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Energy of polygonal and elliptical dislocation loops
Author(s) -
Liu G. C. T.,
Li J. C. M.
Publication year - 1966
Publication title -
physica status solidi (b)
Language(s) - English
Resource type - Journals
SCImago Journal Rank - 0.51
H-Index - 109
eISSN - 1521-3951
pISSN - 0370-1972
DOI - 10.1002/pssb.19660180205
Subject(s) - ellipse , dislocation , isotropy , planar , geometry , peierls stress , strain energy , elastic energy , cylinder , anisotropy , crystallography , materials science , condensed matter physics , physics , dislocation creep , mathematics , chemistry , optics , thermodynamics , computer graphics (images) , finite element method , computer science
A general expression for the elastic strain energy of an arbitrary N ‐sided planar polygonal dislocation loop is obtained from the stress field of dislocation segments using isotropic elasticity. This expression can be used to approximate the energy of any curved dislocation loop to any degree of accuracy. For example, the energies of regular polygonal dislocation loops and irregular polygonal dislocation loops inscribed in several ellipses are calculated and, by extrapolating to N = ∞, are shown to agree with the energies of circular and elliptical dislocation loops for which simple analytical expressions are available. The equilibrium shape of elliptical loops and the possibility of reorientation of these loops along a glide cylinder are consistent with experimental results in h.c.p., b.c.c., and f.c.c. crystals and in α‐uranium. The effect of anisotropy in h.c.p. metals is calculated for large elliptical loops in the basal plane.