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A Method for Computation of Equilibrium Dislocation Configurations
Author(s) -
Shtolberg A. A.
Publication year - 1971
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.2220430209
Subject(s) - dislocation , computation , ordinary differential equation , mathematics , line (geometry) , mathematical analysis , differential equation , physics , geometry , algorithm , condensed matter physics
A numerical method for the solution of non‐linear integro‐differential equations typical for problems on equilibrium dislocation configurations is developed which makes it possible to pass to the ordinary differential equations at every step of the iterative procedure. The presented method contrary to the existing ones provides automatic computation of the equilibrium dislocation shapes and guarantees the equilibrium (with given precision) of all the points of the dislocation line. As an example a problem has been solved which is of importance for the dislocation theory of dispersion strengthening, concerning a dislocation breaking through an array of obstacles. The dependence of the critical applied stress (at which the dislocation becomes unstable) both on the concentration of obstacles and their size is obtained, which is in accordance with the experimental data. In conclusion possible applications and modifications of the method are discussed, which can be used in different (not only dislocation) problems.