On the Fatigue Notch Factor Kf

5/26/2018 On the Fatigue Notch Factor Kf

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U T T E R W O R T HE I N E M A N N Int. J. Fatigue Vol, 17, No. 4, pp. 245-251, 1995Copyright 1995 Elsevier Science LimitedPrinted in Great Britain, All rights reservedI)142-1123/95/ 10.(30O n t h e f a t ig u e n o t c h f a c to r K fY a o W e i x i n g X i a K a i q u a n a n d G u YiAirc raft Department, N anjun g Unive rsity of Aero nautics and Astronautics, Na njing210016, P.R. ChinaReceived 4 May 1994; revised 22 August 1994)This paper reviews the fatigue notch factor, Ke and some expressions for it that are in current use.All the expressions for Kf can be classified into one of three types: the average stress model, thefracture mechanics model and the stress field intensity model analysis. These are compared on thebasis of fatigue mechanism and experimental results. It is found that the stress field intensity modelis the most reasonable, and has the greatest potential.K e y w o r d s : s t r e s s c o n c e n t r a t i o n ; f a t i g u e n o t c h f a c t o r ; a v e r a g e s t r e s s model; fracture mechanics model; s t r e s s f i e l d

s t r e n g t h )

DEFINITION OF FATIGUE NOTCH FACTORNotches are one of the main factors that control thefatigue strength of structures, The fatigue notch factor,Kf, plays a very important part in the estimation offatigue life and fatigue strength of structures. Up tonow, there has been no expression for Kf that iscommonly accepted for different conditions. Theproblem of finding a brief and economical derivationof Kf has not been solved, because the fatigue notchfactor is rather like a black box, with many factorsthat are difficult to determine.The most commonly accepted definition of Kf is theratio of the fatigue strength of a smooth specimen,Se to that of a notched specimen, SN, under the sameexperimental conditions and the same number ofcycles1:

Kf = fatigue strength of smooth specimen, Sefatigue strength of notched specimen, SN 1 )

Obviously, the most direct and reliable way to deter-mine Kf is by experiment, but in practice this wastestime and money; moreover, Kf is related to the sizeand geometry of the specimen, and varies with theloading type. So in the prediction of fatigue strengthor fatigue life Kf is usually obtained by analysis, withsome experimental support.Heywood2 believed that the cyclic properties ofmaterials could be included if the stress concentrationfactor K x of the Neuber formula3 was replaced by thefatigue notch factor Kf. Later , some papers 4-6 gaveanother definition of Kf based on a modified Neuberformula:K f = ~ j K K 2)

where K is the true stress concentration factor andK~ is the true strain concentration factor. There aregreat differences between the above two definitions.Equation 1) is based on experiments; Equation 2)

is based on the fatigue failure criterion of maximumstress at the notch root. Equa tion 1) satisfies thelimit condition 1 - Kt ~ K x but Equat ion 2) doesnot in some cases, leading to K~ > KT. It thereforeseems that Equat ion 2) is not so reasonable.Plentiful experimental results show that the fatiguenotch factor Kf is related to a number of factors,including material properties, material inheren t defects,size and geometry of specimen, stress gradient, loadingtype and number of loading cycles. A notch-sensitivefactor, q, can be introduced to indicate the sensitivityof materials to notches:

Kf - 1q = / T--- ] 3)where 0 -< q _< 1. Kf = K T if q = 1, and K f 1 ifq = 0 .In this paper, the definitions of and some commonlyused expressions for Kf are briefly reviewed. Analysisand comparisons between the expressions are madebased on fatigue mechanism and experimental results.

A BRIEF REVIEW OF EXPRESSIONS FOR K fBased on the definition of Equation 1), manyexpressions for the fatigue notch factor have beendeveloped in the past four decades. All theseexpressions are built up on various assumptions. Thispaper focuses on the analysis and comparison ofrecently and commonly used expressions.These expressions for Kf can be classified into threemodels according to their assumptions:1. the average stress AS) model;2. the fracture mechanics FM) model;3. the stress field intensity SFI) model.T a b l e 1 lists some representative expressions.

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2 4 6T a b l e l S o m e e x p r e s s i o n s f o r K f

Yao W e t a l .

