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S T P 1 2 3 6

St r u ct u r a l I n t eg r i t y o f F asten er s

P i r M . T o o r , e d i t o r

A S T M P u b l i c a t i o n C o d e N u m b e r ( P C N )

0 4 - 0 1 2 3 6 0 - 3 0

A S T M

1 9 1 6 R a c e S t r e e t

Ph i lade lph ia , PA 19103

P r i n t e d i n t h e U . S . A .

C o p y r i g h t b y A S T M I n t l ( a l l r i g h t s r e s e r v e d ); F r i M a y 9 1 1 : 4 1 : 0 0 E D T 2 0 1 4

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L i b r ar y o f C o n g r e s s C a t a l o g i n g - i n - P u b l i c a t i o n D a t a

Structural integr i ty of fasteners. Pi r M. Toot , edi tor.

p . c m . - - (STP ; 1236)

" P a p e r s p r e s e n te d a t th e s y m p o s i u m o f t h e s a m e n a m e h e l d in M i a m i,

F lo ri da on 18 N ov 1992 ... s pons ored by ASTM C o mm i t t ee E -8 on

Fa t igue and F rac t u re " - -C I P f o rew ord .

"ASTM pub l i c a t i on c od e nu mb er (PC N ): 04 -012360-30 . "

Inc ludes b ib l iogra phica l re ferences and index .

I S B N 0-8031-2017-6

1. Fasteners. 2. Struc tura l stab i l i ty. I . Toor, Pir M.

I1. ASTM C om m it te e E-8 on Fat igu e an d Fracture. I II . Ser ies: ASTM

spe c ia l technica l pub l i cat ion; 1236.

TJ 1320 . $77 1995

6 2 1 . 8 ' 8 ~ d c 2 0

95-12078

CIP

Co pyr ight 9 AMERICAN SOCIETY FOR TESTING AND MATERIALS, Phi lade lph ia , PA. A l l

r i gh ts res e rv ed . Th i s m a t e r ia l ma y no t b e rep roduc e d o r c op ied , i n w ho le o r in pa r t , in an y p r i n t ed ,

mec ha n i c a l, e lec t ron ic , fi lm , o r o t he r d i s t r i bu t ion and s t o rage med ia , w i t hou t t he w r i t t en c ons e n t o f

th e publ isher.

P h o t o c o p y R i g h t s

A u t h o r i z a ti o n t o p h o t o c o p y i t e m s f o r i n t e rn a l o r p e r s o n a l u s e , o r t h e i n t e rn a l o r p e r s o n a l

u s e o f s p e ci fi c c li e n ts , i s g r a n t e d b y t h e A M E R I C A N S O C I E T Y F O R T E S T I N G A N D M A T E R I -

A L S f o r u s e r s re g i s t e re d w i t h t h e C o p y r i g h t C l e a r a n c e C e n t e r ( C C C ) T r a n s a c t i o n a l R e p o r t i n g

S e r v ic e , p r o v i d e d t h a t t h e b a s e f e e o f $ 2 . 5 0 p e r c o p y , p l u s $ 0 . 5 0 p e r p a g e i s p a id d i r e ct ly t o

C C C , 2 2 2 R o s e w o o d D r., D a n v e r s , M A 0 1 9 2 3 ; P h o n e : (5 08 ) 7 5 0 - 8 4 0 0 ; F a x : ( 50 8) 7 5 0 - 4 7 4 4 . F o r

t h o s e o r g a n i z a t io n s t h a t h a v e b e e n g r a n t e d a p h o t o c o p y li c e n s e b y C C C , a s e p a r a t e s y s t em

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

v i c e is 0 - 8 0 3 1 - 2 0 1 7 - 6 / 9 5 5 2 . 5 0 + . 50 .

P e e r R e v i e w P o l i c y

Each pap er pub l i s hed i n th i s v o lum e w a s ev a lua t ed by t h ree pe er rev iew ers . The au t ho rs

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ASTM C o mm i t t ee on P ub l ic a t ions .

The qua l i t y o f t he papers i n t h i s pu b l i c a t ion re f lec t s no t on l y t he obv ious e f fo r t s o f t he au t ho rs

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beh al f o f ASTM.

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oreword

T he S ym pos i um on S t r uc tu r a l I n t e g ri ty o f F as te ne r s w a s he l d i n M i a m i F l o r ida on 16 - 19

N ov . 1992. T he s ym pos i um w a s s pons o r e d by t he A m e r i c a n S oc i e t y f o r T es ti ng a nd M a t e -

r i a l s t h r ough Com m i t t e e E 08 on F a t i gue a nd F r a c t u r e . M e m be r s o f S ubc om m i t t e e E 08 . 04

on S t ruc tura l Appl i ca t ions and spec i f i ca l ly the Task Group on F rac ture Mechanics of Fas -

t ene rs s e lec ted papers for the program. Organiza t iona l a s s i s t ance f rom Dorothy Savin i and

Shannon Wainwr ight was mos t he lpfu l . P i t M. Toor of Be t t i s Labora tory Reac tor Technol -

ogy W e s t M i ff li n P e nns y l va n i a s e r ve d a s te c hn ic a l p r og r a m c ha i rm a n . T hos e w ho s e r ve d

as ses s ion cha i rm en were J . L . Rudd Ai r Force W right Labora tory Dayton Ohio ; H . S .

Reenszy nder Be th lehem S tee l Corpo ra t ion Be th lehem Pennsy lvania ; G . T . Em bley Kn ol l

Labo ra tory Schenec tady New York; Alan L iu Ro ckvi l l e In te rna tiona l Ca l i forn ia ; and

R. E . J ohns on U S - N RC W a s h i ng ton D C.

C o p y r i g h t b y A S T M I n t l ( a ll r i g h ts r e s e rv e d ) ; F r i M a y 9 1 1 : 4 1 : 0 0 E D T 2 0 1 4

D o w n l o a d e d /p r i n te d b y

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N o t e o f p p re c ia t io n to R e v ie w e rs

Th e qua l i ty of the papers tha t ap pear in th is publ i ca t ion re fl ec ts no t on ly the ob vious e f for t

of the au thors bu t a l so the unhera lded though es sen t ia l wo rk of the rev iewers . On b eha l f

o f A S T M Co m m i t t e e E 08 I a c know l e dge w i th a pp r e c i a ti on the i r de d i c at ion t o h i gh p r o f e s-

s ional s tandards and thei r sacr i f ice of t ime and effor t .

Pir M Toor

T e c hn i c a l P r og r a m Cha i r m a n

C o p y r i g h t b y A S T M I n t l ( a ll r i g h ts r e se r v e d ) ; F r i M a y 9 1 1 : 4 1 : 0 0 E D T 2 0 1 4

D o w n l o a d e d / p r in t e d b y

U n i v e r s i d a d D e C h i l e p u r s u a n t t o L i c e n s e A g r e e m e n t . N o f u r t h e r r e p r o d u c t i o n s a u t h o r iz e d .

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ontents

O v e r v i e w i x

I n t r o d u c t i o n x x v

FATIGUE IN FASTENERS

E f f e c t s o f

N o n u n i f o r m i t ie s i n

F a s t e n e r s o n L o c a l i z e d V i b r a t i o n a n d

F a t i g u e

DARYOUSH ALLAEI 3

In t roduc t ion 3

Ro le of Fas teners in Loc a l i zed Vibra t ion 5

W ha t I s L oc a l i z e d V i b r at ion 6

M a t he m a t ic a l M ode l 9

Gen era l Rece ptance Form ula t ion of the In te r faces 11

Spec ia l Fea tures of the P ropo sed Ap pro ach 15

Tasks in P rogres s 16

Conc l us ions a nd Re c o m m e nda t i ons 17

E s t a b l i sh m e n t o f F a ti g u e T e s t M e t h o d f o r T u r b i n e B l a d e

FastenerDTADAYOSHI

ENDO YOSHIYUKI KONDO AND YOSHIKI KADOYA 20

In t roduc t ion 20

Tes t ing App ara tus 23

Tes t P rocedure 25

Tes t Resu l t s 26

Conc lus ion 27

R e v i e w o f F a c t o r s T h a t A f f e c t F a t i g u e S t r e n g t h o f L o w A l l o y S t e e l

