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Explicit Expressions for Stress Field of a Circular Dislocation Loop

N. Langdon
Journal / Anthology

Theoretical and Applied Fracture Mechanics
Year: 2000
Volume: 33
Page range: 219-231

It is known that general analytic solutions for simple curved dislocations are intractable. The objective of this work is to derive the explicit formulas for the components of the stress tensor of a circular dislocation loop. The formulas are obtained based on Peach-Koehler formula for the self-stress of a curved dislocation (J.P. Hirth, J. Lothe, Theory of Dislocations, Wiley, New York, 1982; R.W. Lardner, Mathematical Theory of Dislocations and Fracture, University of Toronto Press, Toronto, 1974). In process of deriving the formulas the comprehensive computational system 'Mathematica', version 3 (S. Wolfram, the Mathematica Book, Wolfram Media, Champaign IL/Cambridge University Press, Cambridge, 1996). is utilized. The symptotic formulas at infinity along with the formulas for the stress tensor of an infinitesimal circular dislocation loop are also obtained. The graphs showing the intricacy of the stress field in the vicinity of a dislocation loop accompany the paper.

*Engineering > Mechanical and Structural Engineering