PSEUDOELASTIC BEHAVIOR OF COIL SPRING MADE OF A HIGH-DAMPING Cu-Zn-Al ALLOY

2. Experiment,aZs A c o i l s p r i n g w i t h a f r e e l e n g t h o f 100 mm a t 20°C and an average d i a m e t e r o f 16 mm w i t h e f f e c t i v e number o f t u r n o f 23 was s u p p l i e d by P r o t e u s (F4e ta l lu rg i e Hoboken-Overpel t , Hoboken and N . V . B e k a e r t S .A . , Zwevegem, i n c o o p e r a t i o n w i t h K a t h o l i e k e U n i v e r s i t e i t L e u v e n l . The chemica l c o m p o s i t i o n o f t h e s p r i n g m a t e r i a l i s shown by t h e s o l i d c i r c l e i n F ig . 1 , where t h e e f f e c t o f Zn and A2 c o n t e n t on t h e Mstemperature i t h e s t a r t i n g t e m p e r a t u r e o f t h e m a r t e n s i t e t r a n s f o r m a t i o n on c o o l i n g ) i s shown ( 2 1 . I t was s u p p l i e d a f t e r g i v i n g t h e f o l l o w i n g h e a t t r e a t m e n t : Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jphyscol:19815157 C51020 JOURNAL DE PHYSIQUE s o l u t i o n t r e a t m e n t a t 750°C f o r 15 min and t h e n quenched i n t o i c e w a t e r i n o r d e r t o o b t a i n t h e r m o e l a s t i c m a r t e n s i t e phase t h a t i s r e s p o n s i b l e f o r t h e high-damping c h a r a c t e r i s t i c s and a l s o f o r t h e shape memory e f f e c t ( 3 1 . I t undergoes a t h e r m o e l a s t i c m a r t e n s i t e o r r e v e r s e m a r t e n s i t e t r a n s f o r m a t i o n ,when c o o l e d o r h e a t e d t h r o u g h room t emper a t u r e . The t r a n s f o r m a t i o n t e m p e r a t u r e s were d e t e r m i n e d t o be 2 8 and lS°C(Ms) o r 12 and 16OCfAsl a s shown i n F ig .6 . F ig .2 Impu l se s y s t e m f o r measur ing t h e r e sonance f r equency and t r a n s f e r funct i o n o f t h e c o i l s p r i n g by means o f a f a s t F o u r i e r t r a n s f o r m a n a l y s e r I F . F . F i g . l P a r t o f t h e Cu-Zn-A2 T . ) . t e r n a r y s y s t e m w i t h t h e Mst e m p e r a t u r e s o f t h e quenched B-phase a l l o y s . S o l i d c i r c l e shows t h e c o m p o s i t i o n o f t h e a l l o y i n v e s t i g a t e d i n t h e p r e s e n t paper . F ig . 2 shows t h e p r i n c i p l e o f measurements o f t h e t r a n s f e r f u n c t i o n o f t h e c o i l s p r i n g w i t h a s t a t i c w e i g h t a t t h e l ower end . Because o f t h e v e r y p a r t i c u l a r shape o f t h e c o i l s p r i n g no c o n v e n t i o n a l method o f measur ing i n t e r n a l f i r c t i o n and re sonance f r equency f o r w i r e o r rod spec imens canno t be u s e d h e r e . Hence a new method was a p p l i e d by u s e o f t h e i m p u l s e s y s t e m w i t h an a i d o f a f a s t F o u r i e r t r a n s f o r m a n a l y s e r ( F . F . T . ) . I t g i v e s a l l t h e n e c e s s a r y d a t a f o r d e t e r m i n i n g i n t e r n a l f r i c t i o n and re sonance f r e q u e n c y , when t h e c o i l s p r i n g i s e x c i t e d by an i m p u l s i v e f o r c e s i g n a l x l t l ( S e e t h e t i m e doamin s igna l i n F i g . 3 ) . During t h e d e c a y i n g v i b r a t i o n a l p e r i o d a f t e r e x c i t a t i o n t h e v e l o c i t y a m p l i t u d e y l t l o f t h e l ower end o f t h e s p r i n g was d e t e c t e d by means o f a p i c k u p c o i l and t h e n t h e e l e c t r i c s i g n a l i s i n t r o d u c e d i n t o t h e channe l B i n p u t o f t h e F . F . T . a n a l y s e r . The i m p u l s e f o r c e s i g n a l on t h e o t h e r s i d e i s i n t r o d u c e d i n t o t h e channe l A i n p u t . F i g . 