Fasteners GEO RGE W. SKOCHKO AND THOMAS P. HERRMANN

N om e nc l a t u r e

In t roduc t ion

S u m m a r y

T he D a t a ba s e

Eva lua t ion o f Var iab les tha t Affec t Fa t igue S t rength

Mean S t res s Ef fec t s in Der iva t ion of Fa t igue Fa i lure Curves

32

32

32

33

33

35

41

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Conclusions 43

Appendix 44

F A I L U R E E V A L U A T I O N A N D C R I T E R I A

rhe Regulatory Approach to Fastener Integrity in the Nuclear Indnstrym

R I C H A R D E . JO H N S O N A N D J A M E S A . D A V I S

51

Introduction 51

Regulatory Aspects of Fasteners 53

ASME Requirements for Fasteners 54

Nondestructive Examination Prior to Use 55

In-Service Inspection of Fasteners 57

Failure Criteria and Limiting States of Stress for Cracked Bolts/Studs~vAL

K A G A N

60

Introduction 60

Applications 60

Prediction of Cyclic Strength and Life Service Time) 62

Fracture Mechanics of Threaded Joints 65

Nonlinear Effects in Threaded Joints 72

Conclusion 80

The Effect of Grain B o u n d a r y C a r b o n o n t h e H y d r o g e n A s s i st ed

In t e r g r a n u la r F a i lu r e o f N ic k e l C o p p e r A l lo y K 5 0 0 F a s t e n e r Material--

M A P . J O R IE A N N E . N A T I S H A N A N D W I L L I A M C . P O R R J R . 8 l

Introduction 81

Procedure 83

Results and Discussion 86

Conclusions 91

F R A C T U R E M E C H A N I C S I N F A S T E N ER S

Stress In tens i ty Factors for Surface and C o r n e r C r a c k e d F a s t e n er H o le s b y

the Weight Function MethodmwEI ZHAO AND SATYA N. ATLURI 95

Introduction 95

Three-Dimensional Weight Function Method 96

Results and Discussion 99

Concluding Remarks 106

Stress In tens i ty Factor Approximat ions for Cracks Located at the Thread

R o o t Region of Fasteners---RUSSELL c. CIPOLLA 108

Nomenclature 108

Introduction 109

Fracture Mechanics Applications for Fasteners 110

Model Representation of Thread Root 111

Stress Analysis Applicable to Thread Region 113

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W e i gh t F unc t i on f o r E dg e - Cr a c k i n a C y l ind r ic a l Ba r

Ca lcu la t ion o f S t res s In tens i ty Fac tors

S um m a r y a nd Conc l u s i ons

B e h a v i o r o f F a t i g u e C r a c k s in a T e n s i o n B o l t A L A N F .

LIU

N om e nc l a t u r e

In t roduc t ion

Cr a c k G e om e t r y Cons i de r a t i on

Se lec t ion of Independent Var iab les

Ana ly t i ca l ly De te rmined S t res s In tens i ty Fac tors

Empi r i ca l ly De te rmined S t res s In tens i ty Fac tors

Conc l us i on

115

119

124

126

126

126

127

130

131

134

138

STRUCTURAL INTEGRITY CRITERIA FOR FASTENERS

E a r l y S t a g es o f F a ti g u e D a m a g e o f F a st e n e r H o l e s M o n i t o r e d b y L a s e r

Speekle~FU-PEN CtUANG

MING-LIUNG DU, AND SHEN L1

143

In t roduc t ion 143

S pe c i m e n a nd E xpe r i m e n t 144

E va l ua ti on o f S pe c t r um H a l f W i d th a nd Cr os s Cor r e la t ion 144

Resul t s and Discuss ion 146

Conclus ions 151

D e v e l o p m e n t o f F r a c t u r e C o n t r o l M e t h o d o l o g y f o r T h r e a d e d F a s t e n er s i n t h e

S p a c e Pr og r an l- -J UL i E A. HENKENER, A VrIBELE R. SHAMALA, PAUL L.

CARPER, ROYCE G. FORMAN, AND CHARLES L. SALKOWSKI 55

Int roduct ion 155

Frac ture Con t ro l M ethod ology 156

Non frac ture Cr i t i ca l Fas teners 156

Fracture Cri t ica l Fas teners 159

Non des t ruc t ive Eva lua t ion of Thread ed Fas teners 160

S u m m a r y 1 6 3

T h e

E f f e c t o f a T e n si le L o a d o n t h e U l t i m a t e S h e a r C a p a c i t y o f a F a s t e n e r

Sha nk m SE AN M. OLSON 166

Introduct ion 166

Ex perim ental 16rocedure 167

Pre l iminary Exp er iments 170

Procedure 170

Results 171

Conc lus ions 173

P i tc h D i a m e t e r M e a s u r e m e n t o f T h r e a d e d G a g e s U s i n g a C o o r d i n a t e

M e a s u r i n g M a c h i n e m R A L P H

VEALE

EDGAR ERBER, AND BRUCE BORCHARDT

175

N om e nc l a t u r e 175

Introduct ion 176

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T hr e e - W i r e P i t c h D i a m e t e r M e t hod

Coor d i na t e M e a s u r i ng M a c h i ne s CM M s )

E x t e r na l T h r e a d M e a s u r e m e n t R e s u l ts

I n t e rna l T h r e a d M e a s u r e m e n t R e s u l ts

Conc lus ion

176

178

180

183

185

S u m m a r y 1 8 7

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Pir M. Toor

An Overv iew of S t ructura l In tegr i ty o f

Fas teners

I n t r o d u c t i o n

Threaded members a re impor tan t s t ruc tura l e l ement s and in f luence s ign i f i can t ly the

s t rength and enduran ce o f the wh ole s t ruc ture . Fur the r , beca use o f h igh dem ands to s t ruc tural

re l iab i l it y dur ing the des ign and ana lys i s o f th readed m em bers , t he re usua l ly a r i s es the t a sks

of ach iev ing s t a t i c s t reng th and durab i l i ty under va r i ab le in t e rna l and ex te rna l loads on the

s t ages of c rack in i t i at ion and propaga t ion .

I n d e e d , b o lt s h a v e u n i q u e m a t e r ia l r e q u i re m e n t s a m o n g t h e s t ru c tu r a l d e m e n t s o f a n e n -

g inee r ing component . Mechanica l loads requi re the use of th reads , and func t iona l requ i re -

men t s dem and low res i s t ance to s l id ing m ot ion be tw een th read contac t sur faces . Addi t iona lly ,

fabr i ca t ion and proces s ing opera t ions can in t roduce unfavo rab le ma te r i a l p roper t i e s , r e s idua l

s t resses , and undetected f laws . Also, ac tual service condi t ions can be qui te di f ferent f rom

those pos tu la ted for norm al des ign cons ide ra t ion . Hence , bo l t s used in any sys tem mu s t have

ce r t a in m echanica l p roper t i e s tha t a re s t ipu la t ed by spec i fi ca tions .

In sp i t e o f the fac t t ha t des ign procedu res spec i fy m in im um yie ld s treng th l eve l s , m in im um

tens i le p roper t i e s, and re s i st ance to s t re s s cor ros ion c rack ing , the re a re docu m ented cases o f

s tud c rack ing . Indeed , f rac ture eva lua t ion of de fec t s (c racks ) occur r ing in the th readed por -

t ions of s tuds and bo l t s i s a recur r ing prob lem in s t ruc tures . Cur ren t ly the re i s no expl i c i t

p roced ure fo r f rac ture ana lys is o f bo l t ing appl i ca tions . F rac ture ana lyses have been conduc ted

accord ing to spec i f i c indus t ry need . Due to the complex s t re s s s t a t e a t t he roo t o f a th read ,

the procedure i s compl ica ted and t ime consuming . Hence , a more rea l i s t i c and un i form

frac ture p rocedure for ana lys i s o f th readed members i s needed .

The pr inc ipa l pa ramete rs requ i red for f rac ture mechanics ana lys i s a re :

1. S t ress s ta te in the region of interes t .

2 . Ini t ia l f law shape that may exis t .

3 . Ini t ia l f law s ize tha t may exis t .

4 . F rac ture toughness fo r the bo l t ma te r i a l.

5 . Crack growth ra t e da ta fo r the m a te r ia l .

6 . Des ign fac tor .

The above pa ramete rs a re d i scussed in de ta i l i n the s ec t ions tha t fo l low.

F r a c t u r e P h e n o m e n o n

Brittle Fracture

Bri t t l e f rac ture genera l ly occurs w i thout p r io r p l a s t i c de format ion . The f rac ture sur face

as soc ia t ed wi th th i s type of fa i lu re i s f l at ( c leavage) w i th n o shea r li ps . T hi s typ e of fa i lu re

typ ica l ly occurs ve ry qu ick ly .