A u t h o r s A b b r e v i a t i o n E x p r e s s i o n M a t e r i a l p a r a m e t e r s R e f .A v e r a g e s t r e s s m o d e l sN e u b e r , K u h n a n dH a r d r a h t

P e t e r s o n

H e y w o o d

B u c h

N K H K T - 1f = 1 + - - -

P K T - - 1K f = 1 + . . . . a1 + PH KK , -I + 2 ~

K , : K T 1 - 2 . 1 0 + p ~ A

a = f ( t r , ) is t h e f u n c t i o n o f 1 , 3 ,7u l t i m a t e s t r e s s

a i s a m a t e r i a l c o n s t a n t 6

a = f ( ~ b ) d e p e n d s o n m a t e r i a l 2 ,9a n d s p e c i m e n

A , h d e p e n d o n m a t e r i a l s a n d 1 0 ,1 1s p e c i m e n , t ~ i s a f u n c t i o n o f Aa n d hS t i e l e r a n d S i e b e l S S K T a = f ( o 2 ) i s a m a t e r i a l 8

K f = - - - ~ c o n s t a n t1 + ' 1 + a XW a n g a n d Z h a o W Z K TK f - 0 . 8 8 + A Xh

A , b a r e m a t e r i a l c o n s t a n t s 1 2

F r a c t u r e m e c h a n i c s m o d e l s

Tin g an d La w ren ce TL / D/D-~-~.~ l . i s t h e i n t r in s i c c r ack l en g th , 1 8K j = Y ( a , . ) ~ 1 + .~ 1 ~ '1 l. a ~ . > a * U , ho i s e f f e c t i v e t h r e s h o l ds t r e s s i n t e n s i t y r a t i o f o r a l o n gU * . Y ( a * ) . / D + a * c r a c kK f

TopperYU'u O u e s n a y a n d Y D T F o r s h a r p n o t c h ' : K ~ = I ( 1 + ~ / D ) 1,, i s t h e i n t ri n s ic c r a c k l e n g t h . 2 0A ~ a n d A e a r e t h e l o c a l s t r e s sK ~ AS~F o r b l u n t n o t c h ' : K f - . _ _ a n d s t r a in r a n g e a t n o t c h r o o t\,' A~rAeE

( b ) C ~ i s c r i t i c a l c r ack l en g th , a 2 1Z u . H u a n g a n d C h e n Z H C K f = K T / .; :1 + 4 . 4 C . . / p = 1 .0 a n d b a r e s e m i - a x l e o f a nK f ~ K T / \ " 1 + 3 . 5 Q . / p ( b = 0 . o 5 ) e l l i p s e

S t r e s s f i e l d i n t e n s i t y m o d e l s

Y a o W e i x i n g a n d G u Y i Y G -V1h ~ x St re ss fieldconstantdomain is a 23 ,24K , = f ( ' ~ , ) " q ~ - - I d v m a t e r i a lS h e p p a r d S t ro v e ]M M i s s t r e s s f i e ld d o ma in 2 6Kf - S r~

1 d t rp i s o n e r a d i u s o f t h e n o t c h r o o t , g i s t h e r e l a t i v e s t r e s s g r a d i e n t : X = - -O'm~x dxa F o r b l u n t n o t c h e s t h e m a x i m u m t h r e s h o l d s t r e s s o c c u r s a t c r a c k i n i ti a t i on a t a n o t c h r o o t , a n d f o r s h a r p n o t c h e s t h e m a x i m u m t h r e s h o l ds t r e s s o c c u r s a t a f i n i t e c r a c k l e n g t h f r o m a n o t c h r o o t .

