The influence of elastic anisotropy on dislocation stability in /gb-tin and lead
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P R I O R to the work of de Wit and Koehler, x little was known concerning the equilibrium shape of a d i s l o c a tion line pinned at two points. It was commonly a s sumed that the equilibrium form of the pinned d i s l o c a tion line would be a s t r a i g h t line joining the pinning points. De Wit and Koehler showed, however, that in an a n l s o t r o p i c m a t e r i a l a s t r a i g h t dislocation line is not n e c e s s a r i l y in stable equilibrium when the line tension b e c o m e s negative. They c o n s i d e r e d s e v e r a l p o s s i b i l i t i e s for the final equilibrium shape, but it was Mullins, 2 using the Wulff construction analogy, who showed that the final shape of such d i s l o c a t i o n s is a s e r i e s of s t r a i g h t segments. There then r e s u l t e d two apparent c r i t e r i a for d i s location instability: the negative line tension c r i t e r i o n of de Wit and Koehler, and that of Mullins b a s e d upon the Wulff construction. Head s has c o n s i d e r e d both p r o cedures and showed that the de W i t - K o e h l e r argument iS a sufficient condition for instability, but is s o m e what r e s t r i c t i v e ; m o r e o v e r , Head showed that the ins t a b i l i t y range for a d i s l o c a t i o n is defined p r e c i s e l y by the points of common tangency a c r o s s a concavity in the i n v e r s e e l a s t i c e n e r g y Wulff plot (see also Frank4). Head then computed g e n e r a l t a b l e s for p r e dicting all dislocation i n s t a b i l i t i e s in cubic c r y s t a l s in t e r m s of the two a n i s o t r o p y constants, namely A
--
2Q4 C , ~ : Ct2 ' ( Z e n e r ' s Constant)
[1]
and B=
C11 + 2Cla
.
[2]
C44
To date, only a l i m i t e d number of m a t e r i a l s have been investigated. P e r h a p s the most thoroughly studied alloy is f l - b r a s s , which was investigated both theoC. L. VOLD, R. A. MASUMURA, and M. E. GLICKSMAN are Research Physicist, Research Metallurgist, and Supervisory Metallurgist, respectively, Transformations and Kinectics Branch, Metallurgy Division, Naval Research Laboratory, Washington, D.C. 20375. Manuscript submitted February 1, 1973. METALLURGICAL TRANSACTIONS
r e t t c a l l y and e x p e r i m e n t a l l y by Head, Loretto, and Humble. s'8 These i n v e s t i g a t o r s o b s e r v e d s h a r p l y bent dislocations in H-brass and, m o r e o v e r , showed that the o b s e r v e d orientations of the dislocation line s e g ments a g r e e well with the t h e o r e t i c a l p r e d i c t i o n s . F i s h e r and Alfred 7 then c o n s i d e r e d the effects of e l a s tic a n i s o t r o p y on dislocation behavior in a number of hexagonal close packed m e t a l s . Of the m e t a l s they considered, only titanium and z i r c o n i u m exhibited d i s locations with unstable orientations. Also, Routbort et al. s showed that unstable dislocations may also exi s t in the bcc alloy Fe-5.86 at. pct Si (see also Masum u r a et al. 9) and Chou and Sha 1~ examined s e v e r a l trigonal c
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