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OV RVI W x i

1. Material that is susceptible to stress relaxation.

2. High service temperature during operation.

3. Component having irradiation exposure.

Loss of preload can be minimized or eliminated by taking proper account of these factors

into design.

P a r a m e t e r s I n f l u e n c i n g r a c t u r e

Introduction

There are many parameters that influence the fracture behavior of bolts. For low and

intermediate strength steels, temperature-induced changes in metal grain ductility are known

to introduce fracture state transition. Fracture-state transition temperature for most steels

covers a wide range. Therefore, material characterization from a linear elastic fracture me-

chanics point of view is necessary. An appropriate material must be selected to meet struc-

tural requirements at the specified lowest service temperature for the section size of interest.

The role of environment has received a great deal of attention in most engineering designs.

If environment effects are significant, then environment becomes an important reference for

material characterization and analysis in the brittle fracture criterion. In addition to temper-

ature and environment influence, the influence of loading condition is also an important

factor in a design to resist fracture.

Indeed, a detailed study of fracture state, service temperature and environment effect, and

loading condition and strength levels must be performed to evolve a fracture-resistant design.

Material haracterization

All engineering materials contain imperfections. Subsequent manufacturing and processing

operations may produce additional cracks, inclusions, and other deficiencies. Such flaws can

range in size from the microscopic to the very large. Surprisingly, large cracks often do not

represent as serious a threat to structural integrity because they are more easily detected.

Undetected smaller cracks, however, can grow to critical size as a result of service loading

and environmental conditions. In ductile materials, once a crack has grown to critical size,

it can result in catastrophic failure of the component.

In view of the above phenomena, ductile materials should be used for fabrication of critical

parts. Although these materials have a greater tolerance for flaws, they also have a lower

strength. Ductile materials, therefore, offer an alternative for the problem of material fracture,

but this advantage is paid for by heavier, bulkier, and less efficient designs.

Most often, materials used in design are such that when service conditions are considered,

they typically fall in a brittle manner. Under these conditions, stresses very near a flaw exceed

the strength of the material even though the average design stresses in a part are very low.

Therefore, the safe design of a component demands thorough understanding of the behavior

of a material in the presence of flaws. In other words, the integrity of the material must be

assessed for its intended use.

The plain-strain fracture toughness, Kic, quantitatively relates the critical crack size to

applied load and geometry of a component. This material property is used to estimate min-

imum component loads, to compare candidate materials, and to assist in new alloy devel-

opment. Therefore, the material s integrity must be established for its intended use.




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x STRUCTUR L NTEGRITY OF F STENERS

Temperature Effect

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

a n d s o m e t i t a n i u m a l l o y s h a v e a t e m p e r a t u r e b e l o w w h i c h t h e y b e c o m e b r i t t l e . M a t e r i a l s

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

t e m p e r a t u r e t r a n s it i o n r a n g e . I n t h is l o w t e m p e r a t u r e r a n g e , t h e s e m a t e r i a ls h a v e v e r y l o w

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

I n a d d i t io n , h e a t t r e a t m e n t a n d c o l d w o r k i n g o f m a t e r i a l s a r e p r o c e s s e s u s e d t o i n c r e a se

a m a t e r i a l s d u c t i le s t r e n g t h p r o p e r t ie s , b u t s u c h p r o c e s s e s c a n a l s o r e s u lt i n a d r a s t ic d r o p

i n f r a c t u r e t o u g h n e s s .

T h e r e f o r e , c o m p r e h e n s i v e i n v e s ti g a ti o n m u s t b e m a d e t o u n d e r s t a n d t h e i n f lu e n c e o f t h e

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

t e m p e r a t u r e a p p l i c a t io n i s t h e e s t im a t e o f t h e l o w e s t s e r v i c e t e m p e r a t u re .

Environment

M a n y m a t e r ia l s e x p e r i e n c e a c c e l e r a te d c r a c k i n i t ia t io n a n d p r o p a g a t i o n u n d e r th e j o i n t

a c t i o n o f a c o r r o s i v e e n v i r o n m e n t . F o r c e r t a i n m a t e r i a ls , t h e p r e s e n c e o f c o r r o s i v e e n v i r o n -

m e n t c a n g r e a t ly r e d u c e f r a ct u r e to u g h n e s s . I n t h e p r e s e n c e o f a c o r r o s i v e e n v i r o n m e n t , t h e

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

c o r r o s i o n p i t s a r e f o r m e d .

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

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

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

a c c e l e r a t e d l a b o r a t o r y t e s t s a s t h e s e t e st s g e n e r a l l y r e p r e s e n t a n e x t r e m e c o n d i t i o n . G e n e r a ll y ,

c r a c k p r o p a g a t i o n t e st s o f p r e c r a c k e d f r a c tu r e m e c h a n i c s s p e c i m e n s i n a g g r e s s i v e e n v ir o n -

m e n t s a r e u s e d . T h e s e t y p e s o f t e st s g i v e i n f o r m a t i o n t o o b t a i n : ( 1 ) a li m i t in g s t re s s in t e n s i ty

f a c t o r , K i s c c , b e l o w w h i c h c r a c k i n i t i a t i o n a n d g r o w t h w i l l n o t o c c u r , a n d ( 2 ) t h e r a t e o f

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

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

s u i ta b l e f o r t h e i n t e n d e d s e r v i c e a p p l i c a ti o n . A l s o , l im i t a t i o n s a r e d e t e r m i n e d o n s tr e ss , t e m -

p e r a t u r e , a n d o t h e r p a r a m e t e r s a f f e c t in g t h e f r a c t u r e s t r e n g t h o f th e m a t e ri a l.

Loading Condition

Tensile Loads If t h e b o l t i s p e r f e c t ly s y m m e t r i c a l , t h e f a c e s o f t h e h e a d a n d n u t a r e

e x a c t l y p e r p e n d i c u l a r t o t h e a x i s o f t h e t h r e a d s , j o i n t s u r f a c e s a r e f l a t a n d p a r al le l , a n d

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

a n a l y s i s o f b o l ts h a s s h o w n t h a t th e t e n s i le s t re s s is z e r o a t th e f r e e e n d o f t h e b o l t a n d

t h a t i t r i s e s u n i f o r m l y t h r o u g h t h e h e a d t o t h e s t r e s s l e v e l f o u n d i n t h e b o d y . A s i m i l a r

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

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

t h r e a d s . H o w e v e r , i n re a l s t r u c t u re , c o n s i d e r a t i o n s h o u l d b e g i v e n t o t h e e f f e c t s o f m i s a l i g n -

m e n t s a n d n o n - p e r p e n d i c u l a r i t ie s , m e t h o d s o f a p p l y i n g p r e l o a d , a n d v a r i a t i o n in t h e co e f f i-

c i e n t o f fr i ct io n . F o r m o s t p r a c t i c a l a p p l i c a t io n s , t h e r e i s n o u n i f o r m s tr e ss l e v e l , e v e n i n t h e

b o d y . T h i s h a s a v a r i e t y o f im p l i c a ti o n s w h e n w e a r e c o m p u t i n g s u c h t h in g s a s s tr e ss le v e ls ,

p re loads , sp r ing cons t an t s , e t c .

I n g e n e r a l , t h e r e i s a c o n c e n t r a t i o n o f t h e l o a d a t t h e f i r s t e n g a g e t h r e a d . T h e f i r s t t h r e e

e n g a g e d t h r e ad s c a r r y m o s t o f th e l o a d i n a n y c a s e . T h i s m e a n s t h at m o s t o f th e n u t is n o t

C o p y r i g h t b y A S T M I n t l ( a ll r ig h t s r e se r v e d ) ; F r i M a y 9 1 1 : 4 1 : 0 0 E D T 2 0 1 4


U n i v e r s i d a d D e C h i l e p u r s u a n t t o L i c e n s e A g r e e m e n t . N o f u r t h e r r e p ro d u c t i o n s a u t h o r i z ed .

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O V R V I W x i i i

d o i n g i t s s h a r e o f th e w o r k . T h i s s i t u a t io n c a n b e i m p r o v e d b y t a p e r i n g t h e t h r e a d s o r a lt e r in g

t h e p i t c h o n e i t h e r n u t o r b o l t to h a v e m o r e u n i f o r m i t y i n l o a d d i s tr i b u ti o n . T h e m o s t p o p u l a r

way i s t o use a nu t t ha t i s pa r t i a l l y i n t ens ion .

