Combined Bearing Bypass Loading Crews1986

8/18/2019 Combined Bearing Bypass Loading Crews1986

1/20

Com posite Structures 6 198 6) 21--40

Co m bined Bearing and Bypass Loading on a

Gra phite Epox y Lam inate

J . H . C r e w s , J r a n d R . A . N a i k *

N A SA Langley Research Center, Ham pton, V irginia 23665, US A

A B S T R A C T

A combined experimental and analyt ical s tudy was conducted to

determ ine the behav ior o f a graphi te~epoxy laminate subjected to

combined bearing and bypass loading. Single-fastener quasi-isotropic

specim ens were loaded at various bearing-bypa ss ratios unt i l dam age w as

pro du ce d at the fas tener hole. Dam age-onset s trengths an d dam age

modes were then analyzed using local hole-boundary stresses calculated

by a f in i te-elem ent analysis . The tension data show ed the expe cted linear

interaction for combined bearing and bypass loading with damage

dev eloping in the net-sect ion tension m ode. How ever the com pression

bearing-bypass strengths showed an unexpected interaction involving the

bear ing mod e. Co mp ressive bypass loads reduced the bearing strength by

decreasing the bolt-hole contact arc and thus increasing the severity o f the

bearing loads. The bearing stresses at the hole bou nda ry were not

accurately estima ted by superposition o f the stress com pon ents for

separate bearing and bypa ss loading. How ever superposition p ro du ce d

reasonably accurate estimates for tangential stresses especially near the

specimen net-section.

C

d

P a

N O M E N C L A T U R E

b o l t - h o l e c l e a r a n c e , m

h o l e d i a m e t e r , m

a p p l i e d l o a d , N

* Present address: Old Dom inion Un iversity, Norfolk, Virginia 23508, US A.

21


2/20

J . H . C r e w s J r R . A . N a i k

P b b e a r i n g l o a d N

P p bypa s s l oa d N

r 0 p o l a r c o o r d i n a t e s m d e g r e e s

Sb n o m i n a l b e a r i n g s tr es s M P a

S .p no m i na l ne t - s e c t i on bypa s s s tr e ss MP a

t s pe c i m e n t h i c kne s s m

w s p e c i m e n w i d t h m

x y c a r t e s i a n c oo r d i na t e s m

/3 be a r i ng - b ypa s s r a t io d °p

0c bo l t - ho l e c on t a c t a ng l e de g r e e s

O -rr r a d i a l s tr e s s c o m po ne n t M P a

o-00 t a nge n t i a l s tr e s s c om po ne n t M P a

1 I N T R O D U C T I O N

I n t he p a s t de s i gn p r oc e du r e s f o r m e c h a n i c a l ly f a s t e ne d j o i n t s i n

c om po s i t e s ha ve u s ua l ly be e n ve r y c ons e r va t ive . I n suc h c as e s f a il u r e s

w e r e u s ua l ly a vo i de d by he a v i ly r e in f o r c i ng t he l a m i na t e s in t he v i c i n it y o f

t h e j o i n ts . N e e d e d i m p r o v e m e n t s i n jo i n t e ff ic ie n cy r e q u i r e d a t a b a s e s f o r

l a m i na t e s t e s t e d unde r c ond i t i ons t yp i c a l o f s t r uc t u r a l j o i n t s . W i t h i n a

m u l t i - f a s t e n e r s t r uc tu r a l j o i n t f a s t e ne r ho l e s m a y be s ub j e c t e d to t he

c o m b i n e d e f f e c ts o f b e a r in g l o a d s a n d l o a d s th a t b y p a ss t h e h o l e a s

i l lu s t r a t e d i n F i g . 1 . T he r a ti o o f be a r i ng l oa d t o bypa s s loa d d e p e n ds on

t he j o i n t s t if f ne ss a nd c on f i gu r a ti on . A s t he j o i n t is l oa de d t h is be a r i n g -

bypa s s r a t i o r e m a i ns ne a r l y c ons t a n t un t i l j o i n t da m a ge de ve l ops .

A l t h o u g h t h e c o m b i n e d e f fe c ts o f b e a r in g a n d b y p a ss l o a d s ca n b e

s im ula t ed by t e s t i ng s i ng l e - fa s t ene r spec im ens such t e s ts a re d if f icu l t.

T h e v a r i o u s a p p r o a c h e s u s e d f o r b e a r i n g - b y p a s s te s ti n g h a v e i n v o l v e d

c o m pl e x a pp a r a t u s t o s i m u l t a ne ous l y a pp l y t he be a r i ng a nd bypa s s l oa ds.

A s a r e s u lt ve r y f e w be a r i ng - b ypa s s da t a ha ve be e n r e po r t e d . V i r tua l l y

n o t h i n g h a s b e e n r e p o r t e d f o r b e a r i n g - b y p a s s l o a d i n g i n c o m p r e s s i o n .

T h e f ir st ob j e c t i ve o f t h i s pa pe r is to i n t r oduc e a r e l a t ive l y s i m p l e

a p p r o a c h f o r c o m b i n e d b e a r i n g - b y p a s s t e s ti n g th a t w o r k s e q u a l ly w e l l i n

t e n s i o n a n d c o m p r e s s io n . T h i s a p p r o a c h w a s d e m o n s t r a t e d b y t e st in g a

g r a p h i t e / e p ox y l a m i na t e . T h e s e c o nd ob j e c t i ve is t o a na l yz e t he e f fe c t s o f

c o m b i n e d b e a r i n g a n d b y p as s l o a d in g by e x a m i n i n g t h e c o m p u t e d l o ca l

s t r e s s e s a s s oc i a t e d w i t h l a m i na t e da m a ge a t f a s t e ne r ho l e s . T h i s pa pe r


3/20


4/20

4 J. H. Crews Jr R. A. Naik

2 B E A R I N G - B Y P A S S T E S T I N G

T h r e e a p p r o a c h e s t o b e a r in g - b y p a s s t e s ti n g h a v e b e e n u s e d i n t h e p a s t

w i t h s i m p l e s p e c i m e n s . T h e f i r s t a p p r o a c h u s e s l e v e r s a n d l i n k a g e s t o

d i v i d e t h e a p p l i e d l o a d i n t o t w o p r o p o r t i o n a l p a rt s . 2O n e p a r t a ct s o n t h e

e n d o f t h e s p e c i m e n a n d t h e o t h e r i s r e a c t e d a s a b e a r i n g l o a d a t t h e

s p e c i m e n h o l e . T h e b o l t h o le is t h e r e b y s u b j e c t e d to p r o p o r t i o n a l b e a r i n g

a n d b y p a s s l o a d in g . T h e l e v er f u l c ru m p o i n t s c a n b e c h a n g e d t o p r o d u c e

d i f f e r e n t r a t i o s o f b e a r i n g t o b y p a s s l o a d in g . T h i s le v e r - l in k a g e a p p r o a c h

w o r k s w e l l f o r t e n s i o n b e a r i n g - b y p a s s l o a d i n g b u t is di ff ic u lt t o a p p l y i n

c o m p r e s s i o n . T h e s e c o n d a p p r o a c h t o b e a r i n g - b y p a s s t e s t i n g u s e s a

s c i ss o r m e c h a n i s m t o a p p l y a b e a r i n g lo a d b e t w e e n t w o h o l e s i n t h e t e st

s p e c i m e n . 3 T h i s b e a r i n g l o a d i s h e l d c o n s t a n t w h i le t h e b y p a s s l o a d is

i n c r e a s e d u n t il t h e s p e c i m e n fa ils . A l t h o u g h t h is a p p r o a c h d o e s p r o d u c e

b e a r i n g - b y p a s s l o a d i n g in t e n si o n o r c o m p r e s s io n , i t d o e s n o t m a i n t a i n

t h e d e s i r e d c o n s t a n t r a ti o o f b e a r i n g to b y p a s s l o a d s. F u r t h e r m o r e , t h is

a p p r o a c h c o u l d a l t e r t h e s e q u e n c e o f l o c a l d a m a g e d e v e l o p m e n t . T h e

t h i r d a p p r o a c h u s e s t w o s e r v o - c o n t r o l s y s t e m s : o n e c o n t r o l s t h e b e a r i n g

l o a d w h i l e t h e o t h e r c o n t r o l s t h e b y p a s s l o a d . 4T h e b y p a s s l o a d is a p p l i e d

t o t h e e n d o f t h e s p e c i m e n i n t h e c o n v e n t io n a l m a n n e r ; h o w e v e r , t h e

b e a r i n g l o a d is a p p l i e d t h r o u g h l in k a g e s w i t h t w o h y d r a u l i c c y l i n d e r s

c o n n e c t e d t o t h e e n d s o f a b e a ri n g b a r w h i c h is b o l t e d t o t h e s p e c i m e n .

