Line-integral representations for the elastic displacements, stresses and interaction energy of arbitrary dislocation loops in transversely isotropic bimaterials

INTERNATIONAL JOURNAL OF SOLIDS AND STRUCTURES

卷:50

Article

Yuan, J. H.¹  Pan, E.^2,3  Chen, W. Q.⁴ 

[1] Zhejiang Univ, Dept Civil Engn, Hangzhou 310058, Zhejiang, Peoples R China

[2] Zhengzhou Univ, Sch Mech Engn, Zhengzhou 450001, Peoples R China

[3] Univ Akron, Dept Civil Engn, Akron, OH 44325 USA

[4] Zhejiang Univ, Dept Engn Mech, Hangzhou 310027, Zhejiang, Peoples R China

关键词: Line integral;    Dislocation loop;    Transverse isotropy;    Hexagonal crystals;    Bimaterials;    Elastic fields;    Interaction energy;    Singularity;   

DOI  :  10.1016/j.ijsolstr.2013.06.017

来源: Elsevier

【 摘 要 】

The elastic displacements, stresses and interaction energy of arbitrarily shaped dislocation loops with general Burgers vectors in transversely isotropic bimaterials (i.e. joined half-spaces) are expressed in terms of simple line integrals for the first time. These expressions are very similar to their isotropic full-space counterparts in the literature and can be easily incorporated into three-dimensional (3D) dislocation dynamics (DD) simulations for hexagonal crystals with interfaces/surfaces. All possible degenerate cases, e.g. isotropic bimaterials and isotropic half-space, are considered in detail. The singularities intrinsic to the classical continuum theory of dislocations are removed by spreading the Burgers vector anisotropically around every point on the dislocation line according to three particular spreading functions. This non-singular treatment guarantees the equivalence among different versions of the energy formulae and their consistency with the stress formula presented in this paper. Several numerical examples are provided as verification of the derived dislocation solutions, which further show significant influence of material anisotropy and bimaterial interface on the elastic fields and interaction energy of dislocation loops. (C) 2013 Elsevier Ltd. All rights reserved.

【 授权许可】

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