A b o l t is a l w a y s p u t i n t o s e r v i c e te n s i o n w h e n i t i s p r o p e r l y t ig h t e n e d . S u b s e q u e n t e x t e r n a l

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

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

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

Bending Because j o i n t a n d n u t s u r f a c e s a r e n e v e r e x a c t l y p e r p e n d i c u l a r t o t h e t h r e a d

a x i s , a b o l t a l m o s t n e v e r s t r e t c h e s u n i f o r m l y w h e n i t i s t i g h t e n e d ; i n s t e a d , i t b e n d s t o s o m e

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

m a l g r a d i e n t t h r o u g h t h e d i f fe r e n t c o m p o n e n t s c l a m p e d i n t h e j o i n t o r t h e r e a r e m a t e ri a ls

w i t h d i f f e r e n t c o e f f ic i e n t s o f t h e r m a l e x p a n s i o n s u b j e c t e d t o a u n i f o r m t e m p e r a t u r e c o n d i t i o n .

T h e r m a l d i ff e re n ti a l b e t w e e n t h e f a st e n e r a n d t h e c l a m p e d c o m p o n e n t s w i l l p r o d u c e t en s il e

s t r es s i n t he f as t ener . Th i s s t r es s i s i n add i t i on t o t he i n i t i a l a s sembly pre load t ens i l e s t r es s .

I n a d d i t i o n , i f t h e r e a r e n o n - p e r p e n d i c u l a r i t ie s a n d n o n - p a r a l l e l is m s b e t w e e n t h e v a r i o u s

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

s t r es s g rad i en t t ha t i s add i t i ve t o t he bo l t t ens i l e s t r es s fo r e l as t i c behav ior . For t h i s t ype o f

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

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

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

bending s t r es ses i n bo l t s .

Torsional Shear Stre ss W hen

f a s t e n e r s a r e p r e l o a d e d b y t o r q u e , a t o r s i o n a l s h e a r s t r e s s

i s in d u c e d t h r o u g h o u t th e v a r i o u s c r o s s s e c t i o n s o f t h e fa s te n e r . T h e v a l u e o f t h e t o r si o n a l

s h e a r s t r e s s v a r i e s w i t h r e s p e c t t o t h e r a d i a l d i s t a n c e f r o m t h e c e n t e r l i n e o f t h e f a st e n e r. I t

i s a f u n c t i o n o f th e f r i c t io n a l c o n s t r a i n ts b e t w e e n t h e t h r e a d s o f t h e n u t a n d t h e t h r e a d s o f

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

c o n t a c t s u r f a ce s . A n a v e r a g e v a l u e o f t h e s h e a r s t r e ss d u e t o p r e l o a d i n g b y t o r q u i n g i s

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

Cyclic Loading

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

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

t h e j o i n t c o m p o n e n t s . D u e t o b o t h l in e a r m o t i o n s a n d r o t a t i o n i n t he j o in t s , l o a d s a r e o f

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

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

p r o p a g a t i o n o f a c r a c k f r o m a n i n i ti a ll y u n f l a w e d r e g i o n o f m a t e ri a l.

Combined Loading

I n t h e p r e c e d i n g s e c t i o n s , th e c a u s e s a n d e f f e c ts o f i n d i v i d u a l l o a d i n g c o n d i t i o n s t e n si le ,

b e n d i n g , a n d t o r s i o n ) w e r e d i s c u s s e d . H o w e v e r , i n r e a l s i t u a t i o n s , t h e s e l o a d s i n t e r a c t a n d

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

m u s t a c c o u n t f o r a ll th e l o a d s a c t in g o n a c o m p o n e n t in a c o m b i n e d m a n n e r . T en s il e, b e n d -

i n g , a n d t o r s i o n a l l o a d s a c t i n g o n a c i r c u l a r c y c l i c c o n t a i n i n g a n e x t e r n a l c i r c u m f e r e n t i a l

n o t c h a r e s h o w n i n F i g . 2 .

Copyr igh t by ASTM In t l ( a ll r igh ts r e serve d) ; F ri Ma y 9 11 :41 :00 EDT 2014

Downloa de d /pr in te d by

Univers idad De C hile pursuant to License Agreem ent . No fur ther reproduct ions author ized.

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x v

S T R U C T U R L NTEGRITY OF F STENERS

Stress Relaxation

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

c o m p o n e n t t h a t i s r e s t r a i n e d t o a f i x e d d e f o r m a t i o n . I t i s a c r e e p - r e l a t e d p h e n o m e n o n i n

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

T h e s t re s s r e l a x a ti o n p r o c e s s i s a f u n c t i o n o f i n it ia l s t r e s s l e v e l a n d a p p l i e d t e m p e r a t u re .

F o r w o r s t c a s e c o m b i n a t i o n o f t e m p e r a t u r e , s t re s s le v e l, a n d m a t e r i a l, p r e l o a d c a n b e r e d u c e d

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

l o s s o f p r e l o a d d u e t o s t re s s r e l a x a ti o n .

T y p e s

o f l a w s

Introduction

I n o r d e r t o a p p l y f r a c t u r e m e c h a n i c s , i t i s a s s u m e d t h a t a c r a c k o r f l a w e x i s t s i n t h e

s t r u c t u r e i n a t h r e a d e d m e m b e r ; t h e m o s t l i k e l y l o c a t i o n a t w h i c h t h e c r a c k w i l l i n i t i a t e i s

t h e h i g h l y s t r e s s e d r e g i o n o f t h r e a d r o o t . I t i s g e n e r a l l y r e c o g n i z e d t h a t t h e f ir s t e n g a g e d

t h r e a d i n a b o l t /s t u d i s u s u a l l y t h e l o c a t i o n o f th e h i g h e s t s t r es s . F r a c t u r e a n a l y s i s p r o c e d u r e

a l s o r e q u i re s d e f i n it io n o f th e s h a p e a n d s i z e o f th e a s s u m e d c r a c k o r f la w . T h e i n it ia l s i z e

o f th e f l a w is u s u a l l y c o n t r o l l e d b y t h e i n s p e c t i o n c a p a b i l it y , a n d t h e s h a p e i s g o v e r n e d b y

s t ruc tura l con f igura t i on and s t a t e o f s tr es s. Rea l i s ti ca l l y , t he sha pe o f a f l aw is e s t ab l i shed

f r o m e i t h e r l a b o r a t o r y s p e c i m e n s o r i n - s e r v i c e fa i lu r e o b s e r v a t i o n s a n d t h e s i z e is e s t a b li s h e d

f r o m t h e n o n d e s t r u c t i v e e x a m i n a t i o n N D E ) c a p a b il it ie s . H o w e v e r , f r o m t h e d e s i g n v e ri fi -

c a t i o n p o i n t o f v ie w , s i m p l i c i ty o f b a s i c a s s u m p t i o n s a r e im p o r t a n t c o n s i d e r a t io n s . A t th e

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

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

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

i m p o r t a n t r o l e . T h e s tr e ss i n t e n s i t y f a c t o r s o l u t io n s a r e d i f fe r e n t f o r v a r i o u s t y p e s o f c r a c k

conf igura t i ons , and under s imi l a r s t r e s s f i e lds s t ruc tures can have d i f f e ren t s t r eng ths . There -

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

o f t h e f l a w u s e d i n t h e a n a l y s i s b e e s t ab l i sh e d . I n t h is p a p e r f o u r t y p e s o f f la w c o n f i g u r a t i o n s

w i l l b e d i s c u s s e d . A b o l t u n d e r t e n s i le l o a d i s s h o w n i n F i g . 1 . T h e s t r e s s i n te n s i ty s o l u t i o n s

i n th e l i te r a tu r e a r e c a l c u l a t e d a s s u m i n g a s i n g l e g r o o v e i n a c y l i n d r i c a l b a r u n d e r c o m p l e x

l o a d c o n d i t i o n s a s s h o w n i n F i g . 2 .

Semi Circular Surface Defect Model

T h e g e o m e t r y f o r t h is d e f e c t s h a p e i s g i v e n i n F i g . 3 . T h e s t re s s i n te n s i t y f a c t o r s o l u ti o n

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

i n t e n s i t y f a c t o r s o l u t i o n f o r t h i s c a s e i s g i v e n b e l o w .