A ve rage st r ess A S ) m ode lT h e m o d e l fir st p r e s e n t e d b y K u h n a n d H a r d r a h O

( t h e K H m o d e l ) b e c a m e t h e f ou n d a t i o n o f th e a v e ra g es tr e s s m o d e l 3 -7 . T h e K H m o d e l a s s u m e s t h at f a t ig u ef a i l u r e o c c u r s i f t h e a v e r a g e s t r e s s o v e r a l e n g t h Af r o m t h e n o t c h r o o t i s e q u a l t o t h e f a t i g u e l i m i t O e o fa s m o o t h s p e c i m e n F i gu r e 1 ) . T h e K H m o d e l g i v e sa n e x p r e s s i o n f o r K f a s f o l l o w s :

K T - - 1Kf = 1 + (4 )1 + ~ r

B'-- .0

w h e r e p i s t h e r a d i u s o f t h e n o t c h r o o t , w i s t h e o p e na n g l e o f t h e n o t c h , a n d A i s a m a t e r i a l c o n s t a n t , w h i c hi s a fu n ct i o n o f th e m a ter i a l t e n s i l e s t rn eg th l i m i t , Orb,a n d l i e s b e t w e e n 0 . 0 2 5 a n d 0 . 5 1 m m .

N e u b e r 3 r e w r o t e E q u a t i o n ( 4 ) a s t h e N K H m o d e l :K , - - 1 + K _ ~ 7 1 5 )

wh ere a = f (~ rb) is a m a te r i a l co n s ta n t .P e t e r s o n 6 a s s u m e d t h a t f a t i g u e f a i l u re o c c u r s w h e nt h e s t r es s o v e r s o m e d i s ta n c e d o a w a y f r o m t h e n o t c h


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On the fat igue notch factor K 247

Figure 1 A vera ge s t ress mo del

i s e q u a l t o o r g r e a t e r t h a n t h e f a t i g u e s t r e n g t h o f as m o o t h s p e c i m e n F i g u r e 1 ) . O b v i o u s l y , P e t e r s o n ' sm o d e l i s a p o i n t s t re s s m o d e l , w h i c h c a n b e c o n s i d e r e da s a sp e c i a l c a s e o f t h e a v e ra g e s t r e s s m o d e l . P e t e r s o nt h e n s u p p o s e d t h a t t h e s t r e s s n e a r t h e n o t c h d r o p sl i n e a rl y , a n d o b t a i n e d t h e f o l l o w i n g e x p r e s s i o n f o r K f .K r - 1

wh e re a i s a m a t e r i a l c o n s t a n t . B a s e d o n a s i m i l a ra s s u m p t i o n t o t h a t o f P e t e r s o n , S i e b el a n d S t i e l e r 8o b t a i n e d t h e f o l l o w i n g e x p r e s si o n :K~K ~ = - _ _ ( 7 )

1 + \ a ~wh e re a = f l t ro . 2 ) is a m a t e r i a l c o n s t a n t a n d X is t h es t r e s s g r a d i e n t a t t h e n o t c h ro o t .H e y w o o d 2'~ o b t a i n e d a n e x p re s s i o n b a s e d o n i n t r in s i cd e fe c t s :

K TKf = (8 )1 + 2 ~ 0

w h e r e a d e p e n d s o n t h e t y p e o f m a t e r i a l a n d s p e c i m e n .B y c o n s i d e r i n g t h e s t r e s s g r a d i e n t , B u c h m , l l d e d u c e da n e x p r e s s i o n w i t h t w o p a r a m e t e r s :

Aw h e r e A a n d h d e p e n d o n t h e m a t e r i a l a n d t h e t y p eo f s p e c i m e n , a n d t ~ i s a fu n c t i o n o f A a n d h .W a n g a n d Z h a C a ga v e a n o t h e r e x p r e s s io n w i t h t w op a r a m e t e r s a f t e r a n a ly s i n g a n u m b e r o f e x p e r i m e n t a lresu l t s :

K TK t = 0 . 8 8 g A ) t~ (10 )w h e r A a n d b a r e m a t e r i a l c o n s t a n t s , a n d X i s t h es t r e s s g r a d i e n t a t t h e n o t c h r o o t .T h e re a r e n u m e ro u s o t h e r e x p re s s i o n s 4 ,1 3-~ 5 t h a tc a n b e r o u g h l y c l a ss i fi e d a s A S m o d e l s .

