1987127-Reduction Residual Stress

8/12/2019 1987127-Reduction Residual Stress

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REL X TION OF RESIDU L STRESSESN OVERVIEWM R ames

Kockturll lnfernu~~orrulue m r Cerrter Thorirand O u k ~ A 91360 USA

ABSTRACTT h i s p ap er r e vi e ws t h e v a r i o u s s o u r c e s f o r r e l a x a t i o n o f r e s i d u a l s t r e s s e s byt h e r m a l a n d m e c h a n i c a l m e a ns . S i n c e r e s i d u a l s t r e s s e s i n du ce d d u r i n g m a n uf a c tu r i n gc a n b e d e t r i m e n t a l t o t h e i n t e g r i t y and s e r v i c e b e h av io u r o f a c om po nents t r e s s r e l i e f o p e r a t i o n s a r e a n i n t e g r a l s t e p i n many p r o d u ct i o n s eq ue n ce s.T he b a s i c p r i n c i p l e s of t h e r m a l m e c ha n i ca l an d v i b r a t i o n a l m et ho ds o f s t r e s sr e l i e f a r e o u t l i n e d . B e ne f i c i a l r e s i d u a l s t r e s s d i s t r i b u t i o n s c an r e l a x du r i n gs e r v i c e by t h e s e same m ec ha ni sm s l e a d i n g t o l o s s o f t h e i r wo rt h. S p e c i a le mp ha si s i s p l a ce d o n f a t ig u e - i n d u ce d r e l a x a t i o n . r e v i ew o f t h e l i t e r a t u r esh ow s a c o p i o u s s u p p l y o f d a t a w i t h f e w c o m p r e h en s i v e m o de l s f o r p r e d i c t i n gs p e c i f i c e f f e c t s .

INTRODUCTIONT he n ee d f o r r e l a x i n g m a n uf a c tu r i ng - i nd u c ed r e s i d u a l s t r e s s e s e nc om pa ss es a l lm a t e r i a l t y p e s i n c l u d i n g m e t a l l i c c e r a m i c g l a s s a nd p o ly m er i c s y s te m s a sw e l l a s s em i co n du ct o r an d t h i n f i l m s t r u c t u r e s . R e s id u a l s t r e s s e s l o ck e d i nd u r i ng ma nu f ac tu r in g p r o c e s s e s a r e o f t e n d e t r i m e n t a l t o t h e i n t e g r i t y a nds e r v i c e b eh a v i o u r o f c o mp o ne n ts . S t r e s s r e l i e f i s common i n many p r o d u c t i o no p e r a t i o n s o f t e n t a k i n g p l a c e d u r i n g a n n ea l i n g an d o t h e r t h e r ma l t r e a m en t si n t en d e d f o r u n r e l a t e d pu rp o se s. F o r i n s t a n c e p o st - we l d h e a t t r e a t m e n t s n o to n ly r e l a x t h e h ig h t e n s i l e s t r e s s e s in du ce d by d i f f e r e n t i a l t he rm al c o n t r a c t i o nb u t a l s o im pr ove m e t a l l u r g i c a l p r o p e r t i e s s u c h a s f r a c t u r e t o u gh n es s. Whilet he rm al s t r e s s r e l a x a t i o n i s t h ou gh t t o p r od uc e b e t t e r d i m en s io n al s t a b i l i t yt h a n o t h e r m e th o ds s o me t im e s o n l y m o de s t r e d u c t i o n c a n b e a c h i e v e d be c a u s e o fm i c r o s t r u c t u r a l l i m i t s o n t h e t e mp e r a tu r e r a n g e a l l o w a b l e o r b ec au se of h i g hc r e e p r e s i s t a n c e of t h e m a t e r i a l . When m i c r o s t r u c t u r a l e f f e c t s o f t he r ma lt r e a t m e n t s a r e u n d e s i r a b l e s t r e s s r e l i e f c a n b e a ch i e ve d by m ec h an ic a l me ans .T h i s i s u s u a l l y a cc om pl is he d by p l a s t i c a l l y s t r e t c h i n g o r o v e r s t r e s s i n g t h em a t e r i a l ab ov e t h e m on ot on ic y i e l d . A l t e r n a t i v e m et ho ds t h a t r e d i s t r i b u t er a t h e r t h an r e l i e v e t h e r e s i d u a l s t r e s s s t a t e i n c l u d e v i b r a t i o n a l s t r e s s r e l i e fa nd e x p l o s i v e o r s h o ck l o a d i n g .R e l ax a t io n o f r e s i d u a l s t r e s s e s c a n a l s o o cc u r d u r i n g t h e l i f e o f a componentand ca n l e a d t o a l t e r e d p r o p e r t i e s . C y c l i c f a t i g u e and c r e e p c an r e s u l t i n ar e d i s t r i b u t i o n o f t h e i n i t i a l e l a s t i c r e s i d u a l s t r e s s e s l e a d i n g t o s t r e s s


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M R Jamesr e l a x a t i o n d u r i n g s e r v i c e . 'This i s e s p ec i a l 1 y t r u e o f s h o r t - rn n g c r ~ s i d u n ls t r e s s e s t h a t e x i s t a s a c on se qu en ce o f l o c a l p l a s t i c d e fo r m a ti o n . T h es es t r e s s e s a r e s i g n i f i c a n t l y a l t e r e d by c y c l i c o r t h e r ma l s o f t e n i n g t h a t r e s u l t si n d i s l o c a t i o n m o t i o n and a l t e r a t i o n o f t h e e l a s t i c s t r e s s s t a t e . C re ep andr e c o ve r y e f f e c t s c a u s e t im e- de pe nd en t s t r e s s r e l a x a t i o n o f s t a t i c a l l y l o ad e dp a r t s .T h es e e f f e c t s a r e d i s c u s s e d i n more d e t a i l by s e p a r a t i n g them i n t o t h e r m al ,m e ch a ni ca l and v i b r a t o r y s t r e s s r e l i e f o p e r a t i o n s . W i th i n t h e l i m i t e d s co p e o ft h i s r ev i e w, a t t e n t i o n i s f oc u s ed o n t h e m ech an isms i n v o l v e d d u r i n g t h e i n d i v i d u a lr e l a x a t i o n p r o c e s s e s , wlii l e i l l u s t r a t i n g t h e u s e a nd p ro bl em s o f e a c h t c c h n i q u ewit-h rn ou gh r e f e r e n c e s t o g i v e t h e r e a d e r s o u r ce s f o r s o l u t i o n s t o s p e c i f i cp r o b l e m s .