C o n s t a n t b e a r i n g - b y p a s s r a ti os c o u l d b e m a i n t a i n e d b y s y n c h r o n iz i n g t h e

t w o c o n t r o l s y s te m s . A l t h o u g h th is c o n c e p t w o r k s i n te n s i o n a n d c o m -

p r e s s i o n , t h e t e s t a p p a r a t u s is r a t h e r c o m p l e x a n d q u i t e d i f f e r e n t

a p p a r a t u s a r r a n g e m e n t s a r e n e e d e d f o r th e t w o t yp e s o f lo a d in g .

A l t h o u g h d e v e l o p e d i n d e p e n d e n t l y , t h e n e w te s t s y s te m h a s s o m e

s i m i l a r i t y t o t h a t i n R e f . 4 . A s in R e f . 4 , t h e n e w s y s t e m h a s t w o

s e r v o - c o n t r o l s y s t e m s . H o w e v e r , t h e p r e s e n t d u a l - c o n t r o l a r r a n g e m e n t

u s e s a n a p p a r a t u s t h a t i s m u c h s i m p l e r t h a n t h a t i n R e f . 4 . F i g u r e 2 ( a )

s h o w s t h e t e s t s p e c i m e n a n d F i g . 3 s h o w s a b l o c k d i a g r a m o f t h e t e s t

s y s t e m . T h e c e n t e r o f th e s p e c im e n is c l a m p e d b e t w e e n t w o b e a r in g -

r e a c t i o n p l a t e s th a t a r e a t t a c h e d t o th e l o ad f ra m e . T h e t w o e n d s o f t h e

s p e c i m e n a r e t h e n l o a d e d i n d e p e n d e n t l y b y th e t w o s e r v o -c o n t r o l s y s te m s

( c a l l e d u p p e r a n d l o w e r in F ig . 3 ). A n y d i f f e r e n c e b e t w e e n th e s e t w o

l o a d s p r o d u c e s a b e a r i n g l o a d a t t h e c e n t ra l b o l t h o le . T h i s b e a r i n g l o a d is

m e a s u r e d b y t h e t w o lo a d ce ll s u n d e r t h e b e a r in g - r e a c t i o n p la t e s . T h e e n d

l o a d s a r e s y n c h r o n i z e d b y a c o m m o n i n p u t si gn a l. A s a r e s u lt , a c o n s t a n t

b e a r i n g - b y p a s s r a t io is m a i n t a i n e d t h r o u g h o u t c a c h t es t.


5/20

om bin ed bearing and bypass loading o n a graphite~epoxy laminate 25

:

T e n s i o n

C o m p r e s s i o n

( a ) T e s t s p e c im e n ( b ) B e a r i n g b y p a s s l o ad i n g

Fig. 2 . Specimen conf igurat ion and bear ing bypass oading.

/ / i # ~ / 1 / . / t

H y d r a u lic c y l i n d e r ' ~ - ] ~ U p p e r

L o a d c e l , - ~ . . ~ , ~ _ ~ . S e : y ; : : ~ r o l j ~

G r i p ~ l I / S p e c im e n

B ° l t ~ . ~ i ' i I ~ f j . ~ ' e a n - ~ 2 i c l ° io P l t e

i i

a r i p ~

L o a d c e I ~ se r vo L ° cW e r tr o , ]_

. y d r s o , l° o y , l n d o r / l I

s y s t m

-

i i f l f i

Fig . 3 . B lo ck d iag ra m o f the co m bined bea r ing -by pa ss te s t s~ stem.

I n p u t

s i g n a l

g e n e r a t o r

A p h o t o g r a p h o f t h e a p p a r a t u s is s h o w n i n F i g. 4 . O n l y a s m a l l p o r t i o n

o f t h e s p e c i m e n e d g e is v i si b le . T h i s p h o t o g r a p h s h o w s t h e f r i c t io n g r ip s

t h a t l o a d e a c h e n d o f t h e s p e c i m e n a n d t h e h e a d o f th e 6 .3 5 m m s t e e l b o lt

t h a t a t t a c h e s t h e s p e c i m e n to t h e b e a r i n g r e a c t i o n pl a te s . N o t i c e th a t t h e

b e a r i n g r e a c t i o n p l a t e s a r e b o l t e d t o t h e b e a r i n g l o a d c e l l s . T h i s a l l o w s

e i t h e r t e n s i o n o r c o m p r e s s i o n b e a r in g l o a d s to b e r e a c t e d b y t h es e l o a d


6/20

26 J . H . C r e w s J r R . A . N a i k

i ~ i i i i i i i i i ~ i i i i

~i Liiiiiiiii i iii...

lql . 4. Pho tograp h of bearing--bypass est appara tus.

c e ll s. D u r i n g c o m p r e s s i o n l o a d i n g , t h e b e a r i n g - r e a c t i o n p l a te s p r e v e n t

s p e c i m e n b u c k li n g .

T h e s p e c i m e n d e f o r m a t i o n w a s m e a s u r e d t h r o u g h o u t ea c h t es t u s in g

d i s p l a c e m e n t tr a n sd u c e rs . T h e s e t r an s d u ce r s (D C D T ) w e r e m o u n t e d

s y m m e t r i c a l l y o n t h e f r o n t a n d b a c k o f t h e b e a r i n g r e a c t io n p l a te s . ( T h e s e

p l a t e s w e r e m a d e w i t h n o n m a g n e t i c 3 47 s ta i nl e ss st e e l s o th e y w o u l d n o t

a f f ec t t h e t r a n s d u c e r p e r f o r m a n c e . ) T h e t r a n s d u c e r r o d s w e r e c e m e n t e d

t o s m a l l b a r s t h a t w e r e a t t a c h e d t o t h e s p e c i m e n s li g ht ly a b o v e t h e

g r i p li n e , a s s h o w n i n F ig . 4. T h i s a r r a n g e m e n t p r o v i d e d a m e a s u r e m e n t o f

t h e r e la t iv e d i s p l a c e m e n t b e t w e e n t h e b e a r in g - r e a c ti o n p l a te s a n d t h e

s p e c i m e n . T h e s e m e a s u r e m e n t s w e r e u s ed to d e t e r m i n e t h e d a m a g e

o n s e t , a s e x p l a i n e d i n t h e n e x t s e ct io n .

