The interaction of dislocations with an applied stress in anisotropic crystals
De Wit, Gloria E.
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https://hdl.handle.net/2142/16611
Description
Title
The interaction of dislocations with an applied stress in anisotropic crystals
Author(s)
De Wit, Gloria E.
Issue Date
1959
Doctoral Committee Chair(s)
Koehler, J.S.
Department of Study
Physics
Discipline
Physics
Degree Name
Ph.D.
Degree Level
Dissertation
Keyword(s)
anisotropic crystals
Language
en
Abstract
"The differential equation of equilibrium is derived for a dislocation pinned at two points in the same glide plane in an elastically anisotropic crystal with an applied stress. It is assumed that the dependence of the dislocation energy on the geometry of the dislocation line is accounted for by using an energy per unit length, E, which for fixed Burgers vector is a function only of θ, the angle between the Burgers vector and the dislocation segment. A parametric solution of the differential equation is found in terms of E and its derivatives.
When the orientation dependence of E is approximated by that of the elastic energy per unit length of a long straight dislocation, numerical work done for some real face centered cubic and body centered cubic crystals indicates that the first few terms in a Fourier expansion give a good fit to E. Using this expansion, the solution of the differential equation is plotted in such a way that only one curve is needed to obtain the equilibrium shape of the dislocation for all values of the stress. Appreciable deviation from a circle is found.
The above information about dislocation shape versus applied stress, together with some simple assumptions concerning dislocation density enables one to calculate
the ""average"" strain produced in a crystal under applied stress when dislocations are present as compared to a crystal with no dislocations. Such a change in strain
would cause an apparent change in measured elastic moduli. The calculation is carried out for face centered cubic crystals and a numerical estimate of the result is made."
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