K~ = 1.22 ~ 1)

w h e r e

KI - - - the s t ress intensi ty factor ,

= t h e a v e r a g e s t r e s s o v e r d e f e c t ,

a = t he i n i t i a l f l aw s i ze , and

~b = t h e c o m p l e t e e l l ip t i c i n t e g r a l o f t h e s e c o n d k i n d ;

~b i s I r / 2 fo r a sem i -c i r cu l a r f l aw.

C o p y r i g h t b y A S T M I n t l ( a ll r i g h ts r e s er v e d ) ; F r i M a y 9 1 1 : 4 1 : 0 0 E D T 2 0 1 4

D o w n l o a d e d / p ri n t e d b y

Unive r s ida d De Chi le pur sua n t to L ic e nse Agre e me nt . No fu r the r r e produc t ions a u thor iz e d .

char 12

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O V R V I W X V

O m

A

J

9 J

J

f

t~ m

FIG. 1--Bolt under tension load.

A

S i n g l e E d g e N o t c h M o d e l

This model is illustrated in Fig. 4. Assessment of cracked solid cylinder was carried out

by Johnson [1] and an edge crack model was developed. This model is also used by PVRC

AD Hoc Group on Toughness Requirement. The stress intensity solution for this model is

given as

K I = t r ~ F a iD , . )

2 )

where




char 12

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x v STRU CTUR L INTEGRITY O F F STENERS

T

p

MAJOR DIAMETER DM

MINOR -

DIAMETER D a

HOLE DIAMETER D H

I -

~

P

FIG. 2- -C irc ula r cyl inder containing external circumferential notch u nder com bined loading.

F a l D m ) = 1.12 - 0.231 a / D , ) + 10.55 a i D , , ) 2 - 21.72 a i D , , ) 3 + 30.39 a/Din)4 , and

o = gross stress.

For application in the thread region:

a = a i -~- a n

ai = initial flaw size,

a, = thread depth, and

D m = major diameter of the threaded region.

C i r c u m f e re n t ia l C r a c k M o d e l

This model is shown in Fig. 5. Harris [2] has given a solution for stress intensi ty factor

for this type of model as




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O V E R V I E W x v i i

a m S E C T I O N B B

THRE D M JOR DI METER

THRE D MINOR DI METER

DI METER OF HOLE

i

FIG. 3--Sin gle- edg e cracked plate in tension representing an asym me tric crack configuration in a

circular cylinder.

where

c = gross membrane stress,

4P

c r . = = / 9 2 . _

~ )

M. = geometric correction factor.

r , = o - M . ~ 3 )

M m =

1 - D f f D m ) :

[ 1 - ~ D . ) 2 -

DJDm YI 0.8 + 1 ---~-[Dm 4 +

1 1 , o

1 - O d D - - 2 a l D m / J

(4)

where




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x v STRUCTUR LNTEGRITY OF F STENERS

o

~ 0 ~ THREAD AJOR IAMETER

/ r ,, / - T E A O ' O R O 'A M E T E

SECTIONA A ON FIGURE

FIG. 4--Semi-c ircular crack

configurat ion

a = t o t a l c r a c k l e n g t h i n i t i a l c r a c k l e n g t h p l u s t h r e a d d e p t h ,

D m = m a j o r d ia m e te r ,

D h = d i a m e t e r o f th e h o l e , a n d

P = t ens i l e l oad .

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

T h e a b o v e s o l u t io n i s a p p l i c a b l e o n l y t o th e m e m b r a n e c a s e . A s u g g e s t e d l i m i t o f a p p l i-

cab i l i t y o f t h i s so lu t i on i s

Dh/D, ,


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O V E R V I E W x i x

r T H R E A D M A J O R D I A M E T E R , D

T H R E A D M I N O R D I AM E T E R , De

/ - N O T C H D E P T H , 3

I - I N IT I A L C R A C K S I Z E , I ~

~ ~ s D I A M E T E R O F H O L E , Du

S E T I O N A A O F F I G U R E 2

FIG. 5 C ircum feren t ia l crack conf igurat ion.

o ~ ~

2 R

FIG. 6m Sick le sh ape d crack fu l ly surrounding the cy l inder c ircumference.

Copyright by ASTM Int l (all rights reserved); Fri May 9 11:41:00 EDT 20 14



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XX STRUCTUR L INTEGRITY OF F STENERS

H = ( 1 ~ E v 2 ) f o r p l a n e s t r a in , a n d

H = E f o r p l a n e s t r e ss .

K , = , t o V q--d~ a F , a / R )

w h e r e ro i s t h e t e n s i l e s t r e s s.

a n d

(7 )

F r ( a / r ) = 1 . 1 21 5 + 0 . 1 6 4 4 ( a / R ) + 5 . 1 3 9 6

a / R ) 2

- 15 .932

a / R ) 3 +

2 4 . 7 4 6 ( a / R ) 4 - 1 0 . 9 8 6 ( a / R ) 5 (8 )

T h e c r a c k o p e n i n g d i s p l a c e m e n t U r ( x , a ) a s a f u n c t i o n o f x a n d a i s c a l c u l a t e d a ss u m i n g

t h e f o l l o w i n g r e l a t i o n s h i p .

u ( x , a) = Umax(a)

=

(1 - x l z ) l a (9 )

Um~x i s c a l c u l a t e d b y 3 - D f i n i t e e l e m e n t a n a l y s i s a t x = 0 u n d e r a t e n s i l e s t r e s s , a n d t h e

n o r m a l i z e d d i s p l a c e m e n t e x p r e s s io n i s g i v e n a s

u m ~ E - - ~ C i ( a / R ) ]

( 1 0 )

1 -

V2~oR =

w i t h C i = 0 . 1 9 6 5 , C 2 = 2 2 . 5 1 5 , C 3 = - 4 4 . 3 1 7 , a n d C4 = 3 9 . 0 8 8 .

F r o m t h e a b o v e e q u a t io n s , K , i s o b t a i n e d a s

K r = Oro V ~ r a F r ( a / R ) ( 1 1 )

w h e r e F ( r ) i s g i v e n

F ( r ) = 1 . 1 2 1 5 + 0 . 1 6 4 4 ( a i R ) + 5 . 1 3 9 6 ( a / R ) z - 1 5 . 9 3 2 ( a / R ) s

+ 2 4 . 7 4 6 a / R ) 4 - 1 0 .9 8 6 ( a / R ) s (1 2 )

T h e w e i g h t fu n c t i o n s f o r t h e s p e c i a l c a s e s o f l i n e a r s t re s s d i s t r ib u t i o n ( 1 - x / a ) a n d

q u a d r a t i c s t r e s s d i s t r i b u t i o n ( 1 - x l a ) 2 a r e g i v e n a s

F , , , ( a ) = 0 .A,~A.6 + 1 .1086 (a /R ) - 3 .4 58 2 ( a / R ) 2

+ 5 . 3 9 6 ( a / R ) 3 + 0 . 2 0 5 7 ( a / R ) 4 - 1 . 4 8 4 4 ( a i R ) s ( 1 3 )

F q ua = 0 .6 0 4 8 + 1 .2 5 4 2 ( a / R ) - 3 . 4 0 9 5 ( a / R ) 2 + 4 . 6 1 8 9 ( a i R ) 3

+ 2 . 4 9 8 4 ( a / R ) 4 - 2 . 6 8 0 6 ( a / R ) 5 ( 1 4 )

T h e s e e q u a t i o n s a r e v a l i d a n d a p p l i c a b l e f o r 0 -< a i r -< 1 . T h e s u p e r p o s i t i o n m e t h o d c a n

b e u s e d t o d e t e r m i n e t h e s t re s s i n t e n s i t y f ac t o r s.



U n i v e r s i d a d D e C h i l e p u r s u a n t t o L i c e n s e A g r e e m e n t . N o f u r t h e r r e p ro d u c t i o n s a u t h o r i z ed .

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OV RV I W xx i

E m p i r i c a l A p p r o a c h t o S t r e s s I n t e n s i t y F a c t o r s

A n e m pi r i c a l a pp r oa c h t o de t e r m i ne t he s tr e ss i n te ns it y f a c t o r ha s be e n p r opos e d by J a m e s

and Mi l l s [4 ] . They deve loped a func t ion based on the ana ly t i ca l and exper imenta l da ta for

s t ra igh t f ron t c rack , s em i -c i rcu la r c rack f ron t , and th reads for t ens ion and ben ding load

condi t ions . They agreed tha t the re a re reg imes of a /D where each of the so lu t ions i s appl i -

cab le . Th e s t re s s in t ens i ty fac tor sub jec ted to t ens ion i s g iven as :

K = o ( t r a ) 1 /2

F alD)

15)

w he r e

F a l D ) = A ~ a l D ) + C + D a l D )

+

E a/D ) 2 q- F a l D ) 3 + G a / D )4 16)

w he r e

A = 2.043, B = 31.332, C = 0.6507, D = 0.5367, E = 3.0469, F = -19.504, G = 45.647

T he a u t ho r s c l a i m t he a bove e qua t i on i s r e a s ona b l y a c c u r a t e f o r a / D > 0.004. A s imi lar

so lu t ion i s p roposed for loads sub jec ted to bending . An addi t iona l d i scuss ion on th i s ap-

proach i s g iven by A . F . L iu and R . C. Cipol l a in th is vo lum e STP 1236).