F r a c tu r e m e c h a n i c s F M ) m o d e lF ro s t a n d P h i l l i p s 16 f i r st u s e d f r a c t u re m e c h a n i c s t os t u d y t h e f a t i g u e s t r e n g t h o f n o t c h e d s p e c i m e n s .M i l l e r t7 b e li e v e s t h a t s h o r t c r a c k s a r e t h e k e y p r o b l e mi n t h e f a t i g u e s t r e n g t h o f n o t c h e d s p e c i m e n s . T i n g a n dL a w r e n c C 8 p r o p o s e d a c r a c k - c lo s u r e- a t -a - n o tc h ( C C N )m o d e l , o n e o f t h e F M m o d e l s , t o s t u d y t h e f a t i g u e

s t r e n g t h o f n o t c h e d s p e c i m e n s . T h e F M m o d e l a s s u m e st h a t c r a c k s i n i t i a t e a t t h e n o t c h , b u t b e c o m e n o n -p ro p a g a t i n g c r a c k s o f l e n g t h a t h Figure 2) . T h e re i sa n i n t r i n s i c c r a c k w i t h l e n g t h l o fo r s m o o t h s p e c i m e n s t9t t l llo = 7r \ A Se }

wh e re AKIn i s t h e l o n g c r a c k t h r e s h o l d s t r e s s i n t e n s i t y ,wh i c h i s a m a t e r i a l c o n s t a n t a t a c e r t a i n s t r e s s r a t i oR , a n d AS c i s t h e s t r e s s r a n g e a t t h e f a t i g u e l i m i t o fa s m o o t h s p e c i m e n . T h e e f f e c t iv e th r e s h o l d s t r e s si n t e n s i ty f a c t o r r a n g e AK eff ,th o isAKeff , thO = U t h 0 A S c \ , 7 r lo (1 2 )

w h e r e U t h O i s t h e e f f e c t i v e t h r e s h o l d s t r e s s i n t e n s i t yf a c t o r f o r a l o n g c r a c k I s. F o r a n o t c h e d s p e c i m e n , t h ee f f e c t i v e t h r e s h o l d s t r e s s i n t e n s i t y r a t i o fo r a c r a c klength ath isAKcff , thO =- Uth Y a th )ASth \ / r r ( D + a th ) (1 3 )

wh e re U t h i s t h e e f f e c t i v e t h r e s h o l d s t r e s s i n t e n s i t yr a t i o fo r a c r a c k l e n g t h a th , a n d Y(a t h ) i s a g e o m e t ryf a c t o r f o r t h e s t r e s s i n te n s i t y fa c t o r . A c c o r d i n g t oa s s u m p t i o n , f a t i g u e f a i l u r e o c c u r s w h e n A K e f f t h - ~AKe fc t h o . C o m b i n i n g E q u a t i o n s (1 2 ) a n d (1 3 ) t h e ng i v e s t h e fo l l o w i n g e x p re s s i o n fo r Kf .A S , : U t h Y a t h ) a / - O + a t h

g f = S S t h ~ - a th ~ ; W 1 0 (1 4 )T h e C C N m o d e l f u r t h e r s u p p o s e d t h a t i f a th 3> a* ,E q u a t i o n ( 1 4 ) c a n b e r e w r i t t e n a sK f = Y a t h ) 1 + O~eff)~/o . ( l S a )

wh e re De f t i s t h e e f f e c t i v e n o t c h d e p t h . I f a th < a * ,l e t a ~ h = a * ; t h e n E q u a t i o n (1 4 ) c a n b e r e wr i t t e n a sU~h Y a* ) , / -D + a*K . . . . u . .. .. 15 8 )

Y u et al. T a l s o o b t a i n e d t w o e x p r e s s i o n s b a s e d o ns h o r t - c r a c k f r a c t u r e m e c h a n i c s . Z u et al. el o b t a i n e dt w o e x p r e s s i o n s f o r K t v e r s u s K T b a s e d o n n o n -p r o p a g a t i n g c r a c k a n a l y s is . S m i t h a n d M i l l e r = o b t a i n e da n e x p r e s s i o n b a s e d o n f a t i g u e c r a c k g r o w t h f r o m a ne l l ip se .S t re s s f i e l d i n t e n s it y S F I ) m o d e l

