Yield locus of random-textured fcc metals calculated with lower-bound assumptions
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Table I. Lower Bound Calculations for = o2/o,
I. J. P. Hickerson and R. W. Hertzberg: Met. Trans., 1972, vol. 3, pp. 179-89.
Authors' Reply C. BATHIAS A N D R. M. P E L L O U X
The a u t h o r s a g r e e with Dr. H e r t z b e r g that the fatigue c r a c k growth r a t e s should be in s o m e way r e l a t e d to the c y c l i c s t r e s s - s t r a i n b e h a v i o r of the m a t e r i a l w i t h in the r e v e r s e d p l a s t i c zone and n e a r the c r a c k tip. H o w e v e r , at t h i s t i m e t h e r e i s no sound t h e o r y which c o r r e l a t e s n', the c y c l i c w o r k h a r d e n i n g c o e f f i c i e n t with m , the s l o p e of the (dl/dn, AK) c u r v e . F u r t h e r m o r e , it will be n e c e s s a r y to m e a s u r e n' for a c y c l i c d e f o r m a t i o n h i s t o r y defined by the p l a s t i c s t r a i n d i s t r i b u t i o n within the r e v e r s e d p l a s t i c zone. T h i s v a l u e of n' could b e quite d i f f e r e n t f r o m the n' m e a s u r e d on a s t a b i l i z e d c y c l i c s t r e s s - s t r a i n c u r v e . At t h i s point we do not think that n' m a r t e n s i t i c i s g r e a t e r than n ' a u s t e n i t i c . We have m e a s u r e d s o m e v e r y high c y c l i c s t r a i n h a r d e n i n g c o e f f i c i e n t s in a 301 a u s t e n i t i c s t a i n l e s s s t e e l in the M D - M S t e m p e r a t u r e r a n g e (see Scripta Metallurgica, vol. 7, 1973, pp. 657-60) Howe v e r , the s l o p e , m , of t h e s e a u s t e n i t i c s t e e l s was a l w a y s g r e a t e r than the s l o p e , m , of d i f f e r e n t m a r t e n s i t i c s t e e l s . It a p p e a r s f r o m s o m e of o u r o t h e r w o r k that the s l o p e , m , m a y be m o r e d e p e n d e n t on the l e v e l of r e s i d u a l s t r e s s e s on the flank of the c r a c k and n e a r the c r a c k t i p than on the c y c l i c w o r k h a r d e n i n g c o e f f i c i e n t n'.
Yield Locus of Random-Textured fcc Metals Calculated with Lower-Bound Assumptions W. F. HOSFORD An u p p e r bound y i e l d l o c u s c a l c u l a t i o n was r e c e n t l y m a d e for r a n d o m - t e x t u r e d fcc m e t a l s d e f o r m i n g b y {111} s l i p / The m e t h o d of the c a l c u l a t i o n followed that of Bishop and Hill 2 and t h e r e f o r e u t i l i z e d the a s s u m p t i o n that the s t r a i n s in e a c h g r a i n w e r e the s a m e . T h i s note c o n c e r n s the c o r r e s p o n d i n g l o w e r - b o u n d y i e l d l o c u s c a l c u l a t i o n f o r r a n d o m - t e x t u r e d fcc m e t a l s d e f o r m i n g by {111} s l i p . The a3 = 0 s e c t i o n of the l o c u s is c a l c u l a t e d a s s u m i n g that the r a t i o of p r i n c i p a l s t r e s s e s a = a2/a x to be the s a m e in e a c h g r a i n . The l e v e l s of a,/~-, (v is the c r i t i c a l s h e a r s t r e s s f o r slip), n e c e s s a r y to a c t i v a t e the m o s t highly s t r e s s e d s l i p s y s t e m a r e c o m p u t e d
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