The initiation and propagation of adiabatic shear bands is analyzed numerically for an impulsively loaded thick-walled steel tube. A circumferential V-notch located at the outer surface of the center of the tube provides a stress concentration. The material is modeled as strain hardening, strain-rate hardening and thermal softening. The dynamic loading conditions considered are pure torsion, axial pressure combined with torsion, and internal pressure combined with torsion. Because of the stress concentration, a shear band will first initiate in an element adjoining the notch tip and propagate radially inwards through the thickness of the tube. The speed of propagation and the amount of energy required to drive a shear band through the material are calculated. The effects of the pressure preload and the depth of the notch are studied. Also, the influence of thermal softening is investigated by modeling it after a relation proposed by Zhou et al. <i>[Vita removed July 18, 2008 CK/GMc 2/2/2012]<i> / Master of Science

D. Tech. (Department of Mechanical Engineering, Faculty of Engineering and Technology), Vaal University of Technology. / The purpose of this study was to develop analytical and numerical solutions to be used in the design of thick walled high pressure vessels for optimal location of a cross bore. In addition, the effects of internally applied combined thermo-mechanical loading on Stress Concentration Factor (SCF) on these vessels, was also evaluated. An analytical solution, to predict principal stresses on radial circular cross bore, was developed. The developed analytical solution was verified using finite element analysis methods. An optimisation process, using finite element analysis, was further done to determine the optimal combination of the major cross bore geometry that affect stress concentration. The cross bore geometries that were studied included the size, shape, location, obliquity and thickness ratio. The geometrically optimised cross bore was then subjected to combined thermo-mechanical loading to determine the resulting stress concentration effects. A total of 169 finite element part models were created and analysed. Seven thick walled cylinders having either circular or elliptical shaped cross bore positioned at radial, offset or and inclined were investigated. The analytical solution developed correctly predicted all the radial stresses at the intersection of the cross bore and main bore. However, out of 35 studied models, this analytical solution predicted the magnitude of hoop stresses in 9 models and that of axial stresses in 15 models correctly. The lowest SCF given by the radial circular cross bore was 2.84. Whereas, the SCF due to offsetting of the same cross bore size reduced to 2.31. Radial elliptical shaped cross bore gave the overall lowest SCF at 1.73. In contrast, offsetting of the same elliptical shaped cross bore resulted in tremendous increase in SCF magnitude exceeding 1.971. Additionally, the magnitudes of SCF were observed to increase whenever the circular offset cross bores were inclined along the RZ axis of the cylinder. The hoop stress due to internally applied combined thermo-mechanical loading increased gradually with increase in temperature until it reached a maximum value after which it began to fall sharply. In contrast, the corresponding SCF reduced gradually with increase in temperature until it reached a uniform steady state. After which, any further increase in temperature had insignificant change in stress concentration factor. The optimal SCF magnitude due to combined thermo-mechanical loading was 1.43. This SCF magnitude was slightly lower than that due to the pressure load acting alone.

This thesis presents three different approaches to model corrosion-induced crack propagation in reinforced concrete structures. The first approach is solved numerically using finite differences to model the softening behaviour of concrete in tension. The second approach idealizes the concrete cover as either a brittle elastic or an elastoplastic material so that it may be solved using a closed-form solution. Both approaches are based on a thick-walled cylinder (TWC) analogy and consider rust compressibility and rust diffusion into cracks. The third approach uses finite element modelling to validate the application of the TWC and perform a parametric study. The results obtained using each approach are compared against each other as well as against experimental results. The TWC was found to be an appropriate analogy for the geometries and reinforcement configurations considered. Analytical models were found to provide upper and lower limits to the results based on the numerical model. The experimental data found in the literature showed reasonable agreement with predictions from the numerical and elastoplastic models.