A l t h o u g h n o t v i si bl e in F ig . 4, h a r d e n e d s t ee l b u s h i n g s w e r e u s e d

b e t w e e n t h e b o l t a n d t h e b e a r in g - r e a c ti o n p la te s . T h e s e b u s h i n g s h a d a

1 2 .7 m m o u t s i d e d i a m e t e r t h a t w a s m a c h i n e d f o r a sl id i n g f it , t h u s

a l l o w i n g t h e b o l t c l a m p - u p f o r c e t o b e t r a n s m i t t e d t o t h e l o c a l r e g i o n

a r o u n d t h e b e a r i n g - l o a d e d h o l e . T h i s a r r a n g e m e n t w a s e q u i v a l e n t t o

h a v i n g a c l a m p - u p w a s h e r d i re c t ly a g a in s t e a c h fa c e o f t h e l a m i n a t e , a s

u s e d i n R e f s 1 a n d 5 .


7/20

C om bin ed bear ing and b ypass load ing on a graph ite~epoxy lamina te 2 7

T h e b e s t s p e c i m e n s w e r e f a b r i c a t e d f r o m 1 6 -p ly q u a s i - i s o t ro p i c

g r a p h i t e / e p o x y l a m i n a t e s ( T 3 0 0 / 5 2 0 8 ) w i t h a [ 0 / 4 5 / 9 0 / - 4 5 ] : s l a y u p . T h e

s p e c i m e n c o n f i g u r a t i o n i s s h o w n i n F i g . 2 ( a ) . T h e b o l t h o l e s w e r e

m a c h i n e d u s i n g a n u l t r a s o n i c d i a m o n d - c o r e d r i l l . A h o l e d i a m e t e r o f

6 . 39 6 m m w a s u s e d f o r a c l e a ra n c e o f 0 .0 7 6 m m w i t h th e 6 . 3 20 m m s t e el

b o l t s . T h i s c l e a r a n c e w a s 1 . 2 o f t h e h o l e d i a m e t e r a n d is t y p i c a l o f

a i r c r a f t j o i n t s . T h e b o l t s w e r e f in g e r t i g h t e n e d ( a b o u t 0 . 2 N m t o r q u e ) t o

p r o d u c e a v e r y s m a l l c l a m p - u p f o r c e ag a in s t t h e s p e c i m e n .

T h e l o a d i n g n o t a t i o n i s s h o w n i n F i g . 2 ( b ) . T h e t e s t r e s u l t s a r e

p r e s e n t e d i n t e r m s o f n o m i n a l s t r e s s r a t h e r t h a n l o a d . T h e n o m i n a l

b e a r i n g s t re s s S b a n d n o m i n a l n e t - s e c t i o n b y p a s s s tr e ss S .p w e r e c a l c u l a t e d

f r o m t h e f o l lo w i n g e q u a ti o n s :

S b = P b t d

a n d

S .p = P p / t w - d)

T h e b e a r i n g - b y p a s s r a ti o /3 w a s d e f in e d as

-~ S b / S n p

I n e a c h t e s t , t h e n o m i n a l b e a r i n g a n d b y p a s s s t r e s s e s w e r e p l o t t e d

k N )

4 0

B a m a g e - o n s

3 0 -

2 0 - 1 0

- 0 . 0 0 6 m m

o ~ t I I I o

0 . 1 . 2 . 3 . 4 . 5

S p e c i m e n d i s p l a c e m e n t , m m

F i g . 5 . T y p i c a l l o a d - d i s p l a c e m e n t c u rv e s f l = - 1 .

k N )


8/20

28


a g a i n s t s p e c i m e n d i s p la c e m e n t . T h e t e s ts w e r e c o n d u c t e d a t th e r a th e r

s l o w r a t e o f 3 . 7 5 N / s f o r t h e a p p l i e d l o a d P a . T y p i c a l l o a d - d i s p l a c e m e n t

c u r v e s a r e s h o w n i n F i g. 5 f o r a b e a r i n g - b y p a s s r a ti o o f - 1 . T h e t w o

c u r v e s h a v e a s m a l l i n it ia l n o n - li n e a r i ty ( d u e t o v a r y i n g c o n t a c t a r c ) b u t

g r a d u a l l y d e v e l o p a n e a r l y l in e a r r e s p o n s e . A t h i g h e r lo a d l e v e l s , t h e

c u r v e s g r a d u a l ly d e v e l o p a s e c o n d , n o n -l in e a r it y . T h i s s e c o n d n o n -

l in e a r i t y i n d i c a t e s d a m a g e a t t h e b o l t h o l e , a s d i s c u s s e d i n R e f . 1 . A n

o f f s e t o f 0 . 0 0 1 d w a s s e le c t e d t o d e f in e t h e d a m a g e - o n s e t l e v e l, a s s h o w n

i n F i g . 5 . S o o n a f te r th e d a m a g e - o n s e t l ev e l w a s r e a c h e d , t h e s p e c i m e n s

w e r e u n l o a d e d . T h e y w e r e t h e n tr e a te d w i th a n X - r a y o p a q u e d y e -

p e n e t r a n t a n d r a d i o g r a p h e d t o d e t e r m i n e t h e d a m a g e l o c a t io n a l o n g t h e

h o l e b o u n d a r y . T h e d a m a g e - o n s e t m o d e w a s d e d u c e d f r om t h e d a m a g e

l o c a t i o n a s d i s c u s s e d i n t h e n e x t s e c t io n .

3 T E S T R E S U L T S

R e s u l t s fr o m t h e b e a r i n g - b y p a s s t e st s a r e p r e s e n t e d in T a b l e a n d

Fig. 6.

S y m b o l s ( © ) in

Fig . 6

r e p r e s e n t m e a s u r e d S b a n d S ,p v a lu e s c o r r e s-

p o n d i n g t o d a m a g e o n s e t . E a c h s y m b o l r ep r e se n t s an a v e ra g e o f th r e e

t e s t s. T h e r ig h t s i d e o f

Fig . 6

s h o w s t e n s i o n r e s ul ts f o r f o u r / 3 v a lu e s

0 , 1 , 3

T A B L E 1

D a m a g e - on s e t D a t a

B e a r i n g D am a g e o n s et st r en g t h D am a g e

bypass onse t

r a t i o

S b M P a

Snp,

M P a

m o d e a

T e n s i o n


0 0 320 NT

1 250 250 NT

3 47l 157 NT

~c 518 0 TRB

0 0 -44 5 NC

- 1 324 - 324 CR B/ NC

- 3 471 - 157 CR B

-o~ 540 0 CR B

NT, net-section; TRB, tension-reacted bearing; N C net- sect ion compression; CRB,

co m press io n-re a c ted bea r ing .


9/20

C o m b i n e d b e a r in g a n d b y p a s s l o a di n g o n a g r ap h i te ~ e p o xy l a m i n a t e 29

earing s t r e s s S b ,

A

, , / \ ,oo

a \ \ \

/ x ,

D u a l c o n ta c t \ X N N N ~ - I ~ 2 0 0

t h r e s h o l d

I \ ~ \ ,

- 4 0 0 - 2 0 0 0 2 0 0

B y p a s s s t re s s S n p , M P a

Fig. 6. Bearing bypass diagram for damage onset strength.

B e a r i n g c u t o f f ~ P p

4

a n d ~ c). T h e l e ft s id e s h o w s t h e c o r r e s p o n d i n g c o m p r e s s i o n r e s u l ts . F i g u r e

6 a l so i n d i c a t e s t h e o b s e r v e d f a il u re m o d e f o r e a c h t es t c o n d i t io n . T h e N T

b e s i d e s o m e s y m b o l s i n d i c a t e s n e t - s e c t i o n t e n s i o n d a m a g e . F o r t h e s e

c a s e s , r a d i o g r a p h s s h o w e d d a m a g e n e a r 0 = 9 0° o n t h e h o l e b o u n d a r y , a s

s h o w n i n F ig . 7 ( a ). C o n t i n u e d l o a d i n g w o u l d p ro b a b l y h a v e f a i le d t h e

s p e c i m e n s t h r o u g h t h e n e t s e c t io n . T h e T R B i n F i g. 6 i n d ic a t e s b e a r i n g

d a m a g e o n s e t f o r t e n s i o n - r e a c t e d b e a r i n g lo a d s. T h is d a m a g e d e v e l o p e d

a t t h e u p p e r e d g e o f t h e h o l e , a s s h o w n i n F i g . 7 ( b ).

