Peierls-Nabarro hardening in the presence of point obstacles
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In light of the controversy that has existed between proponents of Peierls-Nabarrohardening and dispersed barrier hardening with regard to possible low temperature deformation mechanisms in bcc and hcp metals, this paper examines the effect of point obstacles on PeierlsNabarro hardening. The statics of double kink nucleation over Peierls barrier on finite dislocation segments are studied in detail. Point obstacles such as interstitial impurity atoms are considered to limit the length of the dislocation segments. Adopting the rate theory approach, temperature dependence of the yield stress is then investigated as a function of the concentration of point obstacles. It is found that point obstacles have little or no effect on double kink nucleation processes, when the applied stress is near the Peierls stress or at low test temperatures. At lower applied stresses or at higher test temperatures, the present results are significantly different from predictions of the Dorn-Rajnak calculation. In the present theory, the applied stress on the dislocation, T, is found to be finite and independent of test temperature in dilute solid solutions at elevated temperatures where the Dorn-Rajnak theory predicts vanishing T. This apparent "athermal" component of T increases linearly with the concentration of point obstacles, whereas temperature dependent part of ~- decreases. These predictions are consistent with experimental observations on iron-base alloys. A g r e a t deal of attention has b e e n devoted to a s c e r tain operative m e c h a n i s m s of low t e m p e r a t u r e p l a s t i c d e f o r m a t i o n in both bcc m e t a l s and such hcp m e t a l s a s t i t a n i u m and z i r c o n i u m . Two p r i n c i p a l c l a s s e s of m e c h a n i s m s d i s c u s s e d widely a r e d i s p e r s e d b a r r i e r h a r d e n i n g (DBH) and P e i e r l s - N a b a r r o h a r d e n i n g (PNH). I m p o r t a n t f e a t u r e s of these m o d e l s as well as the e x i s t e n c e a n d / o r n o n - e x i s t e n c e of e x p e r i m e n t a l support f o r them have been r e v i e w e d e x t e n s i v e l y . '-6 At p r e s ent, however, n e i t h e r theory can a c c o u n t for all the i m p o r t a n t p l a s t i c p r o p e r t i e s of these m e t a l s . The p r e s e n t i n v e s t i g a t i o n has e x a m i n e d a p o s s i b l e s t r e n g t h e n i n g model in which l o c a l i z e d o b s t a c l e s and P e i e r l s b a r r i e r s a r e c o n s i d e r e d in c o m b i n a t i o n . In o r d e r to p r e d i c t yield s t r e s s - t e m p e r a t u r e r e l a t i o n s as a function of defect c o n c e n t r a t i o n for the model cons i d e r e d , we i n v e s t i g a t e d the e n e r g e t i c s of double kink n u c l e a t i o n o v e r a P e i e r l s b a r r i e r with the r e q u i r e m e n t that this p r o c e s s o c c u r s on finite r a t h e r than infinite d i s l o c a t i o n s e g m e n t s . It will be shown that a finite loop length m u s t be c o n s i d e r e d b e c
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