dc.contributor.advisor Martin, P. A. dc.contributor.author Floyd, Christopher L. dc.date.accessioned 2007-01-03T04:18:44Z dc.date.accessioned 2022-02-03T11:52:37Z dc.date.available 2007-01-03T04:18:44Z dc.date.available 2022-02-03T11:52:37Z dc.date.issued 2012 dc.date.submitted 2012 dc.identifier T 7100 dc.identifier.uri https://hdl.handle.net/11124/76638 dc.description 2012 Fall. dc.description Includes illustrations. dc.description Includes bibliographical references. dc.description.abstract Penny-shaped cracks are commonly used mathematical models, generally used in the field of fracture mechanics. One specific application is the modeling of micro-structures, within elastic materials. From a purely mathematical perspective, a penny-shaped crack can be described as a flat, disk-shaped crack. In this work, we consider the buried penny-shaped crack problem, consisting of a single crack, buried below the surface of a half-space. Specifically, the flat surface of the crack is taken to be parallel to the boundary, and the radius of the crack is held constant. The primary point of interest in this problem is the depth dependence of the stress intensity factor, which characterizes the fracture conditions near the tip of the crack. Determining the stress intensity factor for this problem is reduced to solving a pair of dual integral equations, specifically looking at these equations evaluated at the upper bound of integration. These equations were amenable to numerical solution, where the distance between the crack and the boundary was allowed to become small. The values of these equations, at the upper bound of integration, both tend toward 0. Based on the numerical results, the stress intensity factors for this problem were dependent on the depth at which the penny-shaped crack is buried. dc.format.medium born digital dc.format.medium masters theses dc.language English dc.language.iso eng dc.publisher Colorado School of Mines. Arthur Lakes Library dc.relation.ispartof 2010-2019 - Mines Theses & Dissertations dc.rights Copyright of the original work is retained by the author. dc.subject reflection seismology dc.subject velocity estimation dc.subject least squares dc.subject waveform inversion dc.subject traveltime inversion dc.subject.lcsh Fracture mechanics dc.subject.lcsh Strains and stresses--Mathematical models dc.title Buried penny-shaped cracks dc.type Text dc.contributor.committeemember Collis, Jon M. dc.contributor.committeemember Ahrens, Cory thesis.degree.name Master of Science (M.S.) thesis.degree.level Masters thesis.degree.discipline Applied Mathematics and Statistics thesis.degree.grantor Colorado School of Mines
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Buried penny-shaped cracks