T h e t e n s i o n c a s es w i t h N T d a m a g e (/3 = 0 , 1 a n d 3 ) c a n b e r e p r e s e n t e d

b y a s tr a i g h t l i n e a n d t h u s s h o w th e l i n e a r i n t e r a c t i o n d i s c u s s e d b y

H ar t -S m i th in Re f . 6 . Th i s l i n ea r i ty su g g es t s t h a t t h e lo ca l s t r e sse s ,

r e s p o n s i b l e f o r d a m a g e o n s e t , c a n b e a s s u m e d t o c o ns i st o f a c o m p o n e n t

d u e t o b e a r i n g a n d a s e c o n d s u p e r i m p o s e d c o m p o n e n t d u e t o b y p as s

l o a d i n g . T h i s a s s u m p t i o n w i l l b e i n v e s t i g a te d l a t e r in t hi s p a p e r . T h e

b e a r i n g c u t o f f r e p o r t e d b y H a r t -S m i t h 6w a s r e p r e s e n t e d b y a h o r i z o n ta l

l i n e t h r o u g h t h e f l = ~c d a t a p o i n t . T h e s e t w o s t r a i g h t li n e s t h r o u g h t h e

d a t a r e p r e s e n t t h e d a m a g e - o n s e t s t r e n g t h f o r c o m b i n a t i o n s o f b e a r i n g -

b y p a s s l o a d i n g i n t e n s i o n .

T h e l e ft s i d e o f F i g. 6 p r e s e n t s d a t a f o r c o m p r e s s i o n l o a d i n g . T h e C R B


10/20


I ~ . 7 . Radiographsof d m ge at fastene r hole.

i n d i c a te s b e a r i n g d a m a g e f o r c o m p r e s s i o n - re a c t e d b e a r i n g l o a d s. A s

s h o w n i n F i g. 7 ( c) , C R B d a m a g e d e v e l o p e d a t t h e l o w e r e d g e o f t h e h o l e .

D a m a g e f o r / 3 = - ~ o c c u r r e d a t a s li gh tl y h i g h e r s t r e n g t h th a n f o r t h e

t e n s i o n - r e a c t e d b e a r i n g /3 = ~ . T h i s sm a l l d i f f e r e n c e m a y b e d u e t o

s t r e n g t h v a r i a b i l i t y a n d i s n o t b e l i e v e d t o b e s i g n i f i c a n t . T h e b e a r i n g -

c u t o f f r e s p o n s e , a s s u m e d f o r t e n si o n , d o e s n o t a p p l y f o r c o m p r e s s i o n .

W h e n c o m p r e s s i o n b y p a ss l oa d i n g w a s c o m b i n e d w it h c o m p r e s s i o n -

r e a c t e d b e a r i n g ( /3 -- - 3 ) , C R B d a m a g e d e v e l o p e d a t a l o w e r l o a d l e ve l

t h a n f o r th e / 3 - - - ~ c a s e. T h is b e a r i n g - f a i l u r e i n t e r a c t io n w a s n o t

e x p e c t e d . E v e n f o r/ 3 = - 1 , C R B d a m a g e w a s o b s e r v e d, a l t h o u g h n e t-

s e c t i o n c o m p r e s s i o n ( N C ) d a m a g e w a s al so p r e s e n t . F o r t h e r e m o t e

c o m p r e s s i o n c a se (/3 -- 0 ) , N C d a m a g e o n s e t o c c u r r e d at - 4 4 5 M P a ,

c o m p a r e d w i t h 3 20 M P a f o r t h e c o r re s p o n d i n g / 3 = 0 te n s i o n c a se . T h e

b a s i c l a m i n a t e s tr e n g t h is o n l y a b o u t 1 0 h i g h e r i n c o m p r e s s i o n th a n in

t e n s i o n , t h e r e f o r e t h e h i g h e r N C d a m a g e - o n s e t s tr e n g t h is b e l i e v e d to b e

a t t r i b u t a b l e t o t h e ' d u a l ' b o l t - h o l e c o n t a c t t h a t a ll o w s l o a d tr a n s f e r a c r o s s

t h e h o l e . T h i s l o a d t r a n s f e r d e c re a s e s t h e n e t - s e c t io n s tr e ss c o n c e n t r a t i o n

a n d t h e r e b y i n c re a s e s t h e d a m a g e - o n s e t st r e n g th fo r th e N C m o d e . T h e

d a s h e d c u r v e in F i g. 6 i n d ic a t e s t h e t h r e s h o l d f o r d u a l c o n t a c t a n d w i l l b e


11/20

om bin ed bearing and bypass loading on a graphite~epoxy laminate 31

d i s c u s s e d i n t h e n e x t s e c t i o n . T h e r a d i o g r a p h s i n F i g . 7 a l s o s h o w a

d i f f e r e n c e b e t w e e n t h e N T a n d N C d a m a g e c as es . G r a y s h a d o w s w h i c h

i n d i c a t e d e l a m i n a t i o n a r e e v i d e n t i n t h e N T r a d i o g r a p h s b u t n o t in t h e

N C r a d i o g r a p h s .

4 F A I L U R E A N A L Y S I S

F i r s t t h i s s e c t i o n d e s c r i b e s t h e fi n i t e - e l e m e n t p r o c e d u r e s u s e d t o

c a l c u l a t e t h e h o l e - b o u n d a r y s tr e ss e s . T h i s s e c ti o n p r e s e n t s l o c a l s t re s s e s

f o r s e p a r a t e b e a r i n g a n d b y p a s s l o a d s a n d t h e n p r e s e n t s s t r e s s e s f o r

c o m b i n e d b e a r i n g - b y p a s s l o a d i n g c o r r e s p o n d i n g t o t h e m e a s u r e d

d a m a g e - o n s e t s t r e n g th s . A s p r e v i o u s ly m e n t i o n e d t h e s e lo c a l s tr e ss e s a r e

u s e d t o a n a l y z e t h e m e a s u r e d s t r e n g th l e v el s a n d f a i lu r e m o d e s . F i n a l ly

t h e s e l o c a l s t r e ss e s a r e u s e d t o e v a l u a t e t h e a s s u m p t i o n t h a t s u p e r p o s i t i o n

o f l o c a l s tr e s s e s f o r s e p a r a t e b e a r i n g a n d b y p a s s l o a d i n g s c a n b e u s e d t o

e s t i m a t e t h e l o c a l s t re s s e s f o r c o m b i n e d b e a r i n g - b y p a s s l o a d i n g .

4.1 Finite element procedures

T h e f i n i t e - e l e m e n t p r o c e d u r e s u s e d i n t h i s s t u d y w e r e p r e s e n t e d a n d

e v a l u a t e d i n R e f . 7 . B e c a u s e a b o lt c l e a ra n c e w a s u s ed i n th e p r e s e n t

s t u d y t h e c o n t a c t a r c at t h e b o l t - h o l e i n t e r fa c e v a r i e d w i t h a p p li e d l o a d .