F a t i g u e f a i l u r e i s c a u s e d b y d a m a g e a c c u m u l a t i o n i nt h e l o c a l d a m a g e d z o n e . M a c r o s c o p i c a n d m i c r o s c o p i cr e s e a r c h i n t o f a i l u r e m e c h a n i s m s h a s s h o w n t h a t t h ea c c u m u l a t i o n o f f a t i g u e d a m a g e a t t h e s i z e o f s e v e r a lg r a i n s, a n d t h e f a t i g u e st r e n g t h o f s t r u c t u r e s , d e p e n dn o t o n l y o n t h e p e a k s t r e s s a t t h e n o t c h r o o t b u t a l s oo n t h e s t re s s f ie l d i n t e n s i t y o f t h e d a m a g e z o n e . B a s e do n t h i s c o n c e p t , Y a o 2 3,2 4 d e v e l o p e d a n e w f a t i g u e


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2 4 8 Y a o W e t a l .

t h

Figure Fracture mechanics model

_ i /

d e s i g n a p p ro a c h : t h e s t r e s s fi e l d i n t e n s i t y a p p ro a c hF i g u r e 3 ) . Th i s a p p ro a c h d e f i n e s a s tr e s s f ie l d i n t e n s i t yfunc t ion , OrFI as fo l lows :OrFi = f o r i j ) q ~ r )d v (1 6 )

w h e r e I I i s t h e f a t i g u e f a i l u re r e g i o n , V is th e v o l u m eo f ~ , q ~ ( r) i s a w e i g h t f u n c t i o n , a n d f ( ~ j ) i s t h e

1

/

e q u i v a l e n t s t r e s s f u n c t i o n . ~ i s a m a t e r i a l c o n s t a n t ,a n d c a n b e a p p r o x i m a t e d a s a s p h e r e w i t h t h e c e n t r ea t t h e n o t c h ro o t . T h e s p a t i a l e x t e n t o f ~ i s u s u a l l ys e v e ra l g r a i n s .A c c o r d i n g t o t h e a s s u m p t i o n o f t h e S F I a p p r o a c h 25,f o r a s m o o t h s p e c i m e n F i g u r e 4 ) the s t res s f i e ldintensi ty cr~ iso~r{, = S~ (1 7 )

F o r a n o t c h e d s p e c i m e n , t h e s t r e s s f ie l d i n t e n s i t yo'~n is1 f ~ j ) q ~ r ) d v (1 8 )

w h e re ~ j = % (S N ) i s a f u n c t i o n o f a p p l i e d s t r e s s ; s of (o -0 ) = S ~( &q ) , and &q = t r a / S N fo r e las t i c i ty , 6 ,j =& q (S N ) fo r e l a s t o -p l a s t ic i t y . Eq u a t i o n (1 8 ) c a n b ew r i t t e n a so'~Fi = f(6 ,q )q~( r )d v (1 9)A c c o r d i n g t o t h e S F I m o d e l , f a t i g u e f a i l u r e o c c u r si f ~F~ = O~FI = O 'e r. Fr om Eq ua t io ns (17 ) and (19 ) , i tc a n b e d e d u c e d t h a t

Sc 1 fg f - - a N = V J I ~ f d r ij ) ~ P r )d r ( 2 0 )F o r t h e p l a n e p r o b l e m , E q u a t i o n ( 2 0 ) c a n b e w r i t t e na s

f of = S f ( ~ l i j ) ~ d s 2 1 )w h e re D i s a p l a n e r e g i o n , a n d S is t h e a r e a o f D .

t S N

qN

tSV

Figure 3 Stress field intensity model Figure 4 Stress field intensity mode l of f


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O n t h e f a t i g u e n o t c h f a c t o r K f 2 4 9Sheppard 26 assumed that the fatigue strength of anotched specimen is related to the average stress overthe volume near the notch, and definedK, - UaveI~t (22)SN

where M is the stress field domain near the notch,and SN is the applied stress.Discussion

The AS model and the SFI model assume that thereare no cracks in the specimen before it is used, andthe expressions for Kf are built up on the traditionalfatigue concept. The FM model assumes that thereare cracks in all specimens, and the expressions forKe are built up on the basis of short crack behaviours.Hence there are the following differences between theFM model and the AS model or the SFI model:1. There are two possible outcomes leading to aninfinite fatigue life. One is that no cracks initiateat the notch root; the other is that cracks initiateat the notch, but become non-propagating cracks.2. In general, Kf is needed no t only for infinite fatiguelife but also for finite fatigue life. It is difficult touse the FM model for the latter case.3. It is probable that there are no non-propagatingcracks for some notched specimens, especially forthose with lower Kw.It can therefore be stated that the FM model has a bettermechanical foundation, but its scope of application isnarrower.

