A theoretical model for creep crack growth

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INTRODUCTION I ~ E C O G N I T I O N that m a n y c o m p o n e n t s at high t e m p e r a t u r e s could f a i l due to c r e e p c r a c k growth has l e a d to m a n y i n v e s t i g a t i o n s on c r a c k growth b e h a v i o r u n d e r c r e e p conditions in t h e r m o s t r u c t u r a l m a t e r i a l s . M o s t of t h e s e i n v e s t i g a t i o n s 1-16 have b e e n c o n c e r n e d with c o r r e l a t i n g c r a c k growth r a t e s in t e r m s of s t r e s s i n t e n s i t y f a c t o r s or n o m i n a l s t r e s s a s w e l l as nonl i n e a r p a r a m e t e r s like J - i n t e g r a l o r C * - i n t e g r a l . 17 L e s s attention, h o w e v e r , is f o c u s e d on u n d e r s t a n d i n g the b a s i c m e c h a n i s m s of c r e e p c r a c k growth. Although the above i n v e s t i g a t i o n s have b e e n m o s t l y on e n g i n e e r i n g m a t e r i a l s with c o m p l e x m i c r o s t r u c t u r e s and p o s s e s s i n g d i v e r s e m e c h a n i c a l p r o p e r t i e s , s e v e r a l c o m m o n f e a t u r e s a s s o c i a t e d with c r e e p c r a c k growth can be e x t r a c t e d which could help e x p l a i n the m e c h a n i s m s of the c r a c k growth p r o c e s s . The m o s t i m p o r t ant o b s e r v a t i o n which is c o m m o n to a l l m a t e r i a l s is that the c r a c k growth is e s s e n t i a l l y of i n t e r g r a n u l a r t y p e . T h e c r a c k growth r a t e s a r e quite s e n s i t i v e to t e m p e r a t u r e and a few a u t h o r s have d i s c u s s e d the g r o w t h in t e r m s of a t h e r m a l l y a c t i v a t e d p r o c e s s , W h i l e the a c t i v a t i o n e n e r g y m e a s u r e m e n t s a r e not e x t e n s i v e , the a v a i l a b l e d a t a I~-~3 show that the e n e r g i e s a p p e a r to be within the r a n g e of g r a i n b o u n d a r y diffusion e n e r g i e s for t h e s e m a t e r i a l s . A n o t h e r c o m mon f e a t u r e a s s o c i a t e d with c r e e p c r a c k growth is a d e v e l o p m e n t of s e v e r e c r a c k tip c u r v a t u r e which inc r e a s e s with i n c r e a s e in t e m p e r a t u r e o r with i n c r e a s e in c r a c k length. Our r e c e n t w o r k ~ on A l l o y 718 showed s o m e a d d i t i o n a l i n t e r e s t i n g f e a t u r e s a s s o c i a t e d with c r e e p c r a c k growth p r o c e s s e s . F o r a given s t r e s s i n t e n s i t y v a l u e , c r a c k growth r a t e i n c r e a s e d s i g n i f i c a n t l y with i n c r e a s e in t e m p e r a t u r e f r o m 540 to 650~ but d e c r e a s e d o r i n c r e a s e d v e r y l i t t l e with K. SADANANDA is Research Metallurgist at the Thermostructural Materials Branch, Engineering Materials Division, Naval Research Laboratory, Washington, DC 20375. Manuscript submitted May 25, 1977. METALLURGICAL TRANSACTIONS A

f u r t h e r i n c r e a s e in t e m p e r a t u r e to 760~ The d e c r e a s e of the growth r a t e at 760~ a p p e a r s to be r e l a t e d to t