T h i s n o n - l i n e a r p r o b l e m w a s r e d u c e d t o a l i n e a r p r o b l e m b y u s i n g a n

i n v e r s e t e c h n i q u e . F o r t h e s i m p l e b e a r i n g l o a d i n g u s e d i n R e f . 7 a

c o n t a c t a n g l e w a s a s s u m e d a n d t h e c o r r e s p o n d i n g b e a r i n g l o a d w a s

c a l c u l a t e d . T h i s p r o c e d u r e w a s r e p e a t e d f o r a r a n g e o f c o n t a c t a r c s t o

e s t a b l i s h a r e l a t io n s h i p b e t w e e n c o n t a c t a n g l e a n d b e a r i n g lo a d I n t h e

p r e s e n t s t u d y t hi s p r o c e d u r e w a s e x t e n d e d t o i n c lu d e c o m b i n e d b e a r i n g

a n d b y p a s s l o a d i n g b y u s in g o n ly c o n s t a n t v al u e s o f t h e b e a r i n g - b y p a s s

r a t i o . F o r e a c h b e a r i n g - b y p a s s r at io / 3 t h e c o m b i n e d b e a r i n g a n d b y p a ss

l o a d i n g w a s e x p r e s s e d i n t e r m s o f b e a r i n g s t re s s S b a n d / 3 . T h u s g i v e n a /3

t h e p r o c e d u r e w a s i d e n t ic a l t o t h a t u s e d in R e f . 7 . A g a i n t hi s p r o c e d u r e

w a s r e p e a t e d t o e s t a b l i s h a r e l a t i o n s h i p b e t w e e n c o n t a c t a n g l e a n d

b e a r i n g - b y p a s s l o a d i n g fo r e a c h /3 v a l u e u s e d in t h e t e s t p ro g r a m .

T h e s e c a l c u l a t i o n s w e r e p e r f o r m e d u s i n g t h e N A S T R A N f i n i t e

e l e m e n t c o d e . T h i s c o d e i s w e l l s u i te d f o r th e i n v e r se t e c h n i q u e b e c a u s e

t h e c o n t a c t a r c c a n b e r e p r e s e n t e d u s in g d is p l a c e m e n t c o n s t ra i n ts a l o n g a

p o r t i o n o f t h e h o l e b o u n d a r y . D i s p l a c e d n o d e s o n t h e h o l e b o u n d a r y


12/20

32


w e r e c o n s t r a i n e d t o l i e o n a c ir c u l ar a r c c o r r e s p o n d i n g t o t h e b o l t s u r f a c e .

T h i s r e p r e s e n t e d a r i g id b o l t h a v i n g a f i i c ti o nl e ss i n t e r f a c e w i t h t h e h o l e .

A v e r y f in e t w o - d i m e n s i o n a l m e s h w a s u s e d t o m o d e l t h e t e s t s p e c i m e n .

A l o n g t h e h o l e b o u n d a r y , e l e m e n t s s u b t e n d e d le ss t h a n 1° o f a r c . A s a

r e s u l t , t h e c o n t a c t a r c c o u l d b e m o d e l e d v e r y a c c u r a t e l y .

4 2 Separate bearing and bypass loading

F i g u r e 8 s h o w s o -00 a n d o -,, s t r e s s d i s t r i b u t i o n s c a l c u l a t e d f o r t h e h o l e

b o u n d a r y f o r t h r e e d i f f e r e n t ca s es . T h e d a sh - -d o t c u r v e s h o w s a fa m i l i a r

d i s t r i b u t i o n o f o 00 f o r t h e c a s e o f r e m o t e t e n s i o n l o a d i n g (t3 = 0 ) u s i n g t h e

m e a s u r e d s t r e n g t h o f S,p = 3 20 M P a . A s p r e v io u s ly m e n t i o n e d , t h e

d a m a g e f o r t h is t es t c as e w a s f o u n d t o d e v e l o p in t h e N T m o d e a n d ,

t h e r e f o r e , w a s g o v e r n e d b y t h e o -~ s tr e ss n e a r 0 = 9 0 °. T h e d a s h - d o t

c u r v e h a s a p e a k v a l u e o f a b o u t 8 30 M P a n e a r 0 = 9 0 °. T h i s c o m p u t e d

p e a k v a l u e g r o s sl y e x c e e d s t h e u n n o t c h e d l a m i n a t e t e ns i le s t r e n g t h o f 41 4

M P a . 8 P a r t o f t h is d i s c r e p a n c y c a n b e e x p l a i n e d b y t h e f a c t th a t t h e p e a k

l o c a l s tr e s s a c t s o v e r a v e r y s m a l l v o l u m e o f m a t e r i a l s u b j e c t e d t o a h i g h

s t r e s s g r a d i e n t . T h e p e a k l o c a l s t r e n g t h s h o u l d b e h i g h e r t h a n t h e

u n n o t c h e d t e n s il e s t r e n g t h o b t a i n e d u s in g a r e la t iv e l y l a rg e t e n s il e

1 0 0 0

500

m 0

500

- 1 0 0 0

r 7 L / °

/ \ / - c =o t ~ =

3 0 6 0 i 9 0/

. /

_ ~ / / / / / /

C o n t a c t a r c ~ -

120

1 ~ 0 , ~ . ~ _ 8 0

O eg

Fig 8 Stresses along hole boundary


13/20

om bin ed bear ing and bypass load ing on a graph ite~epoxy lamina te

coupon under uniform stress. Also the NT damage onset reduced the

stress concentration for the region of peak o-~ stress. Because the stress

analysis did not account for this reduction, the computed peak tr~ was

somewhat overpredic ted. However, Ref. 1 showed that this computed o-e0

pea k corresponding to NT damage should agree with similar peak values

calculated for the othe r cases with NT damage. The peak value of 830 MPa

from Fig. 8 will therefore be used in subsequent analyses to indicate

critical conditions for the onset of NT damage.

The dashed curves in Fig. 8 represent tension-reacted bearing loading

(/3 = ~) with a zero clearance (snug fit) between the bolt and hole. This is

a special r eference case that has been widely analyzed because it is a linear

pro blem (the contact angle does not vary with loading). The dashed O'rr

curve indicates an 82.5 ° contact angle for this case, which agrees quite well

with the 83 ° value repor ted in Refs 9 and 10. Notice that the peak in the

dashed or00 curve occurs slightly beyond the end of the contact arc estab-

lished by the tr~r contac t stress. The magnitude of this o-00peak agrees with

results in Ref . 11.

The two solid curves in Fig. 8 represent the tension-reacted bearing test

case (/3 = ~). The loading for this case corresponded to Sb = 518 MPa,

the observed bearing damage-onset strength in tension. A bolt clearance

of 0.076 mm was also used to correspond to the test program value. The

solid O'rr curve shows that contact developed over about 60 °, compared

with mor e than 80 ° for the snug-fit reference case with the same loading

level. This smaller contact arc resulted in a higher peak value in the O'rr

curve. This peak value of about -730 MPa exceeded the unnotched

laminate compressive strength of 455 MPa, 8 as expected. This peak value

of -73 0 MPa will be used in the remainder of this paper to indicate critical

hole -bounda ry conditions for bearing damage-onset.

4 3 C om bine d bearing and bypass loading

4 3 1 Tension

The two test cases from Fig. 8 (/3 = 0 and ~) are replotted in Fig. 9 for

compar ison with the other two tension test cases (/3 = 1 and 3). All four

sets of curves in Fig. 9 correspond to the measured load levels for damage

onset. For/3 = 0, 1 and 3, the o-0ecurves have peak values nea r 0 = 90 °,

all within about 7 of 830 MPa, the critical value for NT damage. This is

consistent with the earlier observation that all three of these cases

developed damage in the NT mode. Conversely, for the bearing critical


14/20


1

5 0 0

- 5 0 0

- 1 0 0 0

1 3 = 1

r

a

, 3 0 60 90 12 0 15 0 ~ ', -, ,~ 18 0

s

o - - / / /

S b S n p D a m a g e

13 ( M P a ) ( M P a )

mo d e

0 0 3 2 0 N T

o o 1 2 5 0 2 5 0 N T

3 4 7 1 1 5 7 N T

o o 5 1 8 0 T R

Fig. 9. Stresses along hole bou nda ry for tension loading.

