Continuum damage model for plastic fracture of work-hardening materials.
Item
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Title
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Continuum damage model for plastic fracture of work-hardening materials.
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Identifier
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AAI9807964
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identifier
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9807964
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Creator
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Mahmoud, Khaled Mohamed.
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Contributor
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Adviser: Mumtaz K. Kassir
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Date
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1997
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Language
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English
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Publisher
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City University of New York.
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Subject
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Engineering, Civil
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Abstract
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This dissertation proposes a continuum damage model for plastic fracture of work-hardening materials containing cracks subjected to mode I and mode III loadings. The model, which is based on interaction between a well-developed crack and microvoids ahead of its tip, describes the conditions necessary for the onset of crack instability, fatigue crack propagation due to cyclic loading, and rates of crack growth due to steady-state creep. This is accomplished through the introduction of a mechanical damage variable into the constitutive equations of an elastic-plastic formulation of a work-hardening material. The main hypothesis throughout the dissertation is that damage is proportional to the crack opening displacement.;Because of mathematical simplicities, an anti-plane stationary crack subjected to shear loading (mode III) is dealt with first to illustrate the model. A hodograph transformation is used to derive a closed form expression for the displacement, and also to determine a circular damage-zone engulfing the crack-tip. Damage is assumed confined within this damage-zone and any damage outside the zone is neglected. For an embedded stationary crack subjected to remotely applied tensile loading (mode I), under plane strain conditions, the leading term of an asymptotic expression of the displacement is determined. Guided by the results of mode III, a circular damage-zone centered at the crack-tip is postulated.;A critical stress is determined and found to be proportional to a{dollar}\rm\sb0\sp{lcub}-1/(n+1){rcub}{dollar} for crack extension and growth, where a{dollar}\sb0{dollar} is the initial crack length and n is the strain hardening exponent. For fatigue crack propagation, a period of incubation (where damage accumulates without a crack extension) followed by a growth period and then failure are observed. The number of loading cycles required to cause the onset of crack growth and failure increases with reducing the external load and/or reducing the material parameters. For given material parameters, the influence of strain hardening on the number of cycles required for failure is revealed and shown graphically. In the steady-state creep, the incubation and growth periods that precede failure are also demonstrated. The elapsed time required to cause the onset of crack growth and failure is found to increase with a decrease in the external load, a decrease in the material parameter and/or an increase in the modular ratio. Variations of the normalized crack length with time are graphically exhibited.
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Type
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dissertation
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Source
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PQT Legacy CUNY.xlsx
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degree
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Ph.D.
