An analysis of non-propagating fatigue cracks
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AND
V. WEISS
An a n a l y s i s f o r the f o r m a t i o n of n o n p r o p a g a t i n g fatigue c r a c k s at (the b a s e of V - s h a p e d ) notch r o o t s , b a s e d on the c o n s i d e r a t i o n s of the e x t e n t of the c r i t i c a l l y s t r e s s e d r e g i o n a h e a d of a notch o r a c r a c k t i p , and t h e r e s u l t i n g v o l u m e t r i c s t r e n g t h effect, i s d e v e l o p e d . A s s u m i n g that the m i n i m u m l o c a l c y c l i c s t r e s s r e q u i r e d f o r c r a c k i n i t i a t i o n f r o m a notch r o o t i s equal to the unnotched fatigue l i m i t , a e, and that the m i n i m u m l o c a l c y c l i c s t r e s s r e q u i r e d f o r the p r o p a g a t i o n of the c r a c k is equal to the t h e o r e t i c a l s t r e n g t h of the m a t e r i a l , a c , a m o d e l of notch f a t i g u e l i m i t is p r o p o s e d that shows that n o n p r o p a g a t i n g c r a c k s should f o r m a t the notch b a s e if p _< Po, a c r i t i c a l r o o t r a d i u s , p r o v i d e d the notch is s u f f i c i e n t l y deep, i . e . d >_ Pp. T h e r a d i u s Po is a m a t e r i a l c o n s t a n t and can be e s t i m a t e d f r o m known m a t e r i a l p r o p e r t i e s . The e s t i m a t e d v a l u e s of P0 a r e in f a i r l y good a g r e e m e n t with a v a i l a b l e e x p e r i m e n t a l v a l u e s f o r s t e e l s and p u r e c o p p e r . F o r s t r e s s e s n e a r the notch fatigue l i m i t it is s u g g e s t e d that Po be r e g a r d e d a s a r a d i u s above which notch fatigue l i m i t is e s s e n t i a l l y i n i t i a t i o n c o n t r o l l e d and below which e s s e n t i a l l y p r o p a g a t i o n c o n t r o l l e d . The notch fatigue l i m i t b a s e d on c o m p l e t e f r a c t u r e can then be e s t i m a t e d m o r e a c c u r a t e l y with m i l d a s well a s s h a r p n o t c h e s .
IN
a r e c e n t p a p e r the a u t h o r s d e r i v e d an e x p r e s s i o n f o r the t h r e s h o l d condition f o r f a t i g u e c r a c k p r o p a g a tion. x The b a s i s for t h e i r m o d e l w a s t h a t the l o c a l s t r e n g t h a h e a d of the fatigue c r a c k r e a c h e s the t h e o r e t i c a l s t r e n g t h , a c , a s the l i n e a r d i m e n s i o n of the c r i t i c a l l y s t r e s s e d v o l u m e b e c o m e s s m a l l e r than the d i s t a n c e b e t w e e n d e f e c t s , p ~ = 2504. A c c o r d i n g l y , the t h r e s h o l d n o m i n a l s t r e s s , a o ( a ) , f o r the p r o p a g a tion of a f a t i g u e c r a c k of length, a, i s given by 2
a o. a . f ( a / w )
3
2
= -~ac " P ' F ,
[1]
w h e r e f ( a / w ) is a d i m e n s i o n l e s s c o r r e c t i o n f a c t o r for f i n i t e width, w, of the s p e c i m e n . The r e l a t i o n s h i p above i s in good a g r e e m e n t with e x p e r i m e n t a l r e s u l t s for a c = 0.1E and p*F = 250A (0.025/~m) w h e r e E is Young's m o d u l u s . The p r o p o s e d m o d e l ~ can
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