It is found that the AS model is a special case ofthe SFI model. If we take D in Equation (21) as L,with length l, then Equation (21) can be written asIILK, = ~ /(6'y )~(x)dx (23)

where f(&y) = /SN. If ~(x) = 1, Equation (23) is1= f ~ y dx ( 2 4 a )f ]

Equation (24a) is the AS model. If ~(x) is a deltafunction, (x) = 8(x - do), Equa tion (23) isKf = ~- - (24b)

Equation (24b) is Peterson's model.COMPARISON BETWEEN THE MODELSSome comparisons between the three main modelsreviewed above can be made on the basis of experimen-tal results. Figure 5 presents a general comparisonbetween experimental values of fatigue notch factorand the predicted values based on the formulaedescribed in the preceding sections. For the SFI model,assuming weight ~ = 1 - xr (1 + sina), where g isthe stress gradient of notch root, r is the distancefrom the notch root and a is the angle from thex-axis within the damaged region, the fatigue notchfactor is calculated according to Equation (22), inwhich a finite element method is used for stress

K p oa~ KrrE. ~1 4

1

0 8

0 . 60

00 0

O 00 0 00 O

0

N A l l M O d e l 0 ~ F I M O a Q | ~ C C N M O 4 e |I L L I h l

2 4 6 8 10 K T

F i g u r e C o m p a r i s o n b e t w e e n e x p e r i m e n t a l r e s u lt s a n d S F I m o d e l ,a n d b e t w e e n A S m o d e l o r F M m o d e l a n d S F I m o d e l

analysis. Three sets of experimental data are employedbelow.Plates with central hole H

The specimens are made of ST52-3 steel(0.15-0.20 C, 1.5-2.1 Mn). The experimentalresults and the results predicted by the AS model andthe SFI model are listed in Table 2. The materialproperties needed in the computation are taken fromref. 11. For the AS model, the fatigue notch factor iscomputed according to Neuber's formula (Equation(5)) in which the material cons tant a = 0.163 mm 1for ST52-3.Figure 5 and Table 2 show that the results of theSFI model agree more closely with the experimentalresults, with lower average error and maximum errors.

Plates with edge notchesReference 18 presents some experimental resultsand the CCN model, one of the fracture models, formild steel (0.15 C) plates with symmetrical edgenotches. The experimental results, the FM model andthe SFI model are presented together in Table 3 andplotted in Figure 5. It can be seen that the fatiguenotch factor predicted by the SFI model has fewererrors, and is much better than that predicted by the

CCN model.In order to investigate how the residual stressinfluences the fatigue notch factor, experimental resultson SAE413027 are employed. Figure 5 and Table 4show the corresponding comparison for a nominalmean stress with the same number of cycles, N = 105.The comparison shows that the SFI model yields agood estimation of the fatigue notch factor.The above results clearly show that the proposedstress field intensity model provides improved perform-ance in prediction of the fatigue notch factor prediction.ACKNOWLEDGEMENTThis work was supported by National AeronauticalScience Foundation of China, Q91B5201.REFERENCES

1 K u h n , P . a n d H a r d r a h t , H . F . ' A n E n g i n e e r i n g M e t h o d f o rE s t i m a t i n g t h e N o t c h - S i z e E f f e c t i n F a t i g u e T e s t s o n S t e e l ' ,


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2 5 0 Y a o W e t a lT a b l e 2 C o m p a r i s o n o f f a t i g u e n o t c h f a c t o r o f p l a t e s w i t h c e n t ra l h o l e a t f a t ig u e l i m i tR a d i u s , r W i d t h , W T S K f K t K f E r r o r ( % ) E r r o r ( % )( m m ) ( m m ) ( M P a ) ( M P a ) ( e x p . ) ( A S m o d e l ) ( S F I m o d e l ) ( A S m o d e l ) ( S F I m o d e l )