3 g i v e s a s c h e m a t i c r e p r e s e n t a t i o n o f t h e o p e r a t i o n o f t h e F.F.T. a n a l y s e r t h a t can p r o v i d e b o t h t ime-domain s i g n a l s c ( t I . y ( t l and f reauencu-domain s i g n a l s X f f ) , Y ( f I . The f u n c t i o n t h a t d e s c r i b e s t h e wau i n wh ich t h e s u s t e m per forms t h e m o d i f i c a t i o n o f a m p l i t u d e and u k a s e i s c a l l e d t h e t r a n s f e r f u n c t i o n , H ( f ) . I n a mechan ica l s u s t e m . H ( f ) s p e c i f i e s t h e f r eauencu r e s v o n s e o f t h e s u s t e m t o a u n i t f o r c e a t each f r eauencu ( t h e spec t rum o f a d e l t a * u n c t i o n f o r c e ) . I f t h e f o r c e i s an a r b i t r a r u one w i t h an i n v u t spec t rum, deno ted b y X ( f l , t h e n t h e o u t p u t spec t rum f u n c t i o n , Y f f I , o f t h e s y s t e m can be e x p r e s s e d F i g . 3 Schemat i c i l l u s t r a t i o n o f t h e o p e r a t i o n o f t h e f a s t F o u r i e r t r a n s f o r m a n a l y s e r I F . F . T . I i n an i m p u l s e s y s t e m shown i n F i g . 2 . The o u t p u t s i g n a l s y ( t I and Y ( f ) i n b o t h t i m e and f r equency domain c o n s i s t o f t h e f o l l o w i n g two s i g n a l s : y 2 ( t I l a t e r a l m o t i o n o f t h e s y s t e m and y 3 f t I v e r t i c a l m o t i o n o f t h e l ower end o f t h e c o i l s p r i n g . The p r i n c i p l e o f s u p e r p o s i t i o n t e l l s t h a t y ( t I = y1 ( t l + y 2 ( t I i n a l i n e a r s y s t e m . The whole mechan ica l s y s t e m was e n c l o s e d i n an environmentaZ chamber s o t h a t measurements a t t e m p e r a t u r e s i n a range b e t w e e n -50° and 80°C may be c a r r i e d o u t . B e f o r e making measurements t h e change i n l e n g t h under c o n s t a n t load o f 100 g and 200 g was made b y a s i m p l e method o f w e i g h t and s c a l e a s aZready shown i n F i g . 2 . The r e s u l t i n g t r a n s f o r m a t i o n c u r v e w i l l g i v e i m p o r t a n t i n f o r m a t i o n s a s w i l l b e shown i n t h e f o l l o w i n g . The F.F.T. a n a l y s e r e n a b l e s measurements o f b o t h i n t e r n a l f r i c t i o n Q-' and re sonance f r equency f o r each component o f t h e spec t rum o b t a i n e d . The f r e q u e n c i e s can b e read d i r e c t l y on t h e CRT d i s p Z a y i n 4 o r 5 d i g i t s , whereas 9-' mus t be c a l c u l a t e d by t h e f o l l o w i n g e q u a t i o n s , , where A , and An a r e a m p l i t u d e s i n t i m e domain f o r t h e 0 t h and n t h c y c l e o f v i b r a t i o n , and A f i s t h e h a l f w i d t h o f t h e r e sonance c u r v e i n f r equency domain and fr i s t h e r e sonance f r equencg . Due t o t h e l i m i t a t i o n o f t h e number o f d i g i t a l f i l t e r s (128 f o r t h e maximum i n t h e c a s e o f t h e i n s t r u m e n t t y p e hp 3582A used i n t h e p r e s e n t w o r k ) , t h e r e was a l ower l i m i t o f r e s o l v a b l e ~ f , and hence t h e r e was a l ower C5-1022 JOURNAL DE PHYSIQUE l i m i t o f Q-' t h a t can be determined by e q u a t i o n ( 3 1 . For v a l u e s o f QI s m a l l e r t h a n t h i s t h e use o f e q u a t i o n ( 2 ) was recommended a f t e r smoothi n g and averaging t h e t ime-domain s i g n a l s . 3 . R e s u l t s and D i s c u s s i o n Fig . 4 shows t h a r e s u l t o f measurements o f load-e longa t ion c u r v e a t v a r i o u s t empera tures under s t a t i c load ing i n t h e env i ronmenta l chamber shown i n Fig .2 . The s p r i n g was p e r f e c t l y e l a s t i c a t 80°C. As t h e t empera ture was l o n ~ e r e d , however, i t became n o t p e r f e c t l y e l a s t i c h u t t h e c u r v e s showed h y s t e r e s i s l o o p s . The Fig . 4 Load-elongat ion c u r v e s o f t h e Cu-Zn-A2 a l l o y c o i l s p r i n g measured a t t empera tures above and below M t empera ture . (M = l g ° C . See F ? ~ . 6 . 1