On the origin of microcracking behind a crack tip
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I. INTRODUCTION S E V E R A L i n v e s t i g a t o r s have r e p o r t e d the p r e s e n c e of " s e c o n d a r y " or " s l i p - b a n d " m i c r o c r a c k s which i n t e r s e c t the m a i n f r a c t u r e s u r f a c e s a f t e r e i t h e r the fatigue f a i l u r e of many d i f f e r e n t a l l o y s 1"4 or a f t e r s t r e s s - c o r r o s i o n c r a c k i n g of an A1 alloy, s Such m i c r o c r a c k i n g is u s u a l l y o b s e r v e d on both faces of the f r a c t u r e s u r f a c e . However, B e a c h e m has shown that when the f r a c t u r e s u r f a c e is i n c l i n e d to the s t r e s s axis, m i c r o c r a c k i n g o c c u r s only on the bottom s u r face of an u p w a r d - s l o p i n g f r a c t u r e s u r f a c e ? B e a c h e m 1 and o t h e r s 3 s u g g e s t that these c r a c k s r e p r e s e n t def o r m a t i o n and local f r a c t u r e behind the c r a c k - t i p a f t e r the c r a c k has p a s s e d . Q u a l i t a t i v e a r g u m e n t s have b e e n p r e s e n t e d for the p r e s e n c e of such c r a c k s i n t e r m s of a n u m b e r of f a c t o r s including: the state of s t r e s s on a s u r f a c e i n c l i n e d to the s t r e s s axis, 1 " e l a s t i c b e n d i n g " of the c r a c k s u r f a c e , 3 and t e n s i l e s t r e s s e s developing b e e a n s e of d e f o r m a t i o n at the c r a c k tip. 3 The p u r p o s e of the p r e s e n t r e s e a r c h is to e x a m i n e the d i s t r i b u t i o n of n o r m a l s t r e s s e s a r o u n d mode I as well as mixed mode I and H c r a c k s in an e l a s t i c - p l a s t i c body in o r d e r to show that m i c r o c r a c k ing can be a n a t u r a l c o n s e q u e n c e of the c r a c k - t i p s t r e s s field of the m a i n c r a c k . We will then apply this concept to a n a l y z e b r i e f l y the c r y s t a l l o g r a p h y of s e c o n d a r y m i c r o c r a c k s in bee T i - 4 0 V alloy single c r y s t a l s and to point out that cleavage can o c c u r on {111} p l a n e s in a bee alloy u n d e r s p e c i a l c i r c u m stances. H. RESULTS AND DISCUSSION A. R e g a r d i n g C r a c k - T i p S t r e s s F i e l d s If m i c r o c r a c k i n g o c c u r s a f t e r the c r a c k has p a s s e d , then s i g n i f i c a n t t e n s i l e s t r e s s e s n o r m a l to p o t e n t i a l m i c r o c r a c k p l a n e s m u s t e x i s t behind the c r a c k tip. Given the c l o s e s p a c i n g b e t w e e n m i c r o c r a c k s in s o m e i n s t a n c e s 1'4 and the large s t r e s s e s n e c e s s a r y to i n i t i ate them, such c r a c k i n g m u s t i n i t i a t e n e a r the c r a c k M. G. STOUT and D. A. KOSS are Postdoctoral Research Associate and Professor, respectively, Department Met. Engineering,Michigan TechnologicalUniversity, Houghton, Mich. 49931. Manuscript submitted August 26, 1977. METALLURGICAL TRANSACTIONSA
tip, p r o b a b l y within the c r a c k - t i p p l a s t i c zone in c e r t a i n c a s e s . In o r d e r t
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