Mechanical Engineering ETDs

Publication Date

12-6-1978

Abstract

A complete elastic-plastic solution for both small and large scale yielding is found for the total stress field surrounding a tensile crack in an infinite sheet of strain-hardening materials under conditions of plane stress. The solution is based on the deformation theory of plasticity in conjunction with strain-hardening stress-strain relations, and is found by using the minimum of a modified complimentary energy principle coupled with a modified Ritz method. Numerical results are obtained for two approximate constitutive laws; a Ramberg-Osgood stress-strain relation and a modified Ramberg-Osgood stress-strain relation. Results indicate that the total stresses are discontinuous as the crack tip and unbounded as the crack tip is approached from the far field. Also, a decrease in strain-hardening reduces the magnitude or the stress in the crack tip region when unloading does not take place.

Using tlhe elastic-plastic stresses, the plastic zone is determined, the Budiansky’s criterion for the acceptability of deformation theory checked and the magnitude of the deformations in the crack tip region examined. The complete solution is compared, with reasonable agreement, to the singular solution of Hutchinson, the numerical solution of Hilton and Sih, the experimental results of Gerberich, and Swellow and Gerberich, and the J integral study of Hickerson.

Degree Name

Mechanical Engineering

Level of Degree

Doctoral

Department Name

Mechanical Engineering

First Committee Member (Chair)

Youn-Chang Hsu

Second Committee Member

Frederick Dsuin Ju

Third Committee Member

Steven Arthur Pruess

Fourth Committee Member

William Ernest Baker

Document Type

Dissertation

Language

English

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