Document Type

Thesis - Open Access

Award Date


Degree Name

Master of Science (MS)

Department / School

Mechanical Engineering


With the increasing attention to failure problems over the last half century went a growing interest in the fracture process in materials. Many previous investigators have studied the elastic distributions around the cracks basing on the idea of Inglis who in 1913 was the first to study an internal crack by use of the elliptical bounding surfaces. Probably the most important concept put forth in this field was Griffith's hypothesis of a brittle fracture which was published in 1921. Employing the idea of Inglis and the principle of conservation of energy, Griffith derived a theoretical formula for the critical stress at the crack tip and a criterion for crack instability. In the study of fracture mechanics in solids, the major interest centers around the crack tip zone. A penny-shaped crack having the diameter 2L is introduced for investigation. As mentioned, there will exist a plastic zone due to the high stress concentration and it is located at the crack tip. A plausible explanation for such plastic behavior develops from continuum mechanics. It has been shown that the density, and consequently the volume, does not change even for very large plastic deformations. Thus, in the plastic range, a material can be considered as incompressible.

Library of Congress Subject Headings

Fracture mechanics


South Dakota State University Theses



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South Dakota State University