THERMAL STRESS RELAXATIONPro ced ure s and Mechan i smsI s ot h er m al s t r e s s r e l i e f i n v o l v e s t h e u n i fo rm h e a t i ng o f a p a r t o r s e c t i o n t o as u i t a b l e t e mp e r a tu r e , h o l d i n g a t t h i s t e m p er a t u re f o r a p e r i o d o f t i m e, f o l lo w edby sl ow c o o l i ng t o p r e v e n t t h e r e i n t r o d u c t i o n o f t he rm al s t r e s s e s . T h is i su s u a l l y d one i n a n a i r c i r c u l a t i o n f u rn a ce w i t h good c o n t r o l o v e r t h e s p e c i f i e dt h e r m a l c y c l e . C r a n e [ l ] i n a n o v e r v ie w o f t h e r m a l m e t h o d s , c o mm en ts o n t h eu s e of lo w t h e r m a l m as s f u r n a c e s made of l i g h t w e i g h t p a n e l s t h a t a r e a s s e m b l e do n - s i t e . The s t r u c t u r e i t s e l f becomes t h e f u r n a ce , u s in g r a d i a n t e l e c t r i ce l em e nt s f o r t h e h e a t i n g sy st em and o v e r a l l t h er m al e f f i c i e n c i e s a s h i g h a s55 .T h r e e pr im a ry me ch an is ms c a u s e r e l a x a t i o n o f t h e l o c k e d - i n s t r e s s e s . A tt e m p er a t ur e s h i g h en ou gh t o c a u s e a s u b s t a n t i a l r e d u c t i o n i n t h e m a t e r i a l y i e l ds t r e n g t h , p l a s t i c i t y mechan isms r e l i e v e t h e e l a s t i c s t r a i n t h r ou g h r a p i d t he rm ala c t i v a t i o n o f d i s l o c a t i o n s . T h i s r e q u i r e s t h a t a c om po ne nt b e h e a t e d t o at e m p er a t ur e wh ere i t s y i e l d s t r e n g t h a pp r oa c he s a v a l u e t h a t c o r r e s p on d s t o a na c c e p t a b l e l e v e l o f r e s i d u a l s t r e s s . U n f o r tu n a t e l y , t h i s u s u a l l y ap pr oa ch es o re x c e ed s t h a t o f t h e s o l u t i o n - a n n e a l i n g t e m p er a t ur e . A t t en d a n t d e c r e a s e s i nm ec ha ni ca l p r o p e r t i e s t h a t re ma in a f t e r s l ow c o o l i ng d i c t a t e t h a t t h i s r e l a t i v e l yt i me - in d e pe n d en t , h i g h t e m p e r a t u r e mec ha nism o f t e n c a n n o t b e u t i l i z e d . A tl ow er t e mp e ra t ur e s, c l a s s i c a l d i f f u s i o n a l c r e ep e n a b l e s t h e c o u n t e r b a l a n c i n gr e g i o n s o f t e n s i l e an d c o mp r es s iv e s t r e s s e s t o c o n t r a c t o r ex pa nd s l i g h t l y , a n dt h u s t o r e d i s t r i b u t e . P r e c i p i t a t i o n a nd a g e i ng e f f e c t s a l s o c a u se volumec h a n ge s t h a t c an r e l a x e l a s t i c s t r e s s . T he se p r o c e s s e s a r e t i me - de p en d en t , a nds i g n i f i c a n t t r a d e o f f s m u st b e made i n d e t e rm i n in g t h e a p p r o p r i a t e t e m p e r a tu r ea n d d u r a t i o n r e q u i r e d . At low t e m p e r a t u r e s , m i c r o p l a s t i c s t r a i n t h a t o c c u r sd u e t o t h er ma l g l i d e ( r a t h e r t h an c l i mb ) of d i s l o c a t i o n s en a b l e s t h e r e l a x a t i o no f h i g h t e n s i l e s t r e s s e s . T h i s pr o c es s i s o n l y w ea kl y te m p e ra t u re - a nd t im e-d ep en de nt a n d d o es not f u l l y r e l i e v e t h e s t r e s s s t a t e . I t i s e a s i l y s up p r es se dby a g e i n g t r e a t me n t s t h a t may t a k e p l a c e p r i o r t o s t r e s s r e l i e v i n g .T y p i c a l s t r e s s r e l i e f t e mp e ra t ur e s f o r low a l l o y f e r r i t i c s t e e l s a r e b et w ee n9 and 675 C , and 900 t o 1065C f o r h i gh a l l o y s t e e l s [ 2 ] T he d u r a t i o n c a nb e e s t i m a t e d b y e x a mi n in g t h e i n f l u e n c e o f t e m p e r a t u r e o n t h e c r e e p a nd y i e l ds t r e n g t h of t h e m a t e r i a l . t lo we ve r, o v e r many of t h e t e m p e r a t u r e r a n g e s e m pl o ye d ,b o t h p l a s t i c i t y and c r e e p p r o c e ss e s o c c u r s i m u l t a n e o u s l y , m ak in g a c c u r a t em o d e ll i n g o f t h e b e ha v io u r d i f f i c u l t . As a r e s u l t , d e t e r m i n a t i o n o f t h e t im e-t e m p e r a t u r e r a n ge i s o f t e n a c c om p l is h e d e x p e r i m e n t a l l y . W h il e t h e d w e l l t im ei s i m po r ta n t , c r e e p i s a l o g a r i t hm i c p ro c es s s u ch t h a t m os t r e l i e f o b t a i ne d a ta g i v e n t em p er a tu re i s a c h ie v e d r e l a t i v e l y r a p i d l y , a s shown by t h e d a t a i nF i g . I . [ f ea t t r e a t m e n t s o f I t o h a r e t y p i c a l . 'Throop e t a l . r 3 have shownt h a t t l ~ i can b e spcc t l ed u p i n c c r t ~ i n i r r ~ m s t a ~ i c c sy u s i n g n o n u n i f o r m r a t h e rt h a n i s o th e r m a l h e a t i n g a nd c o o l i n g . I n a u t o f r e t t a g e d c y l i n d e r s , t h e m a gn it ud e


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Fig. 1 Effect of annealing time on the fractional. residual stressof mild steel [lo].

of relaxation was significantly greater in the presence of thermal gradients ascompared to uniform heating. This may be unique because of the combined compressivestresses induced during autofrettage and the thermal stresses induced near thebore but the example shows that uniform thermal exposure may not be necessary.In fact Woodward et al. [4 report stress relief experiments on Alloy 6steam generator tubi ng using induction heating with thermal exposures of 30 sto 4 min. Obvi ousl y the use of such rapid thermal heating and temperaturegradients must be approached with caution. In investigating the relief ofresidual tensile stresses in injection-molded plastics Thompson and White [5found that thermal gradient annealing left tensile stresses a t the surface.Often of more importance than the time is the choice of temperature because ofthe significant microstructural changes that can take place. Stainless steelsfor instance require considerable care so as not to be sensitized to stresscorrosion cracking through chromium depletion that occurs as a result of chromiumcarbide formation. Many industrial and professional societies cognizant ofsuch problems hav e published recommended specifications for stress-relievingheat treatments. Metals Handbook [ 6 ] for instance provides general data onlow carbon and mild steels austenitic stainless steels tool steels andaluminium copp er lead magnesium nickel and titanium alloys. Problems ofcorrosion sensitization recrystallization and grain grow th hydrogenembrittlement ageing and precipitation reactions are elaborated on. In generalhowever detailed procedures and estimates of the expected degree of relaxationare not specified. This necessitates the use of experimental studies todetermine adequate and useful heat treatments.


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M . R. JamesE x p e r i m e n t a l S t u d i e s

