The flow stress dependence on grain size during microstrain tests
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R. T. HOLT T H E w e l l - k n o w n Petch r e l a t i o n s h i p is n o r m a l l y used to d e s c r i b e the y i e l d or s u b s e q u e n t flow s t r e s s as a function of g r a i n s i z e . In the p r e s e n t c o m m u n i c a t i o n a s i m i l a r a n a l y s i s is applied to the m i c r o s t r a i n r e g i o n . Nickel s t r i p (99.98 pct Ni, containing 0.01 pct C) m a c h i n e d to s t a n d a r d t e n s i l e s p e c i m e n s , was given v a r i o u s s t r a i n - a n n e a l t r e a t m e n t s to p r o d u c e a r a n g e of g r a i n s i z e s . The m a t e r i a l can be e l e c t r o c h e m i c a l l y p o l i s h e d to a highly r e f l e c t i n g s u r f a c e in a solution c o n t a i n i n g 50 pct H3PO4, 30 pct H2SO4, and 20 pet HzO, o p e r a t i n g at 10 V and 10~ A g r a i n b o u n d a r y etch may then be obtained at 2 V for a p p r o x i m a t e l y 15 sec. If a polished s a m p l e is s i m i l a r l y etched at -15~ n o n g e o m e t r i c etch pits f o r m , f i r s t in the g r a i n bounda r i e s until the etched b o u n d a r y is continuous, followed by the f o r m a t i o n of a r e g u l a r a r r a y of pits within the grains, delineating subgrain boundaries. Further attack takes place over the whole s p e c i m e n s u r f a c e . Fig. 1 shows a s p e c i m e n with a g r a i n size of about 32 # m , and a s u b g r a i n size of about 13 /~m. The g r a i n s a r e equiaxed and the s p e c i m e n s contain no p r e f e r r e d o r i e n t a t i o n . In this study, s a m p l e s with an a v e r a g e g r a i n d i a m e t e r D of 20, 32, 48, 70, 120, and 200 p m had a v e r a g e s u b g r a i n d i a m e t e r s , D s , of 12, 13, 20, 24, 35, and 36 # m , r e s p e c t i v e l y . T e n s i l e t e s t s w e r e p e r f o r m e d u s i n g two foil gages (gage factor 2.1) c a r e f u l l y applied to each s p e c i m e n . F r o m each of the s t r e s s - s t r a i n c u r v e s the flow s t r e s s , or, was m e a s u r e d for a r a n g e of p l a s t i c s t r a i n s f r o m 10 • 10 -6 to 200 • 10 -6 . Fig. 2 shows two such r e s u l t s where the flow s t r e s s (at p l a s t i c s t r a i n s of 20 • 10 -6 and 100 • 10 -6) is plotted a g a i n s t the i n v e r s e s q u a r e root of the m e a n s u b g r a i n d i a m e t e r , and the m e a n g r a i n d i a m e t e r . A l i n e a r r e l a t i o n (within the e x p e r i m e n t a l s c a t t e r ) is obtained for a vs D s-1/2 for the higher d e f o r m a t i o n [curve (2)] but at the lower p l a s t i c s t r a i n the c u r v e (3) is d i s t i n c t l y n o n l i n e a r . T h i s i n d i c a t e s that P e t c h - t y p e b e h a v i o r e x i s t s at l a t e r s t a g e s in the m i c r o d e f o r m a t i o n r a n g e . On the s a m e graph, c u r v e (1) ~ vs D -1/z at a p l a s t i c s t r a i n of 100 • 10 -6 is also l i n e a r but the a g r e e m e n t at l a r g e g r a i n s i z e s is not so good as that obtained when using the s u b g r a i n diameter. A
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