The flow and fracture of unidirectional
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e x t e n s i v e d e v e l o p m e n t a l e f f o r t s and the g r o w i n g u s e of o r i e n t e d f i b e r c o m p o s i t e m a t e r i a l s , only a l i m i t e d a m o u n t of e f f o r t h a s b e e n d i r e c t e d t o w a r d s d e v e l o p i n g an u n d e r s t a n d i n g of the p e r f o r m a n c e c h a r a c t e r i s t i c s of t h e s e m a t e r i a l s u n d e r the c o m p l e x s t r e s s s t a t e s e n c o u n t e r e d during a c t u a l s e r v i c e l o a d ing. On the b a s i s of the e x t e n s i v e s t u d i e s c o m p l e t e d to date, it i s g e n e r a l l y a g r e e d that the u s e of t h e s e m a t e r i a l s can be o p t i m i z e d u n d e r u n i a x i a l l o a d i n g s in t h e f i b e r d i r e c t i o n . In p r a c t i c e , h o w e v e r , it i s difficult to a c h i e v e p u r e u n i a x i a l l o a d i n g s . B e c a u s e of the loading r e q u i r e m e n t s of th e s t r u c t u r e of which the c o m p o s i t e i s a p a r t , and b e c a u s e of g e o m e t r i c i r r e g u l a r i t i e s (both i n t e r n a l and e x t e r n a l ) , a c t u a l s e r v i c e l o a d i n g s g e n e r a l l y c r e a t e b i - o r t r i - a x i a l s t r e s s s t a t e s in c o m p o s i t e s . While the u s e of c r o s s - p l y c o m p o s i t e l a m i n a t e s h as b e e n p r o m o t e d in an a t t e m p t to i m p r o v e the m u l t i a x i a l p e r f o r m a n c e of o r i e n t e d f i b e r c o m p o s i t e m a t e r i a l s , t h i s m a t e r i a l d e s i g n d o e s not r e m o v e the p r o b l e m of u n d e r s t a n d i n g the m u l t i a x i a l b e h a v i o r of the m a t e r i a l . Each individual ply i s s t i l l u n d e r a c o m p l e x s t a t e of loading. H e n c e , its i n d i v i d u a l c h a r a c t e r i s t i c s m u s t be r a t i o n a l i z e d b e f o r e th e c h a r a c t e r i s t i c s of the e n t i r e c o m p o s i t e can be fully u n d e r s t o o d . One of the m o s t i m p o r t a n t p a r t s of the u n d e r s t a n d i n g of the p e r f o r m a n c e of f i b e r c o m p o s i t e m a t e r i a l s u n d e r m u l t i a x i a l s t a t e s of s t r e s s is the c a p a b i l i t y of p r e d i c t ing the s t r e s s e s a n d / o r s t r a i n s at which p l a s t i c flow b e g i n s and the extent of the flow which can be e x p e c t e d f o r g i v en i n c r e m e n t a l l o a d i n g s . (The p r e s e n c e of the b r i t t l e f i b e r component of the c o m p o s i t e does not d i m i n i s h t h e i m p o r t a n c e of p l a s t i c flow a s a m o d e of m a terial failure.) PREVIOUS M U L T I A X I A L F A I L U R E STUDIES Of the s e v e r a l c r i t e r i a which h a v e been d e v e l o p e d f o r the p r e d i c t i o n of the o n s e t of p l a s t i c flow in a n i s o t r o p i c m a t e r i a l s , that of Hill 1 is p e r h a p s the m o s t w i d e l y known. T h i s c r i t e r i o n g e n e r a l i z e s the von M i s e s D i s t o r t i o n E n e r
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