P e r t a i n e n t d a t a a r e o f t e n r e q u i r e d t o d e te r mi n e t h e e f f e c t i v e n e s s o f a g i ve nt h e r ma l t r e a t me n t . A m aj or p ro bl em i n t h e s e i n v e s t i g a t i o n s i s q u a n t i f i c a t i o no f t h e r e s i d u a l s t r e s s l e v e l s . One o f t h e m os t a c c ep t e d m et ho ds o f r e s i d u a ls t r e s s d e te r mi n at j on i n vo l ve s x- ra y d i f f r a c t i o n w he re t h e n ea r s u r f a c e s t r e s s e sa r e e v a l u a t e d . P o t t e r a nd M i l l a r d 1 7 1 a nd D i e s n e r C81 h a ve u s ed t h i s t e c h n i q u et o s t u d y t h e t h e rm a l s t a b i l i t y of c o mp r es si v e s t r e s s e s i n du c ed by s h o t pe en i ng .T he f o r m e r de m o ns t r at e d s u b s t a n t i a l r e d u c t i o n o f c o m pr e s si v e s t r e s s e s i n 7 075-T6a lu mi ni um a t r a t h e r low t e m p er a t u r es a nd l o n g t i m e s ( 2 2 5 ~ o r 2 0 h ) , andD i e s n e r d ev el o pe d ma s t er s t r e s s r e l i e f t i m e- t e mp e r at u r e c u r v e s f o r AI SI 5 21 00a nd tl-11 s t e e l s . D i e sn e r m ea su re d t h e t hr o u gh - L h ic k n es s s t r e s s d i s t r i b u t i o n byr e m ov a l o f s u c c e s s i v e s u r f a c e l a y e r s . A l s o u s i n g x - r ay d i f f r a c t i o n , Amin a ndG an es h [ 9 1 showed t h a t t h e rm a l r e l i e f o f c o l d - r o l l i n g i n d uc e d s t r e s s e s i n Cu-2%Be a l l o y s t r i p s was e f f e c t i v e , b u t m ec ha ni ca l s t r e s s r e l i e f u s i ng r o l l e r l e v e l l i n gw a s n o t .T he S a c h s b o r e - o u t m et ho d i s e f f e c t i v e when 1 .o ng -r an ge m a c r o s t r e s s e s i n d u c e d b yt h e r m a l g r a d i e n t s a r e m e as u r ed . T h i s t e c h n i q u e wa s u s e d by Adeyemi e t a l . 1 1 0 1o n m i l d s t e e l , B ak ae v a n d V a in e rm a n [ l l on h a r d f a c e d s t e e l s h a f t s , m n d e r s o ne t a l . [ 1 2 ] o n a U-2.4% N i a l l o y t o d e t e r m in e t h e d e g re e of r e l a x a t i o n . L aye rr e m o v a l p r o c e d u r e s a r e a l s o o f t e n u s e d . Thompson a nd W h it e [ 5 1 e v a l u a t e d t h eu s e o f t h i s t e c h ni q u e i n n e a t po ly me rs a nd f i b r e - r e i n f o r c e d p o ly m er s , a ndc o nc l ud e d t h a t t h e v a r i a t i o n of s t i f f n e s s w i t h d e pt h t y p i c a l o f c om po si te s d oe sn o t s e r i o u s l y a f f e c t t h e c a l c u l a t i o n s . T h ak ka r a nd Br out man L131 c a l c u l a t e dt h e a c t i v a t i o n e n er gy r e q u i r e d t o r e l e a s e r e s i d u a l s t r e s s e s i n cold- workedp o l y c a r b o n a t e u s i n g t h e l a y e r r em ov al t e c h n i q u e . They fo un d t h a t s m a l l p e rc e n t r e d u c t i o n s i n t h i c k n e s s ( t h e me th od u se d t o i n t r o d u c e t h e c o l d w or k)i m p a r t o nl y s u r f a c e t e n s i l e s t r e s s e s t h a t c a n be r e l a x e d by a n n e a l i n g a t 50C.L a rg e r ed u c t i o ns d u r i n g r o l l i n g a l s o c a u s e a h i g h d e g r e e o f m o l ec u la r o r i e n t a t i o nt h a t c a n no t be s u b s t a n t i a l l y r e l a x e d b el ow 1 2 5 C ( T 1 5 0 ~ ) .gT h e s e t e c h n i q u e s , a l t h o u g h q u a n t i t a t i v e , a r e t e d i o u s an d ti me -c on su mi ng , a ndmany s i m p l e r m et ho ds c a n b e u s ed f o r q u a l i t a t i v e d e t e r m i n a t i o n s . T he u s e o fs p l i t r i n g s and l o n g i t u d i n a l s p l i t t i n g h a s b ee n d e s c r i be d by Brown e t a l . 1 14 1a nd Adeyemi e t a l . [ l o ] r e s p e c t i v e l y , i n s t e e l a l l o y s and by ~ a v a l 5 ] nT i a l l o y s . Fox 1 16 1 d e s c r i b e s a number o f si m pl e s t r e s s r e l a x a t i o n t e s t s o nCu a n d Cu a l l o y s , s u c h a s v i b r a t i o n o f a w i r e a n d a t a p e r e d beam be nd in g f i x t u r et h a t c o ul d b e a p p l i e d t o t h e t e s t i n g of t h e r ma l s t r e s s r e l i e f . Woodward e t a l .[ 4 1 t e s t e d i n s i t u s t r e s s r e l i e f o f s t ea m g e n e r a to r t u bi n g by o bs e rv i ng i . t ss u s c e p t i b i l i t y t o s t r e s s c or r o s i o n c r a c k i ng i n a s u l f u r c o n t a i ni n g e nv ir on me nt .T h es e s i m p l e t e c h ni q u e s a r e u s u a l l y us ed t o d e t e rm i n e p e r c e n t r e d u c t i o n s f o rt i m e - t e m p e r a t u r e c u r v e s ; a n d when co mb in ed w i t h m e t a l l o g r a p h i c e x a m i n a ti o n t oe n s u r e m i c r o s t r u c t u r a l s t a b i l i t y , t he y a r e q u i t e a d e q ua t e i n many c i r cu m st a nc e s.E xp er i me n t a l s t u d i e s on t h e i s o t he r m al s t r e s s r e l i e f o f t h i n f i l m s t r e s s e s a r eo f t e n do ne by m e a su r i ng t h e c u r v a t u r e o f t h e f i l m a n d s u b s t r a t e . S es ha n a ndE e r N i ss e [ 1 7] s t u d i e d t h e a n n e a l i n g o f r e s i d u a l s t r e s s e s i n i o n i mp lan ed S il a y e r s and f ound t h r e e d i s t i n c t s t a g e s , w i t h t h e t h i r d s t a g e ( a bo ut 4 5 0 ~ )b e i n g t h e m ost e f f e c t i v e du e t o e p i t a x i a l r e g ro w t h of t h e amorphous l a y e r .T he y m o d e l l e d t h e i r o b s e r v a t i o n s e m pl o y in g t h e maximum s h e a r s t r e s s . B la au wC181 u s e d s a mp l e c u r v a t u r e m ea s u r e d by t h e beam d e f l e c t i o n m et ho d a n d f o u n dt h a t t e m p er a t u r es of 500-700C r e l i e v e d t h e t e n s i l e s t r e s s e s i n c h em i ca l va po urd e p o s i t e d S i 0 2 f i l m s ( b o t h d op ed a nd u n do p ed ) o n GaAs s u b s t r a t e s . H ow ev er ,p l a sm a -e n ha n ce d CVD f i l m s o f S i Nx c o u l d n o t b e s t r e s s - r e l i e v e d a t t h e s et e m p e r a t u r e s . K in ba ra e t a l . [ 19 1 a l s o us ed s u b s t r a t e b e nd in g t o s t u dy s t r e s s e si n MgF2 f i l m s o n s i n g l e - c r y s t a l q u a r t z s u b s t r a t e s . N ob le a nd Reed [ 2 0 ] f o u ndt h a t b ak in g a t 750C r e l i e v e d t h e r e s i d u a l s t r e s s e s i n N i - a n d C r - p l a t e d A I S I8 74 0 h a r de n e d s t e e l . Abermann e t a l . C211 u s e d a c a n t i l e v e r t e c h n i q u e f o rn e as u ri n g i n t e r n a l s t r e s s i n t i n f i l m s and d i s c u s s e d Lhe n e c e s s a r y c o r r e c t i o n sf o r t h er m al e f f e c t s i n t h e s u b s t r a t e . P a rk e r LZ21 f ou nd t h a t t h e s t r e s s s t a t e


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35 M . R . JamesA n a l y t i c a l t r e a t m e n t s h av e a l s o b ~ e n o nd uc te d f o r c e r a m ic s . Ev an s a nd C l a r k eL 3 3 1 d e s c r i be m eth od s f o r c a l c u l a t i n g t h e r e l a x a t i o n o f r e s i d u a l s t r e s s e sd ev e lo p ed a t t h e m i c r o s t r u c t u r a l l e v e l b e c a u se o f t h e r m a l c o n t r a c t i o n i nh o mo g en e it y.Th e r a t e o f r e l a x a t i o n w as shown t o be a s t r o n g f u n c t i o n of t h e m i c r o s t r u c t u r e ,w i t h r ap i d r e l a x a t i o n o b t a i n a b le i n f i n e g r a in e d m a t e r i a l s o r i n m a t e r i a l sc o n t a i n i n g a n a mo rp ho us b o un d ar y p ha s e t h a t p r o v i d e s v i s c o u s f l o w . T r e e e t a l .E34 fou nd t h a t q ue n ch t e n s i l e s t r e s s e s i n al um i ni um o x i d e s c o u l d n o t b e t h e r m a l l yr e l i e v e d b e c au s e o f s u b c r i t i c a l m ic r oc ra c k g ro wt h t h a t t a k e s p l a c e a t t e m p e r at u r e sh r l ow t h a t r e q u i r e d f o r d i f f u s i o n a l c r e ep . s sh ow n i n F i g . 2 t h e minimums ~ v e s s n t v n s i t y KC r r q u i r ~ d o r s u bc r i t i c a l c r a c k g ro wt h d e c re a s e s w i t h t em pe ra tu res uc h t h a t t h e t e n s i l e c t r e s s f i e l d b y i t s e l f p r o v id e s e no ug h e n e r g y f o r c r a c kg t- cx gt l~ . I hi c r c s u l l s i n e l n - t i c r c l n x n t j on o f t h c r c s i t l u a l s t r e s s s t a t e , b utn a manner d e t r i m e n t a l t o t h e l o ad - be a ri n g c a p a b i l i t y o f a b r i t t l e c er am i c.

T h u s , o n ly when t h e t e n s i l e s t r e s s e s a r e s u f f i c i e n t l y lo w c a n h i g h en ou ght e m p e ra t u r es h e a c h ie v ed t o e n a b le d i f f u s i o n a l c r e e p m ec ha nis ms t o r e l a x t h es t r e s s e s i n a s a f e manner .

TEMPER TURE

F i g . 2 S ch e ma t ic o f r e l a t i v e m ag ni tu de o f r e s i d u a l s t r e s s j - n te n s i tyf a c t o r w i t h c o r r e sp o nd i ng v a lu e s f o r f a s t f r a c t u r e K ~ ~ )nd minimum

v a l u e K r e q u i r ed f o r s u b c r i t i c a l c r a c k g ro wth . From T r ee e t a 1 [ 3 4 ]

P o st - We l d H e a t T r e a t m e n t sT h er m al s t r e s s r e l i e f i s p e r ha p s more o f t e n us e d i n w el dm en ts wh er e pe ak t e n s i l es t r e s s e s o c cu r w i t h m a gn i tu d es t h a t a p pr o ac h o r e xc ee d t h e n om in al y i e l d s t r e n g t ho f m a t e r i a l . S i m u lt a n e o us l y , t h e we ld m e t a l a nd h e a t a f f e c t e d zo ne o f t e nh a v e po or m i c r o s t r u c t u r e s o f f e r i n g low f r a c t u r e t o ug h ne s s a nd d u c t i l i t y . s ac o n se q u e nc e , c o n s i d e r a b l e a t t e n t i o n h a s b ee n p l ac e d o n p o s t- w e ld h e a t t r e a t m e n t sw i t h a v ie w t o w a r ds i m p r o v i n g t h e s a f e t y of a s t r u c t u r e f r o m b r i t t l e f r a c t u r e ,m a k i n g i t more t o l e r a n t of d e f e c t s , and r ed u c in g t h e r e s i d u a l s t r e s s s t a t e f o rl o w e r f a t i g u e c r a c k gr ow th an d s t r e s s c o r r o s i o n c r a c k i n g r a t e s . B ec au se o f t h ei m po r ta n ce o f t h i s p r o ce s s t o i n d u s t r y , e s p e c i a l l y t h e e l e c t r i c power i n d u s t r y ,many i n d u s t r i a l a nd p r o f e s s i o n a l s o c i e t i e s h a ve d e ve lo p ed e x t e n s i v e r e q u i r e m e n tso n t h e r a t e s o f h e a t i n g , s o ak i n g a nd c o o l in g . p a r t i a l r e vi ew o f t h e s e h a sI)cen pub1 i shed by C ot t r c l l 3 5 1 ,ind many o t h e r l ) . lpe r s p r r t i r ie nl t o r c s i t l u a ls L ~ c s s n welds c a n b e f o u n d i n R e f . 36 A g a pa k is eL a l . 3 7 p u b l i s h e d a


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R e l a x a t i o n o f R e s i d u a l S t r e s s e s 3 5 5l i t e r a t u r e s u r ve y o f s t r e s s r e l i e v i n g i n s t r u c t u r a l w e ld me nt s, s o no a t t em p t i smade h e r e t o s u mm ar iz e t h e s e f i n d i n g s . Much i n f o r m a t i o n p e r t a i n i n g t om i c r o s t r u c t u r a l m o d if i ca t io n , r e s i d u a l s t r e s s r e l a x a t i o n , s t r e s s r e l i e f c ra c k in g ,an d f a t i g u e c r a c k p r o pa g a t io n i n w eld ed j o i n t s c an b e f o un d i n t h e s e r e f e r e n c e s .

