Theory of deformation of eutectic composites during temperature changes under controlled external displacements
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a r e c e n t p a p e r 1 a method f o r c a l c u l a t i n g the m e c h a n i c a l d e f o r m a t i o n s of t h e r m a l l y cycled e u t e c t i c composites, assuming elastic-plastic matrix deformation, was p r o p o s e d . While not e x p l i c i t l y s t a t e d t h e r e , the d e r i v e d a n a l y s i s was for the c a s e of c o n t r o l l e d e x t e r n a l (applied) loading. This type of b o u n d a r y c o n d i tion is p r e s e n t in c e r t a i n s i t u a t i o n s , but in o t h e r s the applied d i s p l a c e m e n t , not the applied load, is d e t e r m i n e d by the p a r t i c u l a r a p p l i c a t i o n . As shown below, these two c l a s s e s of b o u n d a r y c o n d i t i o n s - - c o n t r o l l e d d i s p l a c e m e n t and c o n t r o l l e d l o a d - - m u s t be c a r e f u l l y d i s t i n g u i s h e d , as the n a t u r e of and f a c t o r s c o n t r o l l i n g the c o m p o s i t e d e f o r m a t i o n a r e m a r k e d l y d i f f e r e n t in the two c a s e s . An i l l u s t r a t i o n i n v o l v i n g two p o s s i b l e a p p l i c a t i o n s of e u t e c t i c c o m p o s i t e s m a k e s the d i f f e r e n c e in b o u n d a r y c o n d i t i o n s m o r e c l e a r . The p r e s e n t m a j o r p r o j e c t e d u s e s of e u t e c t i c c o m p o s i t e s a r e in the h i g h - t e m p e r a t u r e stage of gas t u r b i n e s and in r o c k e t e n g i n e s . A e u t e c t i c t u r b i n e blade is fixed only at the b a s e and c a n expand and c r e e p f r e e l y within d e s i g n l i m i t s . The l o a d ing on the blade is d e t e r m i n e d p r i n c i p a l l y by c e n t r i f u g a l f o r c e s . T h e r e f o r e the e x t e r n a l l y i m p o s e d b o u n d a r y c o n d i t i o n is one of c o n t r o l l e d (but not n e c e s s a r i l y c o n s t a n t ) loading. A l t e r n a t i v e l y , the e u t e c t i c c o m p o s i t e m i g h t be used as a t u r b i n e v a n e . In m a n y a p p l i c a t i o n s v a n e s a r e attached at both ends to the s u r r o u n d i n g s t r u c t u r e ; t h e i r l o n g i t u d i n a l length change is not f r e e , as for the b l a d e s , but i s c o n s t r a i n e d to a d i s p l a c e m e n t d e t e r m i n e d by the t h e r m a l - e x p a n s i o n p r o p e r t i e s of the e n g i n e ' s s t r u c t u r e . In m o s t u s e s of c o m p o s i t e s c o m p a r a b l e s i t u a t i o n s a r e p r e s e n t . A p a r t attached to a c o n s t r a i n t only at one end is d e f o r m e d in c o n t r o l l e d l o a d i n g d u r i n g t e m p e r a t u r e changes, while a p a r t a t t a c h e d at both ends to a m a s s i v e s t r u c t u r e is d e f o r m e d in c o n t r o l l e d d i s p l a c e m e n t . This p a p e r extends the a n a l y s i s p r e v i o u s l y developed for c o n t r o l l e d loading to c o n t r o l l e d - d i s p l a c e m e n t d e f o r m a t i o n d u r i n g t e m p e r a t u r e c h a n g e s . The a p p r o a c h
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