/3 = 3c c a s e , n o t e t h a t t h e o r00 p e a k o f a b o u t 6 0 0 M P a is w e l l b e l o w t h e

c r i ti c a l 8 3 0 M P a l e v e l f o r N T d a m a g e . T h e O rr p e a k s f o r / 3 = 1 a n d 3 a r e

w e l l b e l o w t h e c r it ic a l - 7 3 0 M P a l ev e l f o r b e a r i n g d a m a g e .

4 3 2 Compression

F i g u r e i 0 c o m p a r e s t h e h o l e - b o u n d a r y s t re s s d i s tr i b u ti o n s f o r t h e f o u r

c o m p r e s s i o n t e s t c a s e s (/3 = 0 , - 1, - 3 a n d - ~ ) . A s e x p e c t e d , t h e o -0 0a nd

O rr c u r v e s f o r / 3 = - ~ a r e q u i t e s i m i l a r t o t h o s e f o r / 3 = ~ . T h e o-00 p e a k

o f a b o u t 5 0 0 M P a is s li g h tl y l o w e r th a n t h e 6 00 M P a p e a k f o r / 3 = zc a n d

m u c h l o w e r t h a n t h e c r it ic a l 83 0 M P a l ev e l f o r N T d a m a g e . T h e O rr p e a k

o f a b o u t - 8 1 0 M P a f o r C R B d a m a g e i s s lig ht ly la rg e r t h an t h e - 7 3 0 M P a

l e v e l d e t e r m i n e d f r o m t h e T R B / 3 = ~ c a s e . T h i s h i g h e r o-~r p e a k f o r

c o m p r e s s i o n l o a d in g s h o u l d h a v e c a u s e d a l o w e r s t re n g t h , c o m p a r e d w i th

t h e c o r r e s p o n d i n g t e n s io n c a se . H o w e v e r , ju s t t h e o p p o s i t e w a s s h o w n

e a r l i e r in F ig . 6 . T h i s d i s c r e p a n c y i s r a t h e r s m a ll a n d m a y b e d u e t o

m a t e r i a l s t r e n g t h v a r i a b i l i t y .

I t is r e c a l le d t h a t t h e C R B d a m a g e - o n s e t s t r e n g th d e c r e a s e d a s t h e

b y p a s s l o a d w a s in c r e a s e d ; s e e t h e / 3 = - ~ , - 3 a n d - 1 c a s e s in F ig . 6 .

T h i s i n t e ra c t i o n w a s u n e x p e c t e d b e c a u s e th e d a m a g e d e v e l o p e d in t h e

C R B m o d e a n d t h e c o m p r e s s i v e b y p a s s l o ad s w a s n o t b e l i e v e d to


15/20

o m b i n e d b e a r i n g a n d b y p a s s l o a d i n g o n a g r a p h i te ~ e p o x y la m i n a t e 35

I Sb S n p D a m a g e

1000 13 (M P a) (M P a) m o d e

. 0 0 - 4 4 5 N C

p = - o o - I 3 2 4 - 3 2 4 C R B/N C

X , - 3 4 7 1 1 5 7 C R B

5 0 0 - ~ i - • 5 4 0 0 C R B

1

0

i 3

0 / 9 0 1 2 0 / /1 f f0 ~ ' - - 1 8 0

- 5 0 0 0

\ /

1 0 0 0 ~

F i g . 1 0 . S t r e ss e s a l o n g h o l e b o u n d a r y f o r c o m p r e s s i o n l o a d i n g .

c o n t r i b u t e t o th e

O r r

s tr e ss e s t h a t c au s e C R B d a m a g e . T h e i n t e r a c t io n f o r

C R B c a s e s c a n b e e x p l a i n e d u s in g F ig . 10 . T h e p e a k o - r s t r e ss e s f o r

/3 = - ~ - 3 a n d - 1 i n F i g. 10 a r e n e a r l y e q u a l a n d a r e a ll s li g h tl y h i g h e r

t h a n - 7 3 0 M P a t h e c ri ti c al l ev e l f o r b e a r i n g d a m a g e . F i g u r e 1 0 a l so

s h o w s t h a t f o r t h e s e t h r e e c a s e s t h e l o w e r t h e b e a r i n g l o a d t h e s m a l l e r t h e

c o n t a c t a r c . T h e s m a l l e r c o n t a c t a r c s c o m p e n s a t e f o r t h e s m a l l e r b e a r i n g

l o a d s . T h e c o m p r e s s i v e b y p a ss l o a d s d e c r e a s e c o n t a c t a r c l e n g th a n d

a l lo w t h e b e a r i n g l o a d s t o be m o r e d a m a g i n g . T h e r e f o r e t h e e f fe c t o f th e

c o m p r e s s i v e b y p a s s l o a d s o n t h e c o n t a c t a r c i s r e s p o n s i b l e f o r t h e

O b s e r v e d d e c r e a s e i n s t r e n g t h fo r C R B d a m a g e - o n s e t . T h i s d i sc u s si o n o f

c o n t a c t a n g l e s u g g e s t s t h a t a s im i l a r i n t e r a c t i o n p r o b a b l y e x i s ts in t e n s i o n .

T h e h o r i z o n t a l b e a r i n g - c u t o f f l in e p r o b a b l y u n d e r e s t i m a t e s t h e a c tu a l

s t r e n g t h f o r s m a l l S p le v e ls .

A s p r e v i o u s l y m e n t i o n e d t h e c o m p r e s s i v e /3 = 0 c a s e i n F i g. 10

i n v o l v e s d u a l c o n t a c t . F o r th is c a s e t h e h o le d e f o r m s e n o u g h t o c o n t a c t

t h e b o l t s t a r t i n g a t O = 0 a n d 18 0 °. T h e d a s h e d c u r v e in F i g . 6 r e p r e s e n t s

t h e c a l c u l a t e d t h r e s h o l d f o r d u a l c o n t a c t w i t h a 0 . 07 6 m m i n it ia l b o l t

c l e a r a n c e . T h i s d a s h e d c u r v e s h o w s t h a t c o n t a c t s t a r t e d n e a r S .p = - 2 2 0

M P a f o r / 3 = 0 . T h e / 3 = 0 c u r v e i n F i g. 10 f o r S p = - 4 4 5 M P a s h o w s


16/20

36 J . H. Crews Jr R . A . Na ik

t h a t t h e c o n t a c t e x t e n d e d b y a b o u t - --20 a r o u n d 0 = 0 a n d 1 80° . Th e o-s0

c u r v e f o r / 3 = 0 h a s a c o m p r e s s i v e p e a k o f a b o u t - 9 7 0 M P a . T h i s p e a k

c a u s e d t h e n e t - s e c ti o n c o m p r e s s i o n N C ) d a m a g e o b s e r v e d fo r t hi s c a se .

A s d i s c u s s e d e a r l i e r , t h e d u a l c o n t a c t in th i s c a s e e l e v a t e d t h e s p e c i m e n

s t r e n g t h c o m p a r e d w i t h c a se s w i th c l e a r a n ce s s u f fi ci en t t o p r e v e n t s u c h

c o n t a c t . C o n v e r s e l y , t h e p r e s e n t s tr e n g t h is l es s t h a n t h a t e x p e c t e d f o r t h e

s n u g - f i t c a s e .

