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I N E L A S T I C deformation analysis for s t r u c t u r e s used at elevated temperature has traditionally been done u s i n g e m p i r i c a l constitutive relations d e r i v e d from s i m p l e laboratory t e s t s such as c r e e p at c o n s t a n t load, o r deformation at c o n s t a n t s t r a i n r a t e . T h e s e c o n s t i t u t i v e r e l a t i o n s e x p r e s s the s t r a i n r a t e of t h e m a t e r i a l , o r o f t e n s e v e r a l c o m p o n e n t s o f it, a s f u n c t i o n s of h i s t o r y v a r i a b l e s s u c h a s t i m e o r s t r a i n .1 A l t h o u g h t h i s t r a d i t i o n a l a p p r o a c h to c o n s t i t u t i v e r e l a t i o n s h a s b e e n r e a s o n a b l y s u c c e s s f u l in h a n d l i n g def o r m a t i o n d u r i n g s i m p l e l o a d i n g h i s t o r i e s w h i c h do not i n v o l v e l a r g e c h a n g e s i n t h e a p p l i e d l o a d s o r t h e t e m p e r a t u r e with t i m e , it o f t e n p r o v e s u n s a t i s f a c t o r y for handling the complex loading histories routinely e n c o u n t e r e d in r e a l o p e r a t i n g s y s t e m s . Recently t h e r e has been an effort t o reformulate c o n s t i t u t i v e l a w s f o r m a t e r i a l b e h a v i o r i n t e r m s of s t a t e v a r i a b l e concepts.Z'~ I n t h i s a p p r o a c h t h e s t a t e o f t h e m a t e r i a l i s c h a r a c t e r i z e d by o n e o r m o r e i n t e r n a l v a r i a b l e s w h i c h c a n be m e a s u r e d i n a s u i t a b l e e x p e r i m e n t , a n d the c o n s t i t u t i v e e q u a t i o n i s w r i t t e n a s a f u n c t i o n o f t h e s e s t a t e v a r i a b l e s as well as t h e e x t e r n a l variables, s t r e s s and temperature. E x p e r i m e n t a l r e s u l t s h a v e s h o w n that t h e s t a t e s p r o d u c e d i n a m a t e r i a l by w o r k h a r d e n i n g d u r i n g m o n o tonic plastic deformation can with some restrictions be a d e q u a t e l y d e s c r i b e d by t h e u s e of a s i n g l e s t a t e v a r i a b l e . 2-4 D i f f e r e n t a u t h o r s h a v e u s e d d i f f e r e n t d e f i n i t i o n s f o r t h i s v a r i a b l e , but a U of t h e m h a v e i n c o m m o n that t h e v a r i a b l e u s e d i s s o m e m e a s u r e of the c u r r e n t f l o w s t r e s s o r l e v e l o f w o r k h a r d e n i n g in t h e m a t e r i a l . S i n c e cyclic d e f o r m a t i o n also h a r d e n s a m a t e r i a l , i t o f f e r s a n a l t e r n a t i v e p a t h by w h i c h t o p r o d u c e v a r i o u s l e v e l s of f l o w s t r e s s i n t h e m a t e r i a l . I f t h e s i n g l e s t a t e v a r i a b l e a p p r o a c h is c o m p l e t e , t h e n t h e c y c l i c h a r d e n i n g m u s t be e q u i v a l e n t t o m o n o t o n i c w o r k h a r d e n i n g , a n d a m a t e r i a l h a r d e n e d by c y c l i c d e f o r m a t i o n m u s t b e h a v e i n the s a m e w a y a s o n e h a r d e n e d t o A. P . L. TURNER is Metallurgist, Materi