The plastic zone in stage I crack growth during fatigue deformation of copper single crystals

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Fig. 4--Duplex-slip orientation: Dislocation microstructure on the conjugate plane. P r i m a r y and conjugate s c r e w d i s l o c a t i o n s s t r a d d l i n g the cell walls a r e s e e n in m a n y p l a c e s . A detailed a n a l y s i s of the B u r g e r s Vector of the d i s l o c a t i o n s u s i n g the o p e r a t i n g r e f l e c t i o n s g = 202, 111, 111, 022 showed the e x i s t e n c e of C o t t r e l l - L o m e r and Hirth locks in and n e a r the cell w a l l s . The f o r e s t d i s l o c a tion d e n s i t y is higher than in the c r y s t a l s of s i n g l e slip o r i e n t a t i o n and the f o r e s t d i s l o c a t i o n s occur m o s t l y in the cell walls. The d i s l o c a t i o n m i c r o s t r u c t u r e on the conjugate or ( i I 1 ) plane is shown in Fig. 4. The d i s l o c a t i o n m i c r o s t r u c t u r e is v e r y s i m i l a r to that on the p r i m a r y plane. The cell s t r u c t u r e is w e l l - d e v e l o p e d . The f o r e s t d i s l o c a t i o n d e n s i t y is high and the f o r e s t d i s l o c a t i o n s o u t l i n e the cell w a l l s . An a n a l y s i s of the B u r g e r s v e c t o r s of the d i s l o c a t i o n s u s i n g the o p e r a t i n g r e f l e c t i o n s g = i l l , 020, and 111 showed that m o s t of the d i s l o c a t i o n s have e i t h e r the p r i m a r y or the c o n jugate B u r g e r s v e c t o r s . D i s c u s s i o n . The m i c r o s t r u c t u r a l o b s e r v a t i o n s i n d i c a t e that the fatigue h a r d e n i n g and the s a t u r a t i o n s t r e s s i n c r e a s e as the d i s l o c a t i o n cell s t r u c t u r e changes f r o m a diffuse cell wall to one in which the cell w a l l s a r e s h a r p l y defined by a high d e n s i t y of f o r e s t d i s l o c a t i o n s and p r i m a r y edge dipoles. F o r e s t d i s l o c a t i o n s r e s t r i c t the motion of m o b i l e p r i m a r y d i s l o c a t i o n s by f o r m i n g s e s s i l e b a r r i e r s such as C o t t r e l l - L o m e r and Hirth locks as shown in Figs. 3 and 4. Hence, it is p r o b a b l e that the f a c t o r s that cont r i b u t e to an i n c r e a s e in f o r e s t d i s l o c a t i o n d e n s i t y also a c c e n t u a t e the f o r m a t i o n of the cell s t r u c t u r e . Thus, the s i n g l e c r y s t a l s of duplex s l i p o r i e n t a t i o n in which both p r i m a r y and conjugate s l i p a r e e q u a l l y favored show a m o r e s h a r p l y defined cell s t r u c t u r e as shown in Fig. 3 than the c r y s t a l s of s i n g l e - s l i p o r i e n t a t i o n in which slip o c c u r s p r e d o m i n a n t l y on the p r i m a r y p l a n e as shown in Fig. 2. The higher f o r e s t d i s l o c a t i o n d e n s i t y in the d u p l e x - s l i p o r i e n t e d c r y s t a l s also c o n t r i b u t e s to the i n t e r a c t i o n s t r e s s b e t w e e n the f o r e s t d i s l o c a t i o n s and p r i m a r y d i s l o c a t i o n s and i n c r e a s e s fatigue h a r d e n i n