C o l d T r e a t i n gR e si d ua l s t r e s s e s f r e q u e n t l y r e s u l t f ro m n on un if or m t h e rm a l c o n t r a c t i o n du e t ot em pe ra tu re g r nd i e n t s t h ro ug h t h e t h i c k n e s s . C h a r a c t er s i c a l l y , t h e r e s i d u a ls t r e s s e s a r e c om pr es si ve a t t he s u r f a c e and t e n s i l e i n t h e i n t e r i o r u n l e s s ap h as e c h an g e o c c u r s d u r i n g q n c n c h i n g 'The u se o f c o l d t r e a t i n g Lo i n d u c e m i l ds t r e s s r e l i e f and t o a c t a s a s t a b i l i z i n g t r e a t m e nt h as p rov ed b e n e f i c i a l , b o thi n c a s t i n g s and machined p a r t s [ 21 . O f t e n , t h i s o c c u rs du e t o s t a b i l i z a t i o n o fu n tr a ns f or m ed p r o d u c t s l e f t a f t e r t h e qu en ch . H i l l e t a l . [ 38 1 ha ve p r op os eda n u p h i l l H t r ea t m en t of s uc h s e v e r i t y a s t o d ev e l op r e s i d u a l s t r e s s e s t h a tc o u n t e r a c t t h6 s e f or me d d u r i n g a h i g h t e m p e r a t u r e q u en c h. I n t h i s c a s e , t h ep a r t i s c o ol e d t o l i q u i d n i t r o g e n t e m p er a tu r es and t h e n s u b j e c t e d t o a hi g hv e l o c i t y s te am b l a s t t o p r om ot e t he rm a l g r a d i e n t s g r e a t en ou gh t o p ro du ce l o c a lp l a s t i c fl o w. T h i s w or ks w e l l w i t h a l l o y s of low y i e l d s t r e n g t h o r when a p p l i e dt o a component b e f o r e a g e i ng w hi ch r a i s e s t h e y i e l d s t r e n g t h . S i n c e lowt e mp e ra t ur e s a r e u s e d , m i c r o s t r u c t u r a l and s t r e n g t h ch a ng e s a r e n e g l i g i b l e .Recen t work by Se vi ml i [ 3 9 1 h a s shown t h i s t o b e a n e f f e c t i v e method t o s t r e s sr e l i e v e t h e o u t e r s h e l l of l a r g e a lu mi ni um s t r u c t u r e s h av i ng r e s i d u a l s t r e s s e sf or me d b o t h by q u e n c h i n g an d by m a c h i n i n g . W h i l e n o t o f w i d e sp r e a d p o p u l a r i t y ,t h i s t e ch n iq u e m ig ht be p a r t i c u l a r l y u s e f u l o n i r r e g u l ar - s h a p e d p a r t s t h a tc a n n ot be s t r e s s r e l i e v e d by o t h e r me ans .

RESIDUAL STRESS RELAXATION BY MECHANICAL MEANSA g r e a t d e a l o f m i s un d er s ta n di n g e x i s t s i n r e ga r d t o m e ch a ni c al e f f e c t s o ns t r e s s r e l a x a t i o n . The t er m m ec ha ni ca l s t r e s s r e l a x a t i o n o r lo ad r e l a x a t i o n i su se d t o d e s c r i b e an e xp er im en ta l t ec hn iq ue t o me as ur e i n e l a s t i c s t r a i n p r o p e r t i e s ,a t bo th a m b ie n t an d e l e v a t e d t e m p e r a t u r e s , and t h e s e t e rm s d o n o t r e l a t es p e c i f i c a l l y t o r e s i d u a l s t r e s s e s . T h i s t yp e o f d a t a i s u se d m ai nl y t o p r e d i c tc r e e p i n p r a c t i c a l e n g i n e e r i n g components o p e r a t i n g f o r l o ng t i m es u nd er s t a t i can d dynamic l o a ds . On t h e o t h e r h a nd , m e ch a ni ca l r e s i d u a l s t r e s s r e l i e f r e f e r sm ain ly t o o v e r s t r e s s i n g o r s t r e t c h i n g o f a m a t e r i a l o r c omponent t o i n d u cep l a s t i c f lo w i n o r d e r t o r e d i s t r i b u t e t h e r e s i d u a l s t r e s s e s . Y e t , i t i s i m po r ta n tt o u n de rs t a nd l oa d r e l a x a t i o n b ec au se of i t s i n t e r - r e l a t i o n t o r e s i d u a l s t r e s sr e l a x a t i o n . We b e g i n by e x am i ni n g t h e d e l i b e r a t e u s e o f m e ch a ni ca l r e s i d u a ls t r e s s r e l a x a t i o n an d th e n d i s c u s s bo th s t r e s s r e l a x a t i o n t e s t i n g and s e r v i c er e l a x a t i o n by f a t i g u e a n d t h e r m a l m ea ns .

O v e r s t r e s s i n g an d S t r e t c h i n gP l a s t i c d e fo r m at i on an d s u b se q ue n t r e l i e f o f l o ck e d- i n i n t e r n a l s t r e s s e s b e gi nsi n t h o s e r e g i o n s i n w hi ch c o n d i t i o n s o f y i e l d i n g u n d e r t h e c o m bi n at io n o fa p p l i e d and r e s i d u a l s t r e s s a r e s a t i s f i e d . As a lo ad i s a p p l i e d , y i e l d i n g w i l lo c cu r f i r s t i n t h e r e g io n s o f h ig h r e s i d u a l t e n s i o n w i t h t h e d i s l o c a t i o n m ot i ond e c r e a s i n g t h e amount o f m i s f i t , a s e x p l a i n e d by R o s en t h a l [ 40 1. I n v e s t i g a t i n gt h e e f f e c t o f p r e l o a d o n f a t i g u e s t r e n g t h i n 2 024 -T 3 A l , Nawwar a nd S hew chuk[411 found t h a t t e n s i l e s t r e s s e s a r e q u i t e e a s i l y r e l i e v e d by a p r e lo ad o ro v e r l o ad , b u t t h a t c om pr es si ve s t r e s s c a n b e s u s t a i n e d a t h ig h p r e l o ad s w i t h ou tl o s s of t h e i r b e n e f i c i a l e f f e c t . I n f a c t , Fu ch s and S t ep h en s [ 42 ] d e s c r i b et h i s a s a method t o d e l i b e r a t e l y i n du c e b e n e f i c i a l c om pr es si ve s t r e s s e s .P o t t e r and M i l l a r d r 7 h a v e shown i n 7 075-T6 A1 t h a t s t a t i c l o a d s a p p r o x i m a ti n gy i e l d musL be aLL~inet lb e f o r e r e l a x a t i o n o f compress ive s t - r e s s e s i n d u c e d b ys h o t p ee ni ng c an o c c u r . T h ei r d a t a , F i g . 3 , i n d i c a t e t h a t t h e r e s i d u a l s t r e s s


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M R. James

SPECIMEN 1 0 t 250 SPECIMEN 2ors 200 MPa rs = 200 MPaM E A N O F D A T A -- -

ANGE5 0

COMPRESSION TENSION1

PRELOAD STRESS. M Pa

F i g . 3 The e f f e c t of s t a t i c l oa d s t r e s s o n t h e s u r f a c e r e s i d u a ls t r e s s l e v e l ( r e p r i n t e d f ro m P o t t e r a nd M i l l a r d , R e f. 7 .