L o a d i n g R a t e E f f e c t

In general , f rac ture toughness of s t ructura l mater ia ls , par t icular ly s tee ls , decreases wi th

loading ra t e . For a g iven t emp era ture , the f rac ture toughness m easured in an im pac t t e s t, K id ,

genera l ly i s low er than the f rac ture toughness me asured in a s t a ti c t e st , K ic . In o the r w ords ,

i t shows tha t a t a con s tan t temp era ture , f rac ture toughness t e s t s conduc ted a t h igher load ing

ra tes genera l ly re su l t in low er toughness va lues .

The loading ra te effect i s s igni f icant for mater ia ls that exhibi t s t ra in ra te effects , such as

s t ructura l s tee ls having yie ld s t rengths less than about 140 ks i . The loading ra te a t a given

temp era ture can a f fec t the no tch toughness s ign if i can t ly for such mate r i a ls . Idea lly , t he f rac -

ture toughness va lues should be de te rmined a t load ing ra t e s tha t a re exper i enced by the

actual s t ructure . Varia t ion of loading ra te throug hou t the s t ructure wi l l affect the a l low able

s t res s th roug h i ts dep enden ce on p lane s t ra in f rac ture toughness , K ic .

Thus , the ac tua l s e rv ice load ing ra t e wi l l have a s ign i f i can t in f luence on any f rac ture

cr i ter ion speci f ied, e i ther s ta t ic or dynamic.

rack Growth Equation

The use of the concept o f f rac ture mechanics in the des ign and ana lys i s o f s t ruc tures

as sum es the ex i s t ence of in i t ia l f laws or c racks . These c rack s unde r repea ted se rv ice load ing

condi t ions propag a te and be co m e uns tab le fa s t -f rac ture ) wh en a c r it ica l c rack l ength i s

reached . The ra te o f c rack propaga t ion depend s on man y fac tors , such as : 1 ) ma te r ia l , 2 )

env ironm ent , 3) service load his tory, 4) crac k geom etry, 5) local s t ructura l configurat ion.

I t i s known f rom Ref 5 tha t fo r a pa r t i cu la r ma te r i a l t he c rack growth ra t e , d a M N , c a n be

desc r ibed as a func t ion of the s t re s s in t ens i ty fac tor range , AK. At presen t the re i s a l a rge

num be r o f c r a c k g r ow t h e qua t ions . T he F o r m a n c r a c k g r ow t h e qua t ion , R e f 6 , a s de sc r ibe d

be low i s w ide ly used in the indus t ry .

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Univers idad De Chile pursuant to License Agreement . No fur ther reproduct ions author ized.

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x x S TRUCTUR L INTE G RITY O F F S TE NE RS

c a tO n

d a M N = (1 7 )

1 -

R K~ - A K

w h e r e d a / d N i s t h e r at e o f c r a c k g r o w t h , c a n d n a r e m a t e r i a l c o n s t a n t s , A K i s t h e s t r e s s

i n t e n s i t y f a c t o r r a n g e , R i s t h e s t r e s s r a t i o d e f i n e d a s m i n i m u m s t r e s s d i v i d e d b y m a x i m u m

s t r e s s , a n d K c i s t h e c r i t i c a l s t r e s s i n t e n s i t y f a c t o r .

T h e s t re s s in t e n s i t y f a c t o r ra n g e A K i s d e f i n e d a s

A K = A i r ~ / - ~ a . F a l D )

( 1 8 )

w h e r e A t r i s t h e s t r e s s r a n g e , a i s t h e h a l f c r a c k l e n g t h , a n d F a / D ) i s t h e p r o d u c t o f v a r i o u s

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

T h e v a l u e s o f c a n d n ( m a t e r i a l c o n s t a n t s ) a r e c a l c u l a t e d f r o m c o n s t a n t a m p l i t u d e te s t d a t a

b y t h e f o l l o w i n g t e c h n i q u e d e r i v e d f r o m t h e F o r m a n e q u a t i o n .

lo g [ (1 - R ) K ~ - A K ] + lo g d a / d N ) = l o g c + n l o g A K

( 1 9 )

F o r a n y t w o p o i n t s , w h i c h r e p r e s e n t a s e g m e n t o f t h e c r a c k g r o w t h r a t e c u r v e, tw o s i m u l -

t a n e o u s e q u a t i o n s a r e s o l v e d f o r c a n d n .

D e s i g n S a f e t y F a c t o r

A s a f e ty f a c t o r is r e q u i r e d i n a b r i t tl e f ra c t u r e a n a l y s i s p r o c e d u r e t o a c c o u n t f o r p o s s i b l e

v a r i a b i l i t y d u e t o u n k n o w n s a n d i n a c c u r a c i e s a t v a r i o u s s ta g e s . A d e c i s i o n h a s t o b e m a d e

n o t o n l y o n t h e m a g n i t u d e o f th e s a f e t y f a ct o r b u t a l s o o n h o w a n d w h e n i t s h o u l d b e

a p p l i e d . T h e r e a r e v a r i o u s p o s s i b i l i t i e s t h a t e x i s t a n d t h a t s h o u l d b e c o n s i d e r e d b e f o r e a f i n a l

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

1 . S a f e t y f a c t o r s o n f a t i g u e s t r e s s e s .

2 . S a f e t y f a c t o r s o n b a s i c d a ta .

3 . S a f e t y f a c t o r o n i n i t i a l c r a c k s i z e .

4 . S a f e t y f a c t o r o n f i n a l l i f e ( c y c l e s ) .

5 . S a f e t y f a c t o r o n f a i l u r e l o a d .

A c k n o w l e d g m e n t

T h e w o r k r e p o r t e d i n t h i s p a p e r w a s d o n e o v e r a n u m b e r o f y e a r s b y t h e a u t h o r a s t h e

c h a i r m a n o f A S T M T a s k G r o u p E 0 8 . 0 4 .0 7 o n F r a c t u r e M e c h a n i c s o f F a s te n e r s. I w o u l d l i k e

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

o f f a s t e ne r s . T h e a u t h o r a l s o w a n t s t o t h a n k W e s t i n g h o u s e - B e t t i s L a b o r a t o r y f o r it s c o n t in -

u o u s s u p p o r t , w h i c h h a s m a d e i t p o s s i b l e f o r t h e a u t h o r to p a r t i c i p a t e i n A S T M c o m m i t t e e

a c t i v it i e s. T h e v i e w s e x p r e s s e d a r e e n t i r e l y t h o se o f t h e a u t h o r a n d d o n o t r e f l e c t t h e v i e w s

o f t h e A S T M o r t he W e s t in g h o u s e - B e t t is L a b o r a to r y .

R e f e r e n c e s

[1] Johnson, R. N., Fractu re of Cracked Solid Circular Cylinde r, Ph.D. thesis , Univers ity of W isconsin,

1972.

[2] Harris , D. O., Stress Intensity Factors for Hollow Circumferentia lly No tched Round Bars , Trans-

actions o f ASME, Journal o f Basic Engineering, March 1967, pp. 49-54.

Copyr igh t by ASTM In t l ( a ll r igh ts r e serve d) ; F r i Ma y 9 11 :41 :00 EDT 20 14

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Unive r s ida d De C hi le pur sua n t to L ic e nse Agre e me nt . No fu r the r r eproduc t ions a u thor iz e d .

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O V R V I W x x i i i

[3] Mattheck, C., Morawietz, P., and Munz, D., Stress Intensity Factors of Sickle Shaped Cracks in

Cylindrical Bars, International Journal o f Fracture No. 1, 1985, pp. 45-47.

[4] James, L. A. and Mills, W. J., Review and Synthesis of Stress Intensity Factor Solutions Applicable

to Cracks in Bolts, Engineering Fracture Mechanics Vol. 30, 1988, pp. 641-654.

