The stress field and energy of a three-dimensional dislocation loop at a crack tip
type: Item
instance of: scholarly article
title: The stress field and energy of a three-dimensional dislocation loop at a crack tip
zbMATH Open document ID: 0639.73033
DOI: 10.1016/0022-5096(87)90053-6
author: Peter M. Anderson
author: James R. Rice
published in: Journal of the Mechanics and Physics of Solids
publication date: 1987-01-01T00:00:00Z
review text: The self stress field and self energy are estimated for a planar three- dimensional dislocation loop emanating from a half-plane crack tip. While the problem is of greatest interest for analysis of shear loops nucleating from the crack tip in the concentrated stress field there due to applied loadings, it is addressed here in the interest of tractability for three-dimensional prismatic loops lying in the same plane as the crack. Exact elastic calculations for that case are based on recent developments of three-dimensional crack weight function theory and specific results are given for induced stress fields, intensity factors and energy of semicircular and rectangular prismatic dislocation loops. Also, self stresses and energy expressions are derived for the two- dimensional case of a line dislocation lying parallel to the crack for arbitrary Burgers vector type and general orientation of the dislocated plane relative to the crack plane, and those results are used together with the three-dimensional prismatic loop results to estimate approximately the self energy for three-dimensional shear dislocation loops emanating from the tip on planes inclined to the crack plane.
Mathematics Subject Classification ID: 74R05
Mathematics Subject Classification ID: 74G70
zbMATH DE Number: 4043390
zbMATH Keywords: approximate estimate of energy correction factor
zbMATH Keywords: self stress field
zbMATH Keywords: self energy
zbMATH Keywords: planar three-dimensional dislocation loop
zbMATH Keywords: half-plane crack tip
zbMATH Keywords: shear loops
zbMATH Keywords: intensity factors
zbMATH Keywords: semicircular
zbMATH Keywords: rectangular prismatic dislocation loops
zbMATH Keywords: line dislocation
Wikidata QID: Q56997577
MaRDI profile type: Publication
full work available at URL: 0022-5096(87)90053-6
OpenAlex ID: W1988266074
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cites work: Dislocations and Cracks in Anisotropic Elasticity
description: scientific article; zbMATH DE number 4043390