, mode II or shearing mode fracture toughness KIIc of two different rock types were determined by different testing methods commonly employed in recent practice. Core specimens of Ankara andesite and Afyon marble rock types were tested with cracked chevron notched Brazilian disc and cracked straight through Brazilian disc specimens under Brazilian type loading, semi-circular bend specimen and straight edge notched disc bending specimen geometries under three-point bending.For all testing groups, cylindrical cores with diameters varying from 7.5 cm to 12.5 cm were prepared with notch lengths changing from 1.5 cm to 2.6 cm. Effect of specimen thickness on mode II fracture toughness was investigated for three different testing methods. Fracture toughness values remained constant when thickness of the specimens was increased for cracked straight through Brazilian disc, semi-circular bend and straight notched disc bend methods. For cracked straight through Brazilian disc method KIIc values of Ankara andesite and Afyon marble were 0.99 MPa&radic / m and 0.86 MPa&radic / m, respectively. Mode II fracture toughness with semi-circular bend specimen was 0.43 MPa&radic / m for andesite and 0.46 MPa&radic / m for marble. When the results of the two three-point bending type tests were compared straight notched disc under three-point bending resulted in higher KIIc values (0.61 MPa&radic / m for andesite and 0.62 MPa&radic / m for marble) than the results found by semi-circular bend tests.

This study considers the elastostatic contact problem of a semi-infinite cylinder. The cylinder is compressed against a layer lying on a rigid foundation. There is a sharp-edged circular hole in the middle of the foundation. It is assumed that all the contacting surfaces are frictionless and only compressive normal tractions can be transmitted through the interfaces. The contact along interfaces of the elastic layer and the rigid foundation forms a circular area of which outer diameter is unknown. The problem is converted into the singular integral equations of the second kind by means of Hankel and Fourier integral transform techniques. The singular integral equations are then reduced to a system of linear algebraic equations by using Gauss-Lobatto and Gauss-Jacobi integration formulas. This system is then solved numerically. In this study, firstly, the extent of the contact area between the layer and foundation are evaluated. Secondly, contact pressure between the cylinder and layer and contact pressure between the layer and foundation are calculated for various material pairs. Finally, stress intensity factor on the edge of the cylinder and in the end of the sharp-edged hole are calculated.

This thesis presents a study about the determination of the stress intensity factors in cracked sheets with riveted stiffeners. Stress intensity factors are determined with both analytical method and finite element method for different combination of rivet/stringer spacing and stringer to sheet stiffness ratio. Analytical part of the thesis is a replication of the original study of Poe which assumes rigid rivet connections with no stringer offset. In the analytical part, the whole systems of equations of Poe are re-derived, and it is shown that there are two typographical errors in the expressions for the calculation of the influence coefficients of the cracked sheet and the stringer. Major objective of the analytical part is to develop a computer code which calculates the variation of the normalized stress intensity factor with the crack length for any combination of rivet/stringer spacing and stringer to sheet stiffness ratio. Analytical part of the study also covers the effect of broken stiffener on the stress intensity factor of the cracked sheet. The stress intensity factors of stiffened cracked sheets are calculated by the finite element method by incorporating fastener flexibility and stringer offset. Finite element solutions are performed by Franc2D/L and Abaqus, and comparisons are made. The effect of geometry, fastener flexibility, and stringer offset on the stress intensity factors are studied by presenting normalized stress intensity factor versus crack length curves. Finally, as a case study a sample damage tolerant stiffened panel is designed according to FAR 25 safety criteria. Experiments are performed for determining mechanical and crack growth properties of Al 2124 which is used as the material in the case study. Present study showed that the most significant effect on the stress intensity factor is seen when stringer-cracked sheet offset is included in the analysis model.

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.