The fundamentals of non-singular dislocations in the theory of gradient elasticity: Dislocation loops and straight dislocations

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:50

Article

Lazar, Markus^1,2 

[1] Tech Univ Darmstadt, Dept Phys, Heisenberg Res Grp, D-64289 Darmstadt, Germany

[2] Michigan Technol Univ, Dept Phys, Houghton, MI 49931 USA

关键词: Dislocations;    Dislocation loops;    Gradient elasticity;    Size effects;    Green tensor;   

DOI  :  10.1016/j.ijsolstr.2012.09.017

来源: Elsevier

【 摘 要 】

The fundamental problem of non-singular dislocations in the framework of the theory of gradient elasticity is presented in this work. Gradient elasticity of Helmholtz type and bi-Helmholtz type are used. A general theory of non-singular dislocations is developed for linearly elastic, infinitely extended, homogeneous, and isotropic media. Dislocation loops and straight dislocations are investigated. Using the theory of gradient elasticity, the non-singular fields which are produced by arbitrary dislocation loops are given. 'Modified' Mura, Peach-Koehler, and Burgers formulae are presented in the framework of gradient elasticity theory. These formulae are given in terms of an elementary function, which regularizes the classical expressions, obtained from the Green tensor of the Helmholtz-Navier equation and bi-Helmholtz-Navier equation. Using the mathematical method of Green's functions and the Fourier transform, exact, analytical, and non-singular solutions were found. The obtained dislocation fields are non-singular due to the regularization of the classical singular fields. (C) 2012 Elsevier Ltd. All rights reserved.

【 授权许可】

Free