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Finite Dislocation Elements in Finite Media. I. Basic Theory
Author(s) -
Korner A.,
Svoboda P.,
Kirchner H. O. K.
Publication year - 1977
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.2220800205
Subject(s) - dislocation , planar , plane (geometry) , partial dislocations , foil method , moment (physics) , finite thickness , mathematics , physics , mathematical analysis , geometry , classical mechanics , materials science , condensed matter physics , mechanics , computer science , composite material , computer graphics (images)
The interaction of finite co‐planar dislocation pieces in a finite medium is considered with special reference to the case where two partial dislocations split trapezoidally in a thin foil. The calculation is carried out on the force and moment level. The presence of the surface is taken into account by Lothe's theorem. The remaining problem of the interaction of finite pieces in an infinite medium is considered in detail. It is shown that such problems require the execution of integrals involving only the energy E of dislocations (or interaction energy of parallel dislocations) within that plane — no derivatives of E are required. Formulae suitable for numerical evaluation are derived.