h a s no e f f e c t o n t h e t h r e s h o l d s t r e s s f o r r e l a x a t i o n . T h i s i s c o n s i s t e n t w i t hR o s e n t h a l ' s C401 v i ew t h a t t i s t h e maximum s h e a r s t r e s s t h a t mu st e xc ee d t h ey i e l d s t r e n g t h , s i n c e s h o t pe en in g i n t r o d u ce s a n i s o t r o p i c d i s t r i b u t i o n .Many a ge - h ar d e ni n g , h i g h s t r e n g t h al um in iu m a l l o y s u n d e rg o a s t r e t c h i n g o p e r a t i o na f t e r s o l u t i o n t r e a t m e nt an d p r i o r t o t e m p e ri n g an d ag e i ng a s a s t a n da r d meanst o r e l i e v e q ue nc h s t r e s s e s . T he rm al a n n e a l i n g t r e a t m e n t s c a n n o t b e u s ed b ec a us et h e y c a us e c o a l e sc e n c e o f p r e c i p i t a t e s f ro m s o l i d s o l u t i o n t h a t mu st b e d o n ed u r i n g t h e a g e in g t r e a t m e n t . The ANSI s t a n d a r d d e s i g n a t i o n f o r t h i s i s t h eT x 51 t em pe r w h er e r e p r e s e n t s t h e t e mp e r t r e a t m e n t . The Tx52 d e s i g n a t i o na p p l i e s t o p ro d uc t s t h a t a r e s t r e s s r e l j eved by co mp re ss i on a f t e r s o l u t i o nt r e a t m e n t t o p r o du c e a p er ma ne nt s e t o f t o 5 . F o r g e d A1 p r o d u c t s a r e s o me t i me sr e s t r u c k i n t h e d i e w hi le c o l d t o p ro du ce s t r e s s r e l i e f , a nd a r e d e si g na t edTx54 .A s i d e f ro m h i g h s t r e n g t h A1 a l l o y s , s t r e t c h i n g a s a u s u a l means o f a c h i e v i n gs t r e s s r e l a x a t i o n i s d on e o n l y o n c ol d- dr aw n t u b i n g . C ol d- dr aw n t u b e s t e n d t oh a ve h i gh l e v e l s o f l o n g i t u d i n a l t e n s i l e s t r e s s i n t h e o u t e r s u r f a ce . W hi les t r e t c h e s of u p t o 5 l o n g i t u d i n a l p l a s t i c s t r a i n s a r e so me ti mes u s ed , e v ens m a l l am ou nt s o f h omogeneous t e n s i l e s t r a i n w i l l s i g n i f i c a n t l y r e d uc e t h et e n s i l e r e s i d u a l s t r e s s e s c r e a t e d by t h e i nh om ogen eo us d e f o r m a t io n du r i n gd r a w i n g o f t h e t u b e .

S t r e s s R e l a xa t io n T e s t i n gI f a c om ponent a t c o n s t a n t t e m p e r a t u r e s l oa de d and h e l d a t c o n s t a n t s t r a i n ,t h e s t r e s s de c r e a se w i t h t i me du e t o s u b se q ue n t i n e l a s t i c d e f or m at i on i s c a l l e ds t r e s s r e l a x a t i o n . S t r e s s r e l a x a t i o n i.s d e f i n e d a s t h e i n i t i a l s t r e s s minust h e r em ai ni ng s t r e s s C431, a nd t e s t s a r e i ~ s u a l l y o nd uc te d i n t e n s i on b y l o a d i n ga s a m pl e t o a p r e de t e rm i n e d s t r a i n an d h o l d i n g t h e s t r a i n c o n s t a n t o v e r t i me byd e c r e a s i n g t h e a p p l i e d l o a d . S t a n d a r d p r a c t i c e s R ave b ee n p r e s c r i b e d by ASTM


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R e l a x a t i o n o f R e s id u a l S t r e s s e s 5[ 4 3 ]. O th er e x p e r i m e nt a l t e c h n i q u e s , p he no me no lo gi ca l mo d e li n g o f t h e i n e l a s t i cp r o c e s s e s , a nd d ev el op me nt o f g o v er n i ng c o n s t i t u t i v e e q u a t i o n s , a s w e l l a s t h ei n t e r r e l a t i o n o f s t r e s s r e l a x a t i o n a nd r e s i d u a l s t r e s s a r e r e vi ew e d i n a n ASTMs p e c i a l t e c h n i c a l p u b l i c a t i o n [4 41 . M an jo in e [ 4 5 I d i s c u s s e s how s t r e s sr e l a x a t i o n d a t a c a n b e us ed t o e v a l u a t e t h e r e d u c t i o n o f r e s i d u a l s t r e s s upont he r ma l e xp o s ur e , a nd L a f l e n an d J a s k e [ 46 1 u s e r e l a x a t i o n d a t a t o p r e d i c tc r e e p r a t e s i n t h r e e a l l o y s t e e l s . As a l r e a d y m en ti on ed , c r e e p d a t a c a n b eu se d i n a number o f d i f f e r e n t m od el s t o d e t e r m i n e ti m e - t e m p e r a t u re r e l a t i o n s h i p sf o r t h e rm a l e x p os u r e , a nd s t r e s s r e l a x a t i o n s t u d i e s a r e a c on v e n ie n t me thod t oob t a in t he nec es sa ry da t a . A lde rm an and Webs te r C471 have u sed a two-e l emen tc om po si te model t o d e s c r i b e t h e r e l a t i o n s h i p of c r e e p and s t r e s s r e l a x a t i o n t ot h e r e d i s t r i b u t i o n of i n t e r n a l s t r e s s e s w i th i n m a t e r i a l s , t h us u n i f y i n g t h ephenomena.

F a t i g u e I n du ce d R e s i d u a l S t r e s s R e l a x a t i o nP ro po se d mec ha nisms f o r t h e r e l a x a t i o n of r e s i d u a l s t r e s s d u e t o c y c l i c l o a d i n gc a n be s e p a ra t e d i n t o t h r e e r eg im e s t h a t o c cu r a t c y c l i c s t r e s s a mp l it u de s ( i )above t h e m ac ro sc op ic y i e l d s t r e n g t h , ( i i ) b elow t h e e nd ur an ce l i m i t , a nd ( i i i )i n be tween .F a t i g u e Above t h e Y i e l d S t r e n g t h . A c om pl et e r e d i s t r i b u t i o n o f t h e r e s i d u a ls t r e s s s t a t e o c c u r s when g r o s s y i e l d i n g t a k e s p l a c e . T h i s h ap pe ns i f t h ee n t i r e n e t s e c t i o n s t r e s s ex ce ed s t h e y i e l d s t r e n g t h , o r i f o n ly t h e s u r f a c ey i e l d s s uc h a s i n b e nd in g o r t o r s i o n . As m e nt io n ed p r e v i o u s l y , t h i s i s s om et im est ak e n a d v an t a ge o f i n o v e r s t r e s s i n g o p e r a t i o n s t o i n du c e c o mp re ss iv e s t r e s s e sa t th e s u r f a c e . When m ac r os co pi c y i e l d i n g of t h e s u r f a c e t a k e s p l a c e i n f u l l yr e ve r se d l o a d i n g , t h e s u r f a c e s t r e s s sh o u l d, a f t e r u n lo a di ng , b e o p p o s i t e i ns i g n t o t h e d i r e c t i o n o f l o a d in g d ue t o t h e c o n s tr a i n e d i n f l u e n c e of t h e s u b s u r fa c e[48-511. Q u es na l e t a l . [SO] m ea su re d t h e s u r f a c e r e s i d u a l s t r e s s a f t e r e a chh a l f c y c l e d u r i n g c y c l i c l o a d i n g and f ou nd t h e s t r e s s t o be d e pe n de nt on t h ed i r e c t i o n an d m a g n i tu d e o f u n l o a d i n g . T h i s e f f e c t h a s a l s o b e en s e e n by Kodama[ 48 ] and by Z i e ge l d o r f [ 5 11 , t h e l a t t e r s u g g e s t i n g t h a t t h e s e qu e n ce o f u n l o a d i n ga l s o a f f e c t s t h e s t r e s s . Kodama [ 48 ] no t ed t h a t , f o r some m a t e r i a l s , s i g n i f i c a n tm i cr o sc o p ic y i e l d i n g o n t h e s u r f a c e may t a k e p l a c e be lo w t h e b u l k y i e l d s t r e n g t ha nd l e a d t o t h i s s ame t y p e o f b e h a v i o u r .