[5] Pads, E and Erdogan, E, A Critical Analysis of Crack Propagation Laws, Journal of Basic En-

gineering December 1963, pp. 528-534.

[6] Forman, R. G., Keamey, V. E., and Engle, R. M., Numerical Analysis of Crack Propagation in

Cyclic-Loaded Structures, Journal of Basic Engineering September 1967, pp. 459-464.




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ntroduction

In 1986 , ASTM Commi t t ee E24 conc luded tha t the re was enough in te res t to e s t ab l i sh a

T a s k G r oup E 24 . 06 . 04) unde r S ubc om m i t t e e E 24 . 06 , t he A pp l i c a ti on o f F ra c t u re M e c ha n i c s.

The scope inc luded provid ing ana lys i s p rocedure , t e s t me thods , and c r i t e r i a for s t ruc tura l

in tegr i ty eva lua t ion of fa s t ene rs . Two s tudy groups were c rea ted under th i s t a sk group , one

engaged in a s s imi la t ing re fe rences on fa t igue and f rac ture mechanics appl i ca t ion and the

second to com pi le s tre s s in tens ity fac tors appl i cab le to fa s tene rs . In 1993 , E24 me rged wi th

Com m i t t e e E 09 t o f o r m Com m i t t e e E 08 on F a t i gue a nd F r a c t u r e . )

The sym pos ium on S t ruc tura l In tegr i ty of Fas teners , he ld in Miam i , F lor ida , on 18 Nov.

1992, w a s c onc e i ve d a ye a r p r e v i ous l y a t t he A S T M Com m i t t e e W e e k i n D a l l as , T e xas . A t

th i s mee t ing , a workshop on fa t igue and f rac ture of fa s t ene rs was he ld . Pa r t i c ipan t s showed

an in te res t in a one-day sympos ium on s t ruc tura l in tegr i ty of fa s t ene rs .

T he que s t f o r m or e e f f i c i e n t s t r uc t u r e s ha s p r om pt e d t he de ve l opm e n t o f i m pr ove d m a -

ter ia ls , s t ress analys is , and fabricat ion and inspect ion techniques . Higher a l lowable s t ress

usua l ly re su l t s f rom the use of these improved t echniques . Higher s t re s ses a re genera l ly

acceptab le f rom the s t andpoin t o f s t a t ic s t re s ses ; however , when these s t res ses a re cyc l i c in

na ture , c rack in it ia t ion m ay occur . Ge nera l ly speaking , fo r fa s t ene rs , t e s ting i s used to p red ic t

crack ini t ia t ion.

In orde r to rev iew the l a t e s t deve lopments in dea l ing wi th fa t igue and f rac ture behavior

o f f a s t e ne r s , t he M i a m i s ym pos i um w a s he l d . T he s ym pos i um w a s s pe c i f i c a l l y c onc e r ne d

with fa t igue crack ini t ia t ion) , f rac ture of crac k grow th) fa i lure , and evaluat ion and cr i ter ia

for s t ruc tura l in tegr i ty o f fa st ene rs. The sym po s ium cons i s t ed of four ses s ions. Thi s vo lum e ,

which resu l t ed f ro m the sym pos iu m , conta ins the t ex t o f the pap ers presen ted p lus the t ex t

of o the r submi t t ed papers .

M a ny p e op l e c on t ri bu te d t i m e a nd e ne r gy t o m a ke t he s y m pos i um a s uc ce s s. S pe c i a l

thank s are due to: a) the speakers for the t ime and e f for t spent in prepar ing the i r p resen-

ta t ion and fina l man usc r ip t s ; b )

the session chairmen

for the i r e f for t in ke eping the ses s ions

m o v i ng in a t i m e l y m a nne r ; a nd c ) the reviewers for the i r ca re fu l ed i ting of the manu sc r ip ts .

The papers in th i s vo lum e a re s t a t e -of - the -a r t on fa t igue and f rac ture mechanics for fa s -

t ene rs. Th ese pap ers a re use fu l fo r enginee rs , s c i en ti s ts , and resea rch ers wh ose in te rest s l i e

in the s t ructura l integri ty of fas teners .

Pir M Toor

Edi tor

C o p y r i g h t b y A S T M I n t l ( a ll r ig h t s r e se r v e d ); F r i M a y 9 1 1 : 4 1 : 0 0 E D T 2 0 1 4

D o w n l o a d e d /p r i n t ed b y

Unive r s ida d D e Chi le pur sua n t to L ic e nse Agre e me nt . No fu r the r r e produc t ions a u thor iz e d .

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Fa t i gue i n Fas tene rs


D o w n l o a d e d / p r i n t e d b y

U n i v e r s i d a d D e C h i l e p u r s u a n t t o L i c e n s e A g r e e m e n t . N o f u r t h e r r e p ro d u c t i o n s a u t h o r i z e d .

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Daryoush AUaei 1

Ef fec ts o f Nonun i fo rmi t ies in Fas teners on

Loca l i zed V ib ra t ion and Fa t igue

R E F E R E N C E : A l l ae i, D . , " E f f e c ts o f N o n u n i f o r m i ti e s in F ~ e n e r s o n L o c a l i z ed V i b r a t i o n

a n d F a t i g u e , " Structural Integrity o f Fasteners, AST M S TP 1 236 , P. M. Toor , Ed., A merican

Society for Testing an d M ater ials , Phi ladelphia, 1995, pp. 3- 19 .

ABSTRACT:. The purpose of this paper is to report on an ongoing project that combines

recent developments in the f ields o f vibrat ions and m odel ing to increase the service-free l i fe

and the qu ality o f performance and re liab ili ty of fasteners and to reduce unnecessary mainte-

nance and fa ilure in airc raft structures. In this project, th e fea sibili ty of d eveloping an efficient

and effective m athematical model cap able o f incorporat ing the d ynam ic character is tics of fas-

teners, their interfaces with the h ost structure, and the h ost structure i tself is bein g investigated.

Such a co mb ination will resu lt in a significant gain in computational speed and an improvement

in the accuracy of the numerical results, producing a better prediction. The model will be

adaptive based on the close d-loop dynam ic relat ion between fasteners and the host s tructure.

The main contribut ion of this work is to includ e the effect of fasteners on vibrat ion phenomena

such as lo ci veer ing and m ode loc al izat ion and the app l icat ion of the receptance method, which

makes the m odel com pat ible with exist ing computer mo dels , to the d ynam ics of fasteners.

K EY W O RD S: fasteners/ join ts , mo de loca l izat ion, s tructures, receptances, vibrations, fatigue

I n c r e a s e d a p p l i c a t i o n o f l i g h t - w e i g h t a n d t h i n p l a t e s / s h e l l s in s t r u c tu r e s a n d t h e d e m a n d

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

a n d r e s e a rc h e r s d e v e l o p m o r e a c c u r a t e p r e d i c t i o n m o d e l s . L a c k o f e f fe c t iv e d y n a m i c m o d e l s

o f c o m b i n e d f a s t e n e r - st r u c tu r e sy s t e m s a r e a m o n g t h e s h o r t c o m i n g s o f th e p r e s e n t c o m p u t e r

m o d e l s u s e d f o r v i b r a t i o n a n a l y s is .

F a s t e n e r s ( su c h a s a d h e s i v e s , b o l t s a n d n u t s , a n d w e l d e d j o i n t s ) a r e a n i n t e g r a t e d a n d v e r y

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

a n d m a r i n e v e h i c l e s . S i n c e a l l m a c h i n e r y a n d v e h i c l e s a r e s u b j e c t e d t o c o n t in u o u s v i b r a t io n

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

F a s t e n e r f a i l u r e c a n r e s u l t i n r e d u c t i o n ( o r l o s s ) o f p e r f o r m a n c e , u n e x p e c t e d d e s t r u c t i o n o f

s y s t e m s ( s u c h a s m a c h i n e r y a n d v e h i c l e s ) , a n d d e v a s t a t i n g a n d c o s t l y c o n s e q u e n c e s . I n p a r -

t ic u l ar , th i s p r o b l e m i s m o r e s e v e r e i n h i g h - s p e e d v e h i c l e s w i t h l i g h t -s k i n s tr u c tu r e s s u c h a s

a i rc r a ft . T h e p u r p o s e o f t h i s w o r k i s to d e v e l o p a n e f f e c ti v e m a t h e m a t i c a l m o d e l t h a t c a n b e

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

t h e i r u s e f u l l i f e c y c l e a n d t o i n c r e a s e t h e i r s e r v i c e - f r e e l if e , t h e i r q u a l i t y o f p e r f o r m a n c e , a n d

t h e i r re l i a b i l i ty , t h e r e b y r e d u c i n g u n n e c e s s a r y m a i n t e n a n c e a n d t h e r i s k o f s t r u c t u r e f a il u r e .

