Diffusion controlled stress rupture of polycrystalline materials
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The high t e m p e r a t u r e s t r e s s r u p t u r e p r o c e s s in p o l y c r y s t a l l i n e solids is e x a m i n e d in t e r m s of g r a i n b o u n d a r y p a r t i n g by v a c a n c y c o n d e n s a t i o n at the tip of a c r a c k within the b o u n d a r y . The g r a d i e n t for diffusion of these defects is c o n s i d e r e d in the m o d e l to a r i s e f r o m the s t r e s s g r a d i e n t in advance of the flaw tip. A r u p t u r e s t r e s s function is d e r i v e d which is shown to c l o s e l y d e s c r i b e the s t r e s s r u p t u r e b e h a v i o r of a n u m b e r of m e t a l s and high t e m p e r a t u r e alloys. SEVERAL of the features of the sintering process for the densification of powders to polycrystalline solids suggest that the inverse process--unsintering--may play an important role in determining the stress rupture properties of a number of polycrystalline mater i a l s at high t e m p e r a t u r e s . The p r e s e n t work a n a l y z e s such a p r o c e s s , develops a model to be c o m p a r e d with e x p e r i m e n t and d r a w s c o m p a r i s o n s b e t w e e n this model and o t h e r s which have b e e n p r o p o s e d for the t i m e dependent f a i l u r e of m a t e r i a l s which r u p t u r e p r i m a r i l y by n o n p l a s t i c p r o c e s s e s .
BASIS FOR THE MODEL With r e f e r e n c e to Fig. l(a) a notch is p r e s u p p o s e d to e x i s t within or on the s u r f a c e of a p o l y c r y s t a l l i n e body and is located on the g r a i n b o u n d a r y b e t w e e n adj a c e n t g r a i n s of the body. In p r a c t i c e such a defect m a y a r i s e f r o m s u r f a c e d a m a g e or f r o m i m p r o p e r p r o c e s s i n g and is, in g e n e r a l , s t r e n g t h l i m i t i n g for the body. For the p u r p o s e s of the model it is i m p o r t a n t to c o n s i d e r the defect to be located on or n e a r a g r a i n b o u n d a r y s i n c e diffusional t r a n s p o r t by b o u n d a r y m e c h a n i s m s is g e n e r a l l y f a s t e r than that of the bulk, the a t o m i c a l l y i m p e r f e c t r e g i o n s of the b o u n d a r y exhibit l e s s i n t r i n s i c cohesive s t r e n g t h s than bulk l a t t i c e r e gions and thus m a y be s o u r c e s of w e a k n e s s and the b o u n d a r y m a y act as a s o u r c e or sink for l a t t i c e d e fects. Diffusional d r i v i n g f o r c e s can be e s t a b l i s h e d such that a t o m s will leave the s u r f a c e root s e c t i o n s of the Jnotch and deposit on or n e a r the g r a i n b o u n d a r y . As m a t t e r l e a v e s this r e g i o n the notch p r o g r e s s e s t o w a r d s the i n t e r i o r of the s a m p l e and the c a p a b i l i t y of the notch to c o n c e n t r a t e applied s t r e s s e s i n c r e a s e s . C o n c e n t r a t i o n of this s t r e s s to l a r g e r than a c r i t i c a l v a l u e leads to n e a r sound v e l o c i t y p r o p a g a t i o n of the c r a c k and r u p t u r e .
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