Boggs an d By rne [ 5 2 1 i n v e s t i g a t e d t h e r e l a x a t i o n o f s h o t p eene d r e s i d u a l s t r e s s e si n Ni-Co a l l o ys . F o r Ni-20 Co and Ni-60 Co cyc l ed a t am p l i t ud es j u s t abovet h e y i e l d s t r e n g t h i n f u l l y r e v e r s e d c a n t i l e v e r be nd in g, r a p i d r e l a x a t i o n t o okp l ac e i n t h e f i r s t 1 00 c y c l e s b e fo r e e q u i l i b r a t i n g t o a c o n s t a n t de ca y s lo p e .The r e d u c t i o n i n t h e h i g h e r s t r e n g t h , h i g h e r s t a c k i n g f a u l t e n e r gy Ni-60 Coa l l o y was much l e s s t h a n i n t h e l o w er Co c o n t e n t a l l o y , a s w ou ld b e e x p e c t e d .Measu rem en ts o f s u r fa ce ha r dnes s d u r ing f a t i gu e showed no change , f rom wh icht h e a u t h o r s c o nc lu de d t h a t t h e s t r e s s r e l i e f p r o ce s s was d u e t o dyn amic r e c o ve r yi n t h e same s e ns e a s t h e r e c o ve r y pr od uc ed i n t h e r ma l s t r e s s r e l i e f p r i o r t oany r e c r y s t a l l i z a t i o n .S i g n i f i c a n t l y d i f f e r e n t b e h a vi o u r h a s be en ob se rv e d f o r s a mp le s c y c le d i nt e n s i o n - t e n s i o n l o a d i n g . W ei ss e t a l . [ 5 3 , 5 4 ) h a v e shown t h a t i n 304L a nd 3 16s t a i n l e s s s t e e l s c y c le d i n a x i a l t e n s i o n - t e n s i o n l o a di n g ab ov e t h e m on ot on icy i e l d s t r e n g t h , r a p i d r e l a x a t i o n of t h e i n i t i a l c om pr es siv e r e s i d u a l s t r e s st a k e s p l a c e a nd s u b s e q u e n t d e ve l op m en t o f a t e n s i l e s t r e s s o c c u r s . Voskamp ta l . [ 55 ] ha ve r e p o r t e d t h a t d u r i n g o v e r r o l l i n g i n t h e i n n e r r i n g of a d e e p- gr oo v e

a l l b ea r in g , t h e i n i t i a l l y t e n s i l e r e s i d u a l s t r e s s e s j u s t b elow t h e s u r f ac ed e c r ea s e p r o g r e s s i v e l y w i t h f a t i g u e and t h e n ch an ge t o c om pr e ss iv e s t r e s s e s ,w hi ch c o n t i n u e t o i n c r e a s e i n ma g ni t ud e w i t h f u r t h e r d e f o r m a ti o n . M cC li nt onand Cohen [ 5 6] h av e shown t h a t t e n s i l e r e s i d u a l s t r e s s e s d e v e l o p w i t h i n t h ep l a s t i c d e f o r m at i o n b an ds o f a n a n n ea l e d m il d s t e e l , e ve n a t l o a d s c l o s e t o t h ef a t i g u e l m t i n t e n s io n - t e ns i o n f a t i g u e . T he se c a s e s of r e s i d u a l s t r e s s


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358 PI R Jamesg e n e r a t i o n u n de r c y c l i c l o a d i n g c an b e a s c r i b e d t o i nh om og en eo us p l a s t i cd e f o rm a t i on d u e t o m e ch a ni c al o r s t r u c t u r a l c h an g es t h a t t a k e p l a c e . C ha ng esi n t h e y i e l d s t r e n g t h d u e t o work h a r de n i n g may s e t up c o n d i t i o n s wh ere t h es u r f a c e , which i n i t i a l l y p l a s t i c a l l y de fo rm s b e f o r e t h e s u b s u r f a c e and t h u sh a r d e n s t o a g r e a t e r d e g r e e , u n d e rg o es more e l a s t i c d e f o r ma t i o n t h a n t h e s u b s u r f a c ea n d su b se q ue n tl y i s h e l d i n t e n s i o n o n u n lo a di n g. I n a 52 10 0 b a l l b e a r i n gs t e e l , Voskamp e t a l . [ 55 1 showed t h a t d e co m po s it i on o f t h e a u s t e n i t e i s p r i m a r i l yr e s p o n s i b l e f o r t h e d ev el op me nt o f t h e c o mp r es s iv e r e s i d u a l s t r e s s e s . t i so b v i o u s t h a t su ch ch an ge s i n t h e r e s i d u a l s t r e s s s t a t e d ep en d o n t h e s p e c i f i cm a t e r i a l and l o a d i n g c o n d i t i o n s . B ec au s e o f t h i s , u s e o f t h e d e ve l op me n t o ft h e r e s i d u a l s t a t e t o d e te r mi n e f a t i g u e damage C531 i s l i m i t e d t o s p e c i f i cs i t u a t i o n s a nd h a s n o t become a g e n e r a l p u rp o se t o o l .F a t i g u e Near t h e E nd u ra n ce L i m i t . S e v e r a l i n v e s t i g a t o r s h a v e shown t h a t r e s i d u a ls t r e s s r e l a x a t i o n o c c u r s d u r i g g f a t i g u e f o r peak c y c l i c s t r e s s e s w e l l b el ow[ 5 7 , 5 8 1 and n e a r C591 t h e e n d u ra n c e l i m i t . t h a s b ee n s u gg e s t e d t h a t s t r e s sc o n c e n t r a t o r s may p r o v i d e t h e m ech an ism f o r r e l a x a t i o n i n t h i s r e g i m e 1 60 -6 33 ,a l t h o u g h d e f i n i t i v e r e s u l t s a r e l a c k i ng . P a t t i n s o n an d D ug da le C571, f o re xa mp le , f ound t h a t r e l a x a t i o n d i d n o t b e gi n u n t i l 1 0 c y c l e s i n a n A1 a l l o yL65 ( 4 - 1 / 2 Cu) c y c l e d be lo w t h e no mi na l e n du r an c e l i m i t . P o s s i b l y , d e f e c t s o rm i c ro c r a ck s g e n e r a t e d d u r i n g t h e l a t t e r p ha se o f t h e c y c l i n g p r o c e s s may h av ei n i t i a t e d a n e l a s t i c r e l a x a t i o n . A l s o , l o c a l t e m p e r a t u r e i n c r e a s e s d u r i n gf a t i g u e a t h i g h r a t e s o f c y c l i c l o a di n g may i n du c e r e l a x a t i o n . T h er e w i l la l wa y s be some form o f s t r e s s c o n c e n t r a t i o n s , s uc h a s a t g r a i n j u n c t i o n s ,d i s l o c a t i o n p i l e u p s an d p ha se bo u n da r ie s . Wi th t h e e x c e p t i o n o f l a r g e s t r e s sc o n c e n t r a t i o n s s uc h a s n o t c he s [ 60 1 , r e l a x a t i o n a t c y c l i c l o ad s b el ow t h ee n du r an c e l i m i t t a k e s p l a c e , i f a t a l l , o n l y late i n t h e f a t i g u e l i f e o f ac o mp o n en t , a nd p r o b a b l y b y m ec ha ni sm s c o m p l e t e l y d i f f e r e n t f ro m t h o s e i m p o r t a n tf o r l a r g e r c y c l i c s t r e s s a m pl i t ud e s.An a d d i t i o n a l f a c t o r i n s t r a i n h a rd e ni n g m a t e r i a l s i s t h a t e a r l y i n f a t i g u e ,m i c r o p l a s t i c d e f or ma t i on t a k e s p l a c e be low t h e f a t i g u e l i m i t u n t i l s t r a i nh a r d e n i n g o c cu r s i n d efo rm ed g r a i n s . R e la x a t i on i s c e r t a i n l y p o s s i b l e d u r i n gt h i s p e r io d .F a t i g u e a t I n t e r m e d i a t e S t r e s s A m p li t u de s . H ig h p e r fo r m an c e c om po ne nt s a r ecommonly de s ig n ed t o o p e r a t e i n a c y c l i c s t r e s s r eg im e t h a t e x c e e d s t h e m a t e r i a le n du r an c e l i m i t , b u t wh ic h i s l e s s t ha n t h e y i e l d s t r e n g t h . C o n si d er a b l e d a t ah a v e b e e n g e n e r a t e d o n t h e r e l a x a t i o n phenomenon i n t h i s r e g im e , b u t a c o m p le t emo de l e x p l a i n i n g r e l a x a t i o n b eh av i o u r ha s n o t y e t b ee n s u g g e st e d . I n g e n e r a l ,r e l a x a t i o n b e g i n s r a p i d l y w i t h i n t h e f i r s t f ew c y c l e s and d e cr e a s e s i n r a t ew i t h i n c re a s i n g f a t i g u e . I n d i s c u s s i n g i n t e r n a l s t r e s s e s , V a l l u r i E641 s u gg e s t e dt h a t t h e s i t u a t i o n i s a n a l o go u s t o c r ee p . I n s uc h a t h e rm a l l y a c t i v a t e d p r o c e s s ,r a t e t h eo r y i s o f t e n a p p l i c a b l e a nd g e n e r a l l y p r e d i c t s a n e x p on e n t i a l d ec re me nto f r e s i d u a l s t r e s s w i t h t h e number of f a t i g u e c y c l e s . S e v e r a l i n v e s t i g a t i o n s[ 6 5 ,6 6 1 ha v e u s e d r a t e p r o c e s s t h eo r y t o d e s c r i b e t h e r e l a x a t i o n r a t e e m p i r i c a l l y ,b u t t h ey ha ve n o t a t t e m p t e d t o s e p a r a t e t h e i n f l u e n c e o f i m po r ta n t v a r i a b l e ss u c h a s t h e m at e ri a l s p r o p e r t i e s a nd c y c l i c s t r e s s a m p l i tu d e . However, d a t a d os u p p o r t a n e x p o ne n t i a l d ec ay r a t e .S t u d i e s u s in g s u r f a c e r e s i d u a l s t r e s s e s ( me as ure d by x- ra y d i f f r a c t i o n ) t oi n v e s t i g a t e t h e r e l a x a t i o n p r o c e s s ha ve i l l um i n a t e d c e r t a i n a s p e c t s o f t h ep r ob l e m. T a i r a a nd M ur ak am i [ 6 7 ] h a v e shown t h a t t h e a mo un t o f r e l a x a t i o n i s af u n c t i o n of t h e a p p l i e d c y c l i c s t r e s s a mp li tu de . P o t t e r and M i l l a r d [ ] o b s e r v e do n l y m i n or r e l a x a t i o n i n c y c l i n g A1 70 75-T6 a t 0 . 5 w i t h t h e maximum c y c l i cs t r e s s a mp l it u de o f 0. 78 0 i e l d , w e l l a bo ve t h e f a t i g u e l i m i t , b e c a us e t h ec y c l i c s t r e s s r an g e was o n l y 0 . 39 o y i e l d ; t h e c y c l i c s t r e s s ( o r s t r a i n ) r an gei s t h e r e f o r e a l s o a n i m p o r t a n t v a r i a b l e . J am es a nd M o rr i s C68 s h o w e d t h a tc o m p re s s i ve m ac hi ni ng s t r e s s e s d e ca y d u r i n g f u l l y r e v e r s e d l o a d i n g o f A1 a l l o y s ,b u t t h a t i n t e n s i o n - t en s i o n l o a d i n g , b o t h co mp re ss iv e and t e n s i l e s t r e s s e s c anbe i n t r o du c e d d e pe n di n g o n t t ~ e a r t i c u l a r m i c r o p l a s t i c a nd h ar d e n in g r e s p o ns eo f t h e a l l o y 16 91 , a s i l l u s t r a t e d b y t h e c u r v e s o f F i g. 4