(1 - 1 270 - - _1 20 2.72 155 1.74 2.23 1.66 28.16 4.483 60 2.72 140 1.93 2.39 1.97 23.84 1.874 40 2.52 154 1.75 2.26 1.85 29.16 5.4910 64 2.32 165 1.64 1.84 1.75 18.29 6.8312 84 2.3 6 145 1.86 2.22 1.83 19.35 1.5620 68 2.07 155 1.74 1.98 1.64 13.79 5.92

A v e r a g e e r r o r 2 2 . 1 0 4 . 3 6M a x i m u m e r r o r 2 8 . 1 6 6 . 8 3Rad iu s o f r eg ion D = 0 .21 mm

T a b l e 3 C o m p a r i s o n o f f a t i g u e n o t c h f a c t o r o f p l a t e s w i t h e d g e n o t c h e s a t f a ti g u e l im i tRad ius , r K1- ASN ASth K, Kf K , E r r o r ( % ) E r r o r ( )( m m ) ( M P a ) ( M P a ) ( M P A ) ( e xp . ) ( C C N ) ( S F I) ( C C N ) ( S F I)0 1 420 . . . . .0 .10 12.5 100 92 4.20 4.57 4.86 8.81 15.70.25 8.20 108 92 3.89 4.57 4.29 17.48 10.30.50 6.10 100 91 4.20 4.62 3.98 10.0 5.241.27 4.00 124 1(15 3.39 4.00 3.07 17.99 9.44

Av er ag e e r r o r 13 .57 10 .17Ma ximu m er r o r 17 .99 15 .7 (IW = 6 4 m m ; l o a d ra t i o R = - 1 ; r a d i u s o f r e g i o n D = 0 . 1 4 m m ; AS,h i s t h e C C N m o d e l p r e d i c t e d s t r e s s a m p l i t u d e

T a b l e 4 C o m p a r i s o n o f f a t ig u e n o t c h f a c t o r o f p l a t e w i t h e d g en o t c h e s a t f a t i g u e l i m i tM e a n s t r e s s M a x i m a l s t r e s s f K~ E r r o r( k s i ) ( k s i ) ( e x p . ) ( p r e d . ) ( % )

0 40 1.575 1.426 9.4610 50 1.46 1.425 2.4020 60 1.35 1.415 4.8130 69 1.29 1.358 5.27A v e r a g e e r r o r 5 . 4 8M a x i m u m e r r o r 9 . 46

W = 2 .25 in , H = 17 in ; K x = 2 .0 ; D = 0 .00272 inN o m i n a l m a x i m a l s t r e s s f o r u n n o t c h e d s p e c i m e n s i s 6 3 k s i

67

9101 l1213

N A C A T N 2 8 0 5 , L a n g le y A e r o n a u t i c a l L a b o r a t o r y , W a s h -ing ton , 1952H e y w o o d , R . B . Engine e r ing 1955, 179, 146N e u b e r , H . J. A p p l . M e c h. A S M E 1961, 28, 544N i e , H . a n d W u , F . Ac ta Ae ronaut . A s t ronaut . S in . 1988,9 , A 4 2 4H o f f m a n n , M . a n d S e e g e r , T . I n ' P r o c . I n t . C o n f . o n F a t i g u eo f E n g i n e e r i n g M a t e r i a l s a n d S t r u c t u r e s ' , L o n d o n , V o l . 1 ,1986 , pp . 195- 202P e t e r s o n , R . E . I n ' M e t a l F a ti g u e ' ( E d . G . S i n e s ), M c G r a w -H i l l , 1 9 5 9 , p p . 2 9 3 - 3 0 6F r o s t , N . E . , M a r s h , K . J . a n d P o o k , L . P . ' M e t a l F a t i g u e ' ,O x f o r d U n i v e r s i t y P r e s s , 1 9 7 4S iebe l , E . and S t i e l e r , M. V D 1 - Z . 1955, 97, 121H e y w o o d , R . E . ' D e s i g n in g A g a i n s t F a t i g u e ' , C h a p m a n &H a l l , L o n d o n , 1 9 6 2B u c h , A . Mater . Sc i . Eng. 1974, 15, 75B u c h , A . ' F a t i g u e S t r e n g t h C a l c u l a t i o n ' , T r a n s T e c h P u b l i -ca t i ons , Swi t ze r l and , 1988W a n g , Z . a n d Z h a o , S . 'F a t i g u e D e s i g n ' , M e c h a n i c a l I n d u s t r yP u b l i s h e r , 1 9 9 2 ( i n C h i n e s e )C h i n e s e A e r o n a u t i c s a n d A s t r o n a u t i c s E s t a b l i s h m e n t , ' H a n d -

