The elastic field of periodic dislocation networks
- 1 May 1976
- journal article
- research article
- Published by Taylor & Francis in Philosophical Magazine
- Vol. 33 (5) , 825-841
- https://doi.org/10.1080/14786437608221918
Abstract
It is shown that techniques developed by Nye, Kröner, Bilby, Bullough and Smith for continuum distributions of dislocations can be applied to planar periodic distributions of discrete dislocations. The rotation field can be calculated as a Fourier sum and, in some cases, even as a closed expression. The calculation is valid for large rotations and anisotropic elasticity. The stress (strain) field is calculated in the approximation of isotropic elasticity either as a Fourier sum or in some cases as a closed expression. Furthermore, it is shown that the stress (strain) field of a periodic planar distribution of dislocations consists of a long-range stress (strain) field uniform in each half space around the plane of the dislocation distribution and a short-range stress (strain) field decreasing exponentially with distance. It is also shown that energy problems can be treated simply and accurately. Applications to practical cases are considered.Keywords
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