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R e l ax a t io n o f R e s i du a l S t r e s s e s

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F ig . F at ig ue - in du ce d r e s i d u a l s t r e s s e s i n f o u r a lu mi ni um a l l o y s .S amp le s w er e c y c l e d a t c o n s t a n t a m p l i t u de i n z e r o - t e n s i o n b en di ng .E s q u i v e l an d E va ns C701 h a v e shown t h a t t h e d e g r e e o f r e l a x a t i o n i n c r e a s e s w i t hi n c r e a s i ng s t r e s s g r a d i e n t i n s ho t - p e en e d 4 1 3 0 s t e e l , a n d b o t h E s q u i v e l an dE va ns [ 7 0] a nd H a y a sh i a nd Do i C581 f o u n d t h a t t h e g r e a t e s t r e l a x a t i o n t a k e sp l a c e on t h e s u r f a c e . L e ve r a nt e t a l . [ 71 ] h a ve shown t h a t n o t o nl y i s t h es t r a i n a m pl i t ud e a nd r a n g e i mp or ta nt , b u t a l s o t h a t c y c l i n g a b o u t a mean s t r a i ns i g n i f i c a n t l y a f f e c t s t h e r e l a x a t i o n ( a s l o ng a s t h e c y c l i c s t r a i n r an ge i sl a r g e e n o u g h ) . A mean s t r a i n o f -0.3 w as shown t o i n d u c e g r e a t e r r e l a x a t i o ni n s h ot - pe e ne d Ti-6A1-4V t h a n a mean s t r a i n o f +0 .3 ( c y c l i c s t r a i n r a n g e+ 0. 6 ) . T h i s was e x p e c t e d , s i n c e a c o mp r e s s iv e s u r f a c e s t r e s s was i n d uc e d ys h o t p ee ni ng , a nd t h e r e f o r e t h e sum o f r e s i d u a l a nd a p p l i e d s t r e s s e s was g r e a t e s tw i t h a c o m pr e ss i ve mean s t r a i n .Bo t h r e s i d u a l s t r e s s and h ar d ne ss d i s t r i b u t i o n s c a n c ha ng e w i t h r e p e t i t i v er o l l i n g c o n t a c t . Muro e t a l . [ 7 2 ,7 3 1 f ou nd t h a t c om pr e ss iv e r e s i d u a l s t r e s sv a l u e s a nd d e g r e e o work h a r d e n i ng i n c r e a s e a s t h e c o n t a c t s t r e s s a nd n umbero f c o n t a c t c y c l e s i n c r e a s e . I n s l i d i n g - r o l l i n g , F u j i t a and Yoshi da 1 741 a l s of ound a g r a du a l i n c r e a s e i n t h e co mp r es s iv e r e s i d u a l a t r e s s w i t h r o l l i n g c y c l e si n b o th a n n e a l e d a nd c a se - ha r de n ed r o l l e r s . R e l a x a t i o n o f t h e c i r c u m f e r e n t i a l


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3 6 0 M R Jamesc o mp r es s iv e s t r e s s e s was o ssumed t o be d ue t o t h e i n i t i a t i o n o f m i c r o c r ac k s i nt h e r o l l e r s u r f a c e a l o ng t h e a x i a l d i r e c t i o n . Iio e t a l . 753 f ou nd t h a t t h es l i d i n g wear p r o c e s s i n ALSI 1 01 8 and 4340 s t e e l s r a p i d l y a l t e r e d t h e i n i t i a ls t r e s s d i s t r i b u t i o n p ro du ce d by h e a t t r e a t m e n t o r p e e ni ng .

c o nv e ni e n t e x pe r i me n t al a pp ro ac h t o t h e s t u d y of r e s i d u a l s t r e s s r e l a x a t i o ns t o u s e a n e x t e r n a l l y imposed mean s t r e s s . Some b a s i c c h a r a c t e r i s t i c s o f t h er e l a x a t i o n p r oc e ss a r e fou nd t o be s i m i l a r . Mean s t r e s s e s r e l a x a t an e x p o n e nt i a lr a t e w i t h c y c l e s [ 763 and by a power law depen den ce [ 771, t h e r a t e of r e l a x a t i o nbe co mi ng s m a l l e r w i t h i n c r e a s i n g f a t i g u e . H i gh er s t r a i n a m p l i t u d e s p ro du c ef e s t e r r a t e s o f r e l a x a t i o n [ 76-79]. The r a t e o f r e l a x a t i o n d o e s n o t de pe nd o nt h e s i g n o f t h e mean s t r e s s [ 77 ].

