Date of Award

Summer 2006

Document Type

Thesis

Degree Name

Master of Science (MS)

Department

Mechanical & Aerospace Engineering

Program/Concentration

Mechanical Engineering

Committee Director

Stephen G. Cupschalk

Committee Member

Gene Hou

Committee Member

Keith Williamson

Call Number for Print

Special Collections; LD4331.E56 M66 2006

Abstract

Fracture in brittle materials containing pre-existing cracks was studied. The probability of of crack growth under both shear and tensile stresses was determined for an arbitrary distribution of crack sizes. Two different crack orientation distributions, random and uniform, as well as friction were also taken into account. The material's reliability was assumed to depend on the number of active cracks at a particular stress level, and this was expressed as an arbitrary 2-parameter Weibull distribution. Two new and efficient methods for calculating crack growth probabilities based on spherical triangles and spherical caps were developed. They utilized normalized stress coordinates and can be applied to any 3-D state of stress. As observed by Brannon, the material's failure behavior could not be defined by a single specific stress. Rather, it was "fuzzy" over a range of stresses. This same "fuzzy" failure behavior was also observed for the distribution of random crack orientations at individual stress levels; however, it was not observed for the uniform distribution. Finally, calculations indicated that all three principal stresses must be taken into account when describing failure for these materials. Consequently, the traditional Mohr-Coulomb treatment based on the maximum shear stress may be inadequate for this purpose.

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DOI

10.25777/qr9d-3p61

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