T h e r e s u l t s i n t h i s s e c t i o n d e m o n s t r a t e t h a t l o c a l h o l e - b o u n d a r y

s t r e s s e s c a n b e c o m p a r e d w i t h c ri ti ca l s tr e ss l ev e ls to p r e d i c t d a m a g e

m o d e s a n d d a m a g e - o n s e t s tr e ng th s .

4 4 L o c a l s t r es s s u p e r p o s i t i o n

T h e s t re s s d i s t r i b u t i o n s i n th e p r e v i o u s s e c t io n w e r e c a l c u l a t e d w i t h a

s e p a r a t e f i n i t e - e l e m e n t a n a ly s is f o r e a c h b e a r i n g - b y p a s s l o a d i n g in t h e

t e s t p r o g r a m . T h e s e s t r e ss a n a ly s e s w o u l d h a v e b e e n s i m p l i f ie d i f t h e

s t r e s s e s d u e t o t h e s e p a r a t e b e a r i n g a n d b y p a s s l o a d i n g c o u l d h a v e b e e n

s u p e r i m p o s e d t o g e t t h e r e s u lt s f o r c o m b i n e d b e a r i n g - b y p a s s l o a d i n g , as

s u g g e s t e d i n R e f . 1 2. T h i s s e c ti o n in v e s t ig a t e s t h e a c c u r a c y o f s u c h a

s u p e r p o s i t i o n p r o c e d u r e .

O b v i o u s l y s u c h a s u p e r p o s i t i o n m u s t r e p r e s e n t t h e c o n t a c t a n g l e s

p r o p e r l y t o b e a c c u r a t e . F i g u r e 11 s h o w s c o n t a c t a n g le s p l o t t e d a g a i n s t

b e a r i n g s tr e ss f o r v a r io u s b e a r i n g - b y p a s s ra ti os . T h e o p e n s y m b o l s O )

r e p r e s e n t a r a n g e o f c a se s f o r te n s i o n- a n d c o m p r e s s i o n - r e a c t e d b e a r in g .

T h e s o l i d c u r v e s w e r e d r a w n t h r o u g h t h e s e s y m b o l s t o d e t e r m i n e t h e

n o n - l i n e a r r e l a t i o n s h i p b e t w e e n t h e c o n t a c t a n g l e a n d t h e b e a r i n g s tr e ss .

T h e s o l id sy m b o l s O ) r e p r e s e n t te s t c a se s a n d , t h e r e f o r e , c o r r e s p o n d to

t h e m e a s u r e d d a m a g e - o n s e t s tr e n g th s a n d t h e c a lc u l a te d c o n t a c t a n g le s

d i s c u s s e d i n e a r l i e r f i g u r e s . W h e n s u p e r p o s i t i o n i s u s e d t o a n a l y z e a

s p e c i m e n w i t h b e a r i n g - b y p a s s l o a d i n g , t h e c o n t a c t a n g l e w o u l d b e

d e t e r m i n e d s o l el y b y t h e b e a r i ng c o m p o n e n t o f t h e s o lu t io n . T h e c o n t a c t

a n g l e w o u l d , t h e r e f o r e , b e g i v e n b y o n e o f t h e s o l id c u r v e s i n F i g. 1 I .

T h e s e s o li d c u r v e s p r o v i d e r a t h e r p o o r e s t im a t e s o f c o n t a c t a n g le f o r m o s t

o f t h e t e s t c a se s , u n d e r e s t i m a t i n g f o r t e n s i o n a n d o v e r e s t i m a t i n g fo r

c o m p r e s s i o n . T h e c o n t a c t a n g l e e s t i m a t e s a r e e s p e c ia l ly b a d f o r t h e / 3 = 1

a n d - 1 c a s e s. F o r t h is re a s o n , t h e s e tw o ca s es w e r e s e l e c t e d f o r f u r t h e r

a n a l y s is o f t h e s u p e r p o s i t i o n t e c h n i q u e .

C o m p u t e d r e s u l t s f o r t h e 13 = 1 t e s t c a s e a r e s h o w n i n F ig . 12 . T h e t e s t

v a l u e o f S h = 2 5 0 M P a w a s u s e d t o c a l c u la t e t h e c o m p o n e n t o f lo c a l


17/20

om bin ed bearing and bypass loading on a graphite~epoxy laminate 37

6 0 0

o~ 400

¢

._~

2 0 0


~ ~ - ~ . ~ D -

T e n s i o n

e Y

, , ; / / , , i

_ / - I d , ' , '

,

• y

/ ;

- - ' ~ I i I I i I

0 2 0 4 0 6 0 8 0

Con tact Angle 6 c deg

Fig . 11 . Co n tac t ang les fo r range o f bea r ing s t ress .

1 00 0 - S u p e ~ o s e d b e a r i n g a n d b y p a s s

5O0

~ / 3 0 t 6 0 9 0 1 20 1 5 0

/ / /

- - O r r

Q

- 5 0 0

- 1 0 0 o

e d e g

I ~ = 1

S b = 2 5 0 M P a

1 8 0

P

F ig . 1 2 . S u p e r p o s i t i o n o f h o l e - b o u n d a r y s t re s se s f o r t e n s io n l o a d in g .


18/20


s t r e s s e s c a u s e d b y b e a r i n g a n d S ,p = 2 50 M P a w a s u s e d to c a l c u l a t e t h e

b y p a s s c o m p o n e n t . T h e s e s t r e s s d i s t r i b u t i o n s w e r e a d d e d t o g e t t h e

d a s h e d c u r v e s h o w n i n t h e f i g u r e . F o r c o m p a r i s o n , t h e s o l i d c u r v e

r e p r e s e n t i n g t h e c o m b i n e d b e a r i n g a n d b y p a s s l o a d i n g i s r e p l o t t e d f r o m

F i g . 9 . A s e x p e c t e d , t h e l o w e s t i m a t e f o r t h e c o n t a c t a n g l e p r o d u c e d a

h i g h e s t i m a t e f o r t h e o -r, p e a k . H o w e v e r , t h e o-00d i s t r i b u t i o n w a s s u r p r i s-

i n g l y a c c u r a t e , e s p e c i a l l y in t h e n e t - s e c t i o n ( 0 = 9 0 ° ) r e g i o n . A s i m i l a r

1 0 0 0 -

S u p e r p o s e d b ea rin g an d b yp as s

5OO

/ S im u lta n e o u s e a r in ga n d

bypass

) ,_ \ i ~ J J

3 0 / . . 6 0 g o 2 0 5 0 6 o

\ f _ I

- 5 0 0 ~ 13= - 1 I p ( ~ I

~ooo a

Fig. 13. S uperp osi t ion of hole boun dary st resses for compression loading.

c o m p a r i s o n f o r / 3 = - 1 is s h o w n i n F i g . 1 3. A g a i n , t h e O rr d i s t r i b u t i o n is

p o o r l y e s t i m a t e d b y s u p e r p o s i t i o n b u t t h e Cr00d i s t r i b u t i o n i s r e m a r k a b l y

a c c u r a t e n e a r t h e s p e c i m e n n e t - s e c t i o n . S u p e r p o s i t i o n w a s a l s o u s e d t o

c a l c u l a t e lo c a l s t r e ss e s f o r t h e / 3 = 3 a n d - 3 t e s t c a s e s. T h e t r e n d s w e r e

s i m i l a r t o t h o s e s h o w n i n F ig s 1 2 a n d 13.

T h e s e s t r e s s d i s t r i b u t i o n c o m p a r i s o n s s u g g e s t t h a t s u p e r p o s i t i o n c a n

p r o v i d e u s e f u l e s t i m a t e s o f t h e o-00 s t re s s e s a s s o c i a t e d w i t h n e t - s e c t i o n

d a m a g e i n t e n s i o n a s w e l l a s c o m p r e s s i o n . H o w e v e r , c o n t a c t a n g le e r r o r s

p r o d u c e s i g n i f i c a n t e r r o r s i n t h e O rr d i s t r i b u t i o n s . A s a r e s u l t , s u p e r -

p o s i t i o n s h o u l d n o t b e u s e d t o p r e d i c t b e a r i n g st r e n g t h .