book o f S t r a in Fa t igue Ana lys i s ' , Sc i ence Pub l i she r , 1991( i n C h i n e s e )14 Sch i jve , J . Fatigue Eng. Mater. Struct. 1980, 3, 3251 5 H a r d y , S . J . a n d M a l i k , N . H . Int. J. Fatigue 1992, 14, 1471 6 F r o s t , N . E . a n d P h i ll i p s, C . E . I n ' A n E n g i n e e r i n g M e t h o df o r E s t i m a t i n g t h e N o t c h - S i z e E f f e c t i n F a t i g u e T e s t s o nS te e l ( E d . P . K u h n a n d H . F . H a r d r a h t ) , N A C A T N 2 8 0 5.W a s h i n g t o n , 1 9 5 2 , p p . 5 2 0 - 5 2 61 7 M i l l e r , K . J . J . Mech. Eng. Sc i . 1991, 205, 2911 8 T i n g , J . C . a n d L a w r e n c e , F . V . J r Fatigue Fract. Eng. Mater.Struct. 1993, 16, 931 9 T a n a k a , K . , N a k a i , Y . a n d Y a m a s h i t a , M . Int. J. Fatigue1981, 17, 5192 0 Y u , M . T . , D u Q u e s n a y , D . L . a n d T o p p e r , T . H . Int. J.Fatigue 1993, 15, 1092 1 Z u , X . , J u a n g , X . a n d C h e n , J . I n ~ P ro c. F i f t h N a t . C o n f .o f F a t i g u e ' , 1 9 9 1, p p . 8 7 9 - 9 0 3 ( i n C h i n e s e )

2 2 S m i t h , R . A . a n d M i l l e r , K . J . Int. J, Mech. Sci. 1977, 19,112 3 Y a o , W . Compos. Sc i . Technol . 1992, 45, 1052 4 Y a o , W . Int. J. Fatigue 1993, 15, 2432 5 Y a o , W . a n d G u , Y . Eng. Me c h. , t o b e p u b l i s h e d ( i nC h i n e s e )2 6 S h e p p a r d , S . D . I n ' F a i l u r e P r e v e n t i o n a n d R e l i a b i l it y - 8 9 ',A S M E , N e w Y o r k , 1 9 89 , p p . 1 1 9 - 1 2 72 7 G r o v e r , H . J . , B i s h o p , S . M . a n d J a c k s o n , L . R . ' A x i a l - lo a dF a t i g u e T e s ts o n N o t c h e d S h e e t S p e c i m e n s o f 2 4 S - T 3 a n d7 5 S - T 6 A l u m i n u m A l l o y s a n d o f S A E 4 1 3 0 S t e e l w i t h S t r e s s -c o n c e n t r a t i o n F a c t o r s o f 2 . 0 a n d 4 . 0 ' , N A C A T N 2 3 8 9 , 1 9 5 0N O M E N C L A T U R Ea

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On the fa t igue notc h fac tor Kf 2 5 1IoAKoK fK TAKthoAK :ff thOg rK~qSStSNS~

Intrinsic crack length of a smoothspecimenStress intensity factor rangeFatigue notch factorTheoretical stress concentration factorLong crack threshold stress intensityfactor rangeEffective threshold stress intensity factorrangeTrue stress concentration factorTrue strain concentration factorNotch-sensitive factorArea of fatigue failure region DFatigue strength of a smooth specimenFatigue strength of a notched specimenStress range at the fatigue limit of asmooth specimen

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Threshold stress rangeEffective threshold stress intensity ratiofor a long crackVolume of fatigue failure regionGeometry factor of stress intensity factorRadius of notch rootAverage stress over stress field domainnear a notchMaterial tensile strepgthStress field intensity functionStress field intensity function of asmooth specimenStress field intensity function of anotched specimen

Weight functionStress gradient at notch rootOpen angle of a notchFatigue failure region

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On the Fatigue Notch Factor Kf