Mean s t r e s s r e l a x a t i o n t e s t s a r e do ne by c y c l i n g t h e s am pl e i n s t r a i n c o n t r o la t a c .ons tan t s t r a i n r a n ge , u s u a l l y a bove t h e 0.2 o f f s e t y i e l d p o i n t , u n t i l a ne q u i l i b r i u m h y s t e r e s i s l o op i s ob t a i n e d ; a mean s t r e s s i s t h e n i mposed ( b ya d j u s t i n g t h e s t r a i n l i m i t s ) and i t s d ec ay r a t e i s f o ll ow ed w i t h f u r t h e r c y c l i n g .B ec au se of t h e c o n s t a n t s t r a i n am p li t u de c y c l i n g a nd u ni fo rm n e t s e c t i o n s t r e s si n h e r e n t i n t h e s e t e s t s , t h e mean s t r e s s e s r e l a x t o z e r o e xc e pt a t s m al l s t r a i na mp l i t ud es . ( ~ r o m u r pr e vi o us d i s c u s s i o n , t h e s u r f a c e r e s i d u a l s t r e s s wouldb e e x pe c te d t o ch an ge s i g n w i t h e a ch h a l f c y c l e b e ca u se o f t h e d i f f e r e n t v a l u e so f t h e y i e l d s t r e n g t h on t h e s u r f a c e a nd i n t h e b ul k . ) S u rf a ce r e s i d u a l s t r e s s e s ,h ow e ve r , o f t e n r e l a x t o s ome a s ym p t o t i c no n ze r o v a l u e d u r i n g f a t i g u e c y c l i n g i nt h e l oa d re gi me u nd er d i s c u s s i o n . I n t h i s r e g i m e , m a cr o sc o pi c y i e l d i n g o f t h eb u l k d oe s n o t t a ke p l a c e ; b u t , o f c o u r se , l o c a l i z e d y i e l d i n g a t t h e s u r f a c e i ss t i l l p r e s e n t . T h i s g iv es r i s e t o a r e d i s t - r i b u t i o n o f t h e r e s i d u a l s t r e s ss t a t e t o some n on z er o m a gn i tu de r a t h e r t h a n s i m p l y a n e x p o n e n t i a l d ec ay t oz e r o . The r e s i d u a l s t r e s s s t a t e i s a h i gh l y l o c a l i z e d d is t ur b a n ce i n an e l a s t i cc o nt i nu u m, a nd h e nc e i s a n u n s t a b l e c o n d i t i o n . T he d e g r e e o f s t a b i l i t y m us t b ed i c t a t e d by t h e s u r r ou n d i ng m a t r i x a nd s h o u l d d ep en d on s uc h f e a t u r e s a s t h er e s i d u a l s t r e s s g r a d i e n t , i n i t i a l s t r e s s s t a t e , p r i o r f a t i g u e h i s t o r y , a ndh a r d e n i n g o r s o f t e n i n g b e h a vi o u r p ro bl e ms n o t e n c o u n t e r e d i n mean s t r e s sr e l a x a t i o n t e s t s . F o r i n s t a n c e , J h a n s a l e a nd T op pe r [ 7 71 h av e shown t h a ts t r a i n a mp l it u de a nd number o f c y c l e s s eem t o be t h e p r i ma r y v a r i a b l e s i n f l u e n c i n gmean s t r e s s r e l a x a t i o n b e h av i ou r , a nd t o a f i r s t a p pr o xi m at i o n, t h e i n f l u e n c eo f o t h e r v a r i a b l e s i s n e g l i g i b l e ; o ne c an no t b e c e r t a i n t h a t s u c h c o n di t i o nsa r e a p p l i c a b l e d u r i n g r e l a x a t i o n of s u r f a c e r e s i d u a l s t r e s s e s . Even s o , m a t e r i a ld e p e nd e n t p r o p e r t i e s c a n b e e a s i l y s t u d i e d i n t h i s way. F o r i n s t a n c e , Morrowe t a l [ 9 ] f ou nd t h a t t h e amount of r e l a x a t i o n o c c u r r i n g i n m a r t e n s i t i c s t e e l sw as a f u n c t i o n of t h e i r h e a t t r e a t m e n t , w i t h t h e d e ca y b e i n g l e s s p r on ou nc edf o r h a r de r m a t e r i a l s , i n d i c a t i n g a de pende nce o n t h e m a t e r i a l d u c t i l i t y .Landgraf [ 801 a t t r i b u t e d s i m i l a r r e s u l t s t o a n i n c r e a s e i n t h e c y c l i c y i e l ds t r e n g t h w i t h i n c r e a s i n g h a rd n es s .E m pi r i ca l r e l a x a t i o n l aw s t o d e s c r i b e c e r t a i n l i m i t e d d a t a h a ve b ee n pr op os ed .I m p e l l i z z e r i [ 8 11 u s e d a s i m p l e e x p o n e n t i a l d e c a y f u n c t i o n a nd Ne u be r 's r u l e t oc a l c u l a t e t h e c yc l ic -d ep en de n t l o c a l s t r e s s a t a n ot c h , w hich p r e d i c t s r e l a x a t i o ne v e n bel ow t h e e nd ur an ce l i m i t a t t h e n o tc h . P o t t e r [ 82 ], i n s t u d y i n g t h ee f f e c t s o f o v e r l o a d be h a v i o ur , u s ed t h e n o n e qu i l i b r iu m c omponent o f t h e r e s i d u a ls t r e s s ( i . e . , t h e d i f f e r e n c e be t we en t h e i n i t i a l and e q u i l i b r i u m v a l ue o f t h er e s i d u a l s t r e s s ) a nd a n e x p o n e n t i a l r a t e of d e c ay ba se d on t h e c y c l e s t o e qu i l i b r i u mt o d e t er m in e t h e t r a n s i e n t v a l u e o f t h e r e s i d u a l s t r e s s . James and M or ri s [ 68 ]u se d a model o f m i c r o p l a s t i c s t r a i n t o de s c r i b e t h e e f f e c t of s t r e s s a m pl i tu deo n t h e de c ay r a t e i n A1 2219 . None o f t h e s e m od el s a d e q u a t e l y d e s c r i b e s t h ei n f l u e n c e of t h e c y c l i c s t r e s s o r s t r a i n r a n g e , t h e e nd u ra nc e l i m i t , t h e s t r e s sg r a d i e n t , o r p o s s i b l e work h a rd e ni n g o f t h e s u r f a c e .I n summary, r e l a x a t i o n o f s u r f a c e r e s i d u a l s t r e s s i s known t o o c cu r a t o r n e art h e f a t i g u e l i m i t . Well a bove t h i s r e g i o n , i . e . , i n low c y c l e f a t i g u e , t h er e s i d u a l s t r e s s s t a t e i s de pe nd en t on t h e d i r e c t i o n a nd m ag ni tu de o f l o ad i ng .Below t h e f a t i g u e l i m i t , r e l a x a t i o n may s t i l l t a k e p l a c e , i n t h a t t h e r e w i l l


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Relaxation of Residual Stresses 361always be stress concentrators, but definitive studies are lacking. Theseregimes are only intended to define a separation in the apparent behaviour ofthe surface residual stress and are not to be taken as definitive separationsbetween the mechanisms responsible. However, the influence of compressiveresidual stresses in increasing fatigue life is recognized to be highly dependenton stress stability, since relaxation m y take place early in the fatigueprocess.

VIBRATORY STRESS RELIEFProbably no technique has polarized opinions more than vibratory stress relief(vSR). A literature survey of work prior to 1968 was published by BrogdenC831, who remained largely unconvinced of the technique s merits. Since then,however, a number of investigations have shown improvements in dimensionalstability and lowered residual stresses [84-951. Undeniably, when appliedproperly, the method can relax the distribution of residual stresses. Thequestions to be answered are how does relief in stress take place; and, is anydamage induced?Commercial processes normally involve clamping an eccentric mass electric motorto the component of interest and vibrating it at resonant frequencies (usually10-100 Hz) for periods up to 15 min. The workpiece, of course, must be free tomove, but castings up to many tons have been relieved L871. Resonant frequenciesare used to impart the largest stress amplitude with small inputs of energy,but require control of the vibrator s frequency. The necessary feedback controland proper instrumentation to record and display pertinent data have beenelaborated on by Klauba and Adams [92-931. The resonant frequency varies withthe internal state of stress and changes by small amounts during the stressrelieving process. Monitoring shifts in the resonant frequency enables therelaxation process to be quantified and verified. Instrumentation sold byBonal Technologies operates just below the resonant frequency, which is supposedto induce more absorbed energy into a component.An understanding of the mechanism behind VSR can be obtained by reviewing aprevious section, where examples were given of stress relaxation during cyclicloading. The types of stress or strain amplitudes used in successful VSR areequivalent to cyclic loading above the endurance (fatigue) limit. Relaxationtakes place by microplastic deformation, in which the movement of dislocationsredistributes the residual elastic stresses and the microstresses. The dislocationexperiences a force equal to the sum of the vibratory and static stresses. Thevibrations of dislocation segments are highly damped so that in the low frequencyrange there is no possibility of storing energy from one cycle to another.Natural frequencies of vibration of dislocations are in the gigacycle range.Thus, VSR is simply a low cost method of cyclically loading a component torelax the residual stresses through microplastic deformation. Small-scaledeformation takes place above a threshold usually equivalent to the fatiguelimit. As shown in a previous section, the relaxation is dependent on thecyclic amplitude and is modified by cyclic hardening or softening, but it isexponential in rate. Thus, the major relief occurs in l0 -10~ cycles, within 10min or so at the normal frequencies used. Accumulation of cyclic damage mustalso occur during this process. If damage accumulates at rates predicted by aCoffin-Manson type relationship, as suggested by Cooper and Fine [961, the rateof damage accumulation is considerably slower than the exponential rate ofresidual stress relaxation. James and Morris 1681 found that the majority ofrelaxation in A1 22198 took place far before the initiation of surface microcracks.Dawson and Moffat 1971 concur, stating that although the fatigue limit must beexceeded for VSR to work, the accumulated fatigue damage should be minor.By analogy of the VSR process to that of microplastic deformation, we can alsounderstand why the method is relatively ineffective in bent tubing and other


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362 M. R. Jamescomponents having undergone cold-work processes. These processes raise thethreshold limit (fatigue limit) at which VSR is effective by pinning thedislocations and making slip processes more difficult. VSR techniques combinedwith low thermal treatments have been shown to be very effective in stressrelieving welded structures C911, as would be expected by the thermal enhancementof plastic flow. The authors developed a finite-difference model and used thevo n Mises yield criterion to model the VSR process numerically. As a point ofinterest, it is well known that surfaces microplastically yield at lower stresslevels than the bulk due to lack of three dimensional constraints and environmentaleffects. Thus, surface measurement techniques to monitor residual stressshould be most scnitive to the VSR technique.

CONCLUSIONS

This perspective on relaxation of residual stress offers insight into the manyways residual stress can be relieved and redistributed, both deliberately orunintentionally during service. Appropriate research on stress relievingshould focus on correlating creep resistance to thermal relief and models ofmicroplastic deformation to mechanical stress relieving. Many techniques havebeen used to monitor the degree of relaxation with that of dimensional stabilityof a part being the most simple and most used. Recognition of the decay ofbeneficial residual stresses during service should lead to the use of moresophisticated nondestructive measurement techniques t monitor the distribution.Finall y, robust models, whether analytical or numerical, would be of greatvalue in quantitatively predicting the relaxation rat e, a prediction thatcurrently is as much art as science.

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London, 1-10.Metals Handbook, (1971) Ninth Edition, Vol. 2 B.P. Bardes, ed., American

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Stress Relaxation, ed. E. Kula and V. Weiss, Plenum Press, 205-226.Woodward, J., D. van Rooyen and A. R. McHee (1984) In-Situ Stress Relief

of Expanded Alloy 6 00 Steam Generator tubing, DOE Contract No.DE-AC02-76CH00016, Report No. DE84-014560.Thompson, M. and J. R. White (1971) Polymer Eng. and Sci. 24 227-241.

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1987127-Reduction Residual Stress

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