Stress states for {123} <111> multiple slip
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If the m a t e r i a l i s s u f f i c i e n t l y b r i t t l e , the stable p r o p agation will e v e n t u a l l y c h a r g e to unstable p r o p a g a t i o n (strong instability). It was found that notch d u c t i l i t y i s m a i n l y c o n t r o l l e d by two m a t e r i a l p a r a m e t e r s , n a m e l y a) the c r i t i c a l root p l a s t i c s t r a i n (e*) at which the m a t e r i a l s i m u l a t e s the i d eal p l a s t i c body, and b) the t o l e r a n c e f o r weak i n s t a b i l i t i e s which c o n t r o l s the e x t e n t of s t a b l e p r o p a g a t i o n along c h a r a c t e r i s t i c s . As the s t r e n g t h l e v e l i s i n c r e a s e d , e* d e c r e a s e s and the t o l e r a n c e f o r weak i n s t a b i l i t i e s a l s o d e c r e a s e s . T h i s m e a n s that the length of stable p r o p a g a t i o n path d e c r e a s e s . It is s u g g e s t e d that the " p l a s t i c s t r e t c h z o n e " c o r r e s p o n d s to the l o g a r i t h m i c path of stable c r a c k p r o p agation p r i o r to unstable p r o p a g a t i o n , in which f r a c t u r e is e f f e c t e d by i n t e n s e l y l o c a l i z e d d e f o r m a t i o n in t h e s e d i r e c t i o n s of pure s h e a r . Since the notch d u c t i l i t y a l s o depends on E*, it is not e x p e c t e d , in g e n e r a l , to be able to p r e d i c t p r e c i s e l y the K1c value f r o m a p a r a m e t e r r e l a t e d only to the t o l e r a n c e f o r weak i nstabilities.
Stress States for {123} (111} Multiple Slip
note we p r e s e n t the list of s t r e s s s t a t e s f o r (123}(111) sl i p , a p p r o p r i a t e f o r b cc c r y s t a l s . The {123}(111) s y s t e m s a r e defined in Table I and i l l u s t r a t e d in Fig. 1. F o r a set of s t r e s s e s (rij the r e s o l v e d s h e a r s t r e s s T1 on a given slip s y s t e m l can be w r i t t e n 1
G. Y. CHIN AND B. C. WONSIEWICZ
1. C. D. Beachemand D. A. Meyn:IllustratedGlossaryof Fractographic Terms; Section 2, NavalResearchLaboratory MemorandumReport 1547, June, 1964. 2. W.A. Spitzig,G. E. Pellisier,C. D. Beacham,A. J. Brothers, M. Hill, and W. R. Warke: Am. Soc. Testing Mater., Spec.Tech. Publ No. 453, 1969. 3. W. A. Spitzig: Trans. ASM, 1968,vol. 61, p. 344. 4. W. W.Gerberichand P. L. Hemmings:Trans. ASM, 1969, vol.62, p. 540. 5. C. A. Griffisand J. W. Spretnak: Trans. Iron and Steellnstitute of Japan, vol. 9, No. 5, 1969, p. 372.
PREVIOUSLYBishop 1 h a s
d e v e l o p e d a l i s t of s t r e s s s t a t e s which could a c t i v a t e s i m u l t a n e o u s l y five o r m o r e {111}(110) slip s y s t e m s r e q u i r e d f o r an a r b i t r a r y shape change of a d e f o r m i n g c r y s t a l . By invoking Bishop and H i l l ' s p r i n c i p l e of m a x i m u m w o r k 2 one can then s e l e c t the a p p r o p r i a t e s t r e s s s t a t e ( s ) , hence the a c t i v e slip s y s t e m s , f o r a given d e f o r m a t i o n . H o s f o r d and Chin 3 have obtained the list of s t r e s
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