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Theory of Dislocation Cells. II. Dislocation Multipoles

 

作者: J. Moore,   D. Kuhlmann‐Wilsdorf,  

 

期刊: Journal of Applied Physics  (AIP Available online 1971)
卷期: Volume 42, issue 3  

页码: 953-961

 

ISSN:0021-8979

 

年代: 1971

 

DOI:10.1063/1.1660192

 

出版商: AIP

 

数据来源: AIP

 

摘要:

The stresses of infinite edge dislocation multipoles are investigated with the aid of a B5500 computer, and contour maps are obtained using the line printer. These multipoles consist of infinitely long, parallel edge dislocations of same strength, arranged so as to define a prism whose cross section is a regular polygon and with their Burgers vectors in radial orientation. As will be shown in Part III, multipoles are the prototypes of dislocation cells containing the same Burgers vectors, independent of cell shape, in the same way that the quadrupole, discussed in Part I, is the prototype of all cells composed of dislocations involving two mutually perpendicular Burgers vectors. It is found that the stress fields of &tgr;rr, &tgr;&phgr;&phgr;, and &tgr;r&phgr;all exhibit 2Nsimilar leaves of alternating sign for a multipole ofNth order, except that &tgr;&phgr;&phgr;of the dipole has eight rather than the expected four leaves. The magnitude of the stresses falls as 1/rNat large distances, except that &tgr;&phgr;&phgr;of the dipole falls as 1/r4. Lastly, there exists a ``conservation of zero line'' rule to the effect that a fixed number of contours of vanishing stress passes each dislocation, independent ofN, the order of the multipole, namely, six zero contours of &tgr;&phgr;&phgr;and &tgr;r&phgr;, and two of &tgr;rr, respectively.

 

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