19/20

Com bined bearing and bypass loading on a graphite~epoxy laminate

39

5 C O N C L U D I N G R E M A R K S

A c o m b i n e d e x p e r i m e n t a l a n d a n a l y t i c a l s t u d y w a s c o n d u c t e d t o

d e t e r m i n e t h e b e h a v i o r o f a g r a p h i t e / e p o x y l a m i n a t e s u b j e c t e d t o

c om bi ne d be a r i ng - bypa s s l oa d i ng . S i ng l e - f a s t e ne r , qua s i - i s o t r op i c

s p e c i m e n s w e r e l o a d e d a t v a r i o u s b e a ri n g - b y p a s s r at io s u n t i l d a m a g e w a s

p r o d u c e d a t t h e f a s t en e r h o le . D a m a g e - o n s e t s tr e n g th s a n d d a m a g e

m o d e s w e r e t h e n a n a l y z e d u s in g h o l e - b o u n d a r y st re s se s c a lc u l a te d b y a

f i n i t e - e l e m e n t a na l y si s.

A dua l - c on t r o l t e s t s y s t e m , de s c r i be d i n t h i s pa pe r , w a s u s e d t o

s u c c es s fu l ly m e a s u r e d a m a g e - o n s e t s t re n g t h s f o r a w i d e r a n g e o f b e a r i n g -

b y p a s s l o a d r a ti o s i n b o t h t e n s i o n a n d c o m p r e s s io n . T h e t e n s i o n d a t a

s h o w e d t h e e x p e c t e d l i n e a r i n t e r a c t i o n f o r c o m b i n e d b e a r i n g - b y p a s s

l o a d i n g w i th d a m a g e d e v e l o p i n g i n th e n e t -s e c t io n te n s i o n m o d e .

H o w e v e r , t h e c o m p r e s s i o n b e a r i n g - b y p a s s s t re n g t h s s h o w e d an

u n e x p e c t e d i n t e r a c t i o n o f t h e b e a r i n g a n d b y p a s s l o a d s . C o m p r e s s i v e

b y p a s s l o a d s r e d u c e d t h e b e a r i n g s tr e n g th . T h i s e f f e ct w a s a n a l y z e d a n d

e x p l a i n e d u s in g t h e h o l e - b o u n d a r y st re s se s. T h e c o m p r e s s iv e b y p as s

l o a d s w e r e s h o w n t o d e c r e a s e t h e b o l t - h o l e c o n t a c t a r c a n d , t h u s , i n c r ea s e

t h e s e v e r i ty o f t h e b e a r i n g l o ad s .

T h e b e a r i n g s t r e s s e s a t t h e h o l e b o u n d a r y w e r e n o t a c c u r a t e l y

e s t i m a t e d b y t h e s u p e r p o s i t i o n o f t h e s t r e s s c o m p o n e n t s f o r s e p a r a t e

be a r i ng a nd bypa s s l oa d ings . T he e r r o r s w e r e t r a c e d t o d i s c r e pa nc i e s i n

t he c a l c u l a t e d bo l t - ho l e c on t a c t ar cs . H ow e ve r , t he s upe r po s i t i on

a p p r o a c h p r o d u c e d r e a s o n a b l y a c c u r a t e e s t i m a t e s f o r t h e t a n g e n t i a l

s t r e s se s , e s pe c i a ll y ne a r t he s pe c i m e n ne t - s e c t ion .

R E F E R E N C E S

1. Crew s, J . H ., Jr . an d Naik, R. A ., Fai lure analysis of a graph i te/epoxy

lamina te subjec ted to bol t bearing loads, NA SA TM 86297, Nat iona l

A eron aut ics and Space Adm inistration, US A, August 1984.

2. Ra m ku m ar, R. L. , B ol ted joint design, test m ethod s and design analysis for

fibrous com posi tes Ed . by C. C. Chamis), ASTM STP 734, 198l , 376-95.

3. G arb o, S. P., E ffects of bearing/bypass load interaction o n lam inate

streng th, AFW AL-TR-82-3114, Septemb er 1981.

4. Co nca nn on , G ., Design verif ication testing of the X-29 graphite/epoxy wing

covers, P r o c e e d i n g s o f t h e F a ll M e e tin g S o c i e ty o f E x p e r i m e n t a l S t re s s

A n a l y s i s Sal t Lak e City, U tah, US A, 1983, 96-102.


20/20

40 J. H. Crews Jr R. A. Naik

5 . Cre ws , J . H . , J r , B o l t -bear ing fa t igue o f a g raph i te /epox y lam ina te . Jo in ing

o f co m p o s i t e m a t e r i a ls Ed . b y K . T . Ked w ard ) , AST M STP 74 9, 1 9 8 1,

131 A4.

6 . H a r t -Sm i t h , L . J ., B o l t ed j o i n ts in g rap h i t e / ep o x y co m p o s i te s , N A SA C R -

1 4 4 8 9 9 , Na t i o n a l Ae ro n au t i c s an d Sp ace Ad m i n i s t r a t i o n , USA, J an u a ry

1977.

7 . Na i k , R . A . an d C rews , J . H . , J r , S t r es s an a ly s is m e t h o d fo r a c l ea ran ce f it

b o l t u n d e r b ea r i n g l o ad s , p re s en t ed a t A I A A / A S M E / A S C E / A H S 2 6 t h

Structures Structural Dyn am ics and Materials Co nferen ce 1 98 4, A I A A

P ap er 85-0746, 15-17 Ap r i l , O r land o , F lo r ida , U SA .

8 . D O D /N A S A advanced compos i tes design gu ide Vo l. IV-A: Material s 1st

ed n , C o n t r ac t No . F3 3 6 1 5 -7 8 -C -3 2 0 3 , A i r Fo rce W r i g h t Ae ro n au t i ca l

La b o ra t o r i e s , U SA , J u l y 1 98 3. Av a i l ab le a s N A SA C R -17 34 07 an d f ro m

D TI C a s A D B 0 80 1 8 4 L.)

9 . D eJ o n g , T h eo , S t r e s s e s a ro u n d p i n - lo ad ed h o l e s i n e la stic aUy o r t h o t ro p i c o r

i so t rop ic p la tes , J. Composite Materials 11 1977) 313-3 1.

I0. Es h w ar , V . A . , D a t t ag u ru , B . an d R ao , A . K . , Pa r t ia l co n t ac t an d f ri c ti o n in

p i n j o i n t s , R ep . No . AR DB -STR -5 0 1 0 , Dep . Ae ro n au t . En g . , I n d i an In s t .

Sc i ., I n d i a , D ec em b e r 19 77 .

11. Cre w s , J. H . , J r , H ong , C . S . and Ra ju , I . S . , S t ress- -concen t ra t ion fac to rs

fo r f i n i t e o r t h o t ro p i c l am i n a t e s w i t h a p i n - l o ad ed h o l e , NASA TP-1 8 6 2 ,

Na t i o n a l Ae ro n au t i c s an d Sp ace Ad m i n i s tr a t i o n , US A, M a y 1 9 81 .

12. Cre w s , J . H . , J r , A su rvey o f s t reng th ana lysi s m etho ds fo r l amina tes wi th

h o l e s , Journa l o f the Aeronau t ica l Soc ie ty o f Ind ia 36 4) 1984) 287-303.

Combined Bearing Bypass Loading Crews1986

Documents

Transcript of Combined Bearing Bypass Loading Crews1986