A notch analysis of fracture approach to fatigue crack propagation
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FATIGUE
c r a c k p r o p a g a t i o n is a highly localized p h e n o m e n o n . The events in a s m a l l , c r i t i c a l l y s t r e s s e d volume of m a t e r i a l ahead of the c r a c k tip a r e c r u c i a l where the cyclic f a i l u r e i n i t i a t e s and the growth p r o c e s s c o n t i n u e s . The p r o c e s s of c r a c k growth is gene r a l l y b e l i e v e d to involve p l a s t i c b l u n t i n g and r e s h a r p e n i n g of the c r a c k tip which also e x p l a i n s the f o r m a t i o n of ductile s t r i a t i o n s on f r a c t u r e s u r f a c e s of c e r t a i n m a t e r i a l s . 1 The p l a s t i c enclave a r o u n d the c r a c k tip c o n t a i n i n g r e s i d u a l c o m p r e s s i v e s t r e s s e s is also involved in ' c l o s u r e ' a r g u m e n t s 2,s p r e s e n t e d r e cently for e x p l a i n i n g the effect of m e a n s t r e s s , v a r i a ble s t r e s s ampIitude, and n o n p r o p a g a t i o n of fatigue cracks. The plastic deformation characteristics alone, however, do not suffice to explain the c r a c k growth b e h a v i o r in different m a t e r i a l s at d i f f e r e n t s t r e s s a m p l i t u d e s . The Y o u n g ' s modulus, E, i n s t e a d of the yield s t r e s s , o-II, s e e m s to be a d o m i n a n t p a r a m e t e r and P e a r s o n 4 s p e c u l a t e s that e l a s t i c d e f o r m a t i o n plays a s i g n i f i c a n t role at lower s t r e s s a m p l i t u d e s . The a u t h o r s have r e c e n t l y invoked the idea of a volum e t r i c s i z e effect at the c r a c k tip. s,6 A c c o r d i n g l y , fatigue c r a c k p r o p a g a t i o n is viewed as a function of the local b e h a v i o r of m a t e r i a l in the highly s t r e s s e d v o l u m e ahead of the c r a c k tip. They suggested that the s t r e n g t h and d e f o r m a t i o n c h a r a c t e r i s t i c s of the highly s t r e s s e d volume should be r e g a r d e d as a function of the volume s i z e , which, in t u r n , is a function of the applied s t r e s s amplitude. Consequently, n e a r the t h r e s h o l d l e v e l of s t r e s s amplitude, the l i n e a r d i m e n sion of the c r i t i c a l l y s t r e s s e d volume b e c o m e s s m a l l e r than the a v e r a g e s p a c i n g between defects (~- 0.025 /an).*
hesive s t r e n g t h , Oc, and the c r a c k a d v a n c e s by b r i t t l e f r a c t u r e of the a t o m i c bonds. Such a notion has r e suited in a f a i r l y a c c u r a t e q u a n t i t a t i v e d e s c r i p t i o n of the t h r e s h o l d condition for fatigue c r a c k p r o p a g a t i o n 5 and the notch fatigue l i m i t s of d i f f e r e n t m a t e r i a l s . The m a i n objective of this p a p e r is to p r e s e n t a detailed d e s c r i p t i o n of the above m e n t i o n e d fatigue model and its a p p l i c a b i l i t y in the a r e a of fatigue c r a c k p r o p a g a tion. F a t i g u e c r a c k growth has been a n a l y z e d e x t e n s i v e l y d u r i n g r e c e n t y e a
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