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

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

Sen ior scientist , ORDC , Inc., Bo x 562, Excelsior, M N 55331-0562. A lso, prog ram manager, Sound

and Vibration Engineering Technology Program, Hutchinson Technical College, Two Century Ave.,

Hutchinson, MN 55350.

Copyright 1995 by A STM Intemational

3

www.astm.org

Copy right by ASTM Int l (all rights reserved); Fri May 9 11:41:00 EDT 201 4



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4 STRUCTURALNTEGRITY OF FASTENERS

probably been s tud ied as ea r ly a s the deve lopment o f the f i r s t a i rp lane , t h i s d i scuss ion i s

focused on recen t advances in the sub jec t (1980 to the presen t ) .

Inves t iga t ion of ho le p repa ra t ion and fa s t ene r ins t a l l a t ion e f fec t s on graphi t e /epoxy l am-

ina tes was repor t ed by Condon [1] in 1980 . Of in t e res t were the e f fec t o f va r ious ho le

i r regula r i ti e s on the s t a t ic and fa t igue s t rength o f the l am ina te and the in f luence o f the roo m

temp era ture (65 to 250~ (18 to 121~ m ois ture (d ry and we t ) in spec imens , and type of

fas t ene rs . H i s t e s t r e su l t s showed tha t in t e rp iy de lamina t ions caused a s ign i f i can t s t reng th

reduc t ion and tha t b l ind bo l t s and so l id r ive t s caused ins t a l l a t ion damage . No damage was

repor t ed when b l ind r ive t s , t h readed r ive t p ins , and pu l l - type lock bo l t s were ins t a l l ed . I t

should be no ted tha t mos t o f h i s ana lys i s was based on ex tens ive t e s t ing bu t ve ry l i t t l e

ana ly t i ca l work . The loosen ing e f fec t o f fa s t ene rs was no t addres sed .

In Refs 2 and 3 , s eve ra l f a s t ene r pa ramete rs were inves t iga ted whi l e deve lop ing a dura -

b i l i t y t e s t me thod . The goa l was to use f rac tographic da ta to quant i fy the in i t i a l f a t igue

dis t r ibut ion or equivalent ini t ia l f law-s ize cumulat ive dis t r ibut ion for c learance-f i t fas tener

holes . The i r va r i ab les were ma te r i a l , spec t rum leve l , f a s t ene r d i amete r and f i t , pe rcen t bo l t

load t rans fe r , and geomet ry . The au thors used e i the r an F -16 or a B-1 bomber in the i r

expe r imen ta l work . In Refs 4 and 5 , t he re su l t s o f a comp rehens iv e se r ie s o f f l igh t -by- f ligh t

fa t igue te s t s on Mi rage I I I0 wing m a in sp a r were repor t ed . The au thors ind ica ted tha t the

m os t p rom is ing op t ion w as the use of in t e r fe rence - f it st ee l bushes in ho les . An inves tiga t ion

of add-on damping t rea tment to F -15 upper -ou te r w ing sk in was repor t ed [6] in 1991 . The

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

loca l s t i f fene r modes . Fur the rmore , c racks in i t i a t e a t t he fa s t ene r ho les ad jacen t to the "T"

s t i f fene rs , and they propaga te pa ra l l e l t o the s t i f fene rs . Accord ing to Defense Technica l

Informat ion Cente r (DTIC) repor t s , t he re i s ongoing re sea rch

[7,8]

t ha t cou ld be re l a t ed to

t h e s u b je c t, b u t o n l y b r i e f s u m m a r i e s w e r e a v a i la b l e. N o n e o f t h e a b o v e w o r k h a s m e n t i o n e d

the occur rence of the mode loca l i za t ion and i t s app l i ca t ions in s t ruc ture - fas t ene r sys t ems .

Th e i r me tho d o f ana lys is was no t based o n the recep tance m e thod as desc r ibed in th is pape r .

Fur the rmore , t he e f fec t s o f fa s t ene r nonuni formi t i e s on the dynamic re sponse of the com-

bined s t ruc ture - fas t ene r sys t em s have no t p rev ious ly been repor t ed in the op en l i t era ture .

S t ruc tures do no t re spond in the pred ic t ed manner nor do they func t ion proper ly un les s

the i r pa r t s have the cor rec t s i ze and shape re l a t ive to one anothe r and they a re connec ted

(and remain connec ted) accord ing to sys t em spec i f i ca t ions . However , i t i s no t poss ib le to

m ake a pa r t o f any ex ac t s i ze o r shape , nor i t is poss ib le to m a in ta in pe r fec t con tac t be twe en

par t s th roughout the ope ra t ing l i f e o f s t ruc tures . In the case of s t ruc tura l component s , due

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

process , t he i r d imens ions wi l l va ry . Such va r i a t ions a re known as

tolerances.

I n t h e c a s e o f

f a s te n e r s, e v e n i f t h ei r a m o u n t o f v a r ia t io n d u e t o m a n u f a c t u r i n g c a n b e r e d u c e d a n d a s s u m e d

negl ig ib le , t he i r dynamic re sponse va r i a t ions a re usua l ly s ign i f i can t because they a re sub-

j e c t e d t o a w i d e r a n g e o f d i f f e r e n t m a g n i t u d e s a n d t y p e s o f v i b r a t i o n . I t h a s b e e n s h o w n

[10,16,17,21,23,28,34,38,39]

t ha t such pa ramete r va r i a t ions could re su l t i n d ras t i c changes

in the dynamic re sponse of s t ruc tures and thus in rap id fa i lu res . There fore , t he ana lys t and

the des igne r mus t ca re fu l ly p lan the amount o f va r i a t ion tha t i s accep tab le in the sys t em to

ga in the bes t poss ib le ba lance be tween cos t , func t ion , and fa i lu re .

The ob jec t ive of th i s p ro jec t i s t o inves t iga te the feas ib i l i ty o f deve lop ing an e f f ic i en t and

ef fec t ive ma them at i ca l m ode l capable o f incorpora t ing the dyn am ic cha rac te r is t i c s o f fa s t en-

ers , the i r interfaces wi th the hos t s t ructure , and the hos t s t ructure i t se l f . Such a combinat ion

wi l l r e su l t i n a s ign i fi can t ga in in com puta t iona l sp eed and im pro vem ent in accuracy o f the

numer ica l re su l t s , p roduc ing a be t t e r p red ic t ion . The mode l w i l l be adapt ive based on the

c losed- loop dy nam ic re l a tion be twee n fas t ene rs and the hos t s t ruc ture . Pa ramete rs mo re c ru-

C o p y r i g h t b y A S T M I n t l ( a ll r i g h ts r e s er v e d ); F r i M a y 9 1 1 : 4 1 : 0 0 E D T 2 0 1 4


Unive r s ida d De C hi le pur sua n t to L ic e nse Agre e m e nt . No fu r the r re produc t ions a u thor iz e d .

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ALLAEI ON EFFECTS OF NONUNIFORMITIES 5

c ia l i n the v ibra t ion re sponse of fa s t ene rs and the hos t s t ruc ture wi l l be iden t i f i ed and in -

corpora ted in the mode l .

Th e m a in cont r ibu t ions of th is w ork a re the inc lus ion o f the e f fec t o f fa s tene rs on v ibra t ion

p h e n o m e n a s u c h a s l o c i v e e r i n g / c r o s s i n g a n d m o d e l o c a l i z a ti o n / t ra n s i ti o n a n d t he a p p l i c a -

t i o n o f t h e r e c e p t a n c e m e t h o d t o t h e d y n a m i c s o f f a s t en e r s . T h e s e v i b r a ti o n p h e n o m e n a h a v e

b e e n s h o w n t o h a v e a s ig n i fi ca n t e ff e c t o n t h e p e r f o r m a n c e o f m e c h a n i c a l c o m p o n e n t s a n d

s t ructures as descr ibed in the next sec t ion.

R o l e o f F a s t en e r s i n L o c a l iz e d V i b r a t io n

T o l e ra n c e s a n d p a r a m e t e r v a ri a ti o n s c a n n o t b e r e d u c e d t o z e r o a n d t h e r ef o r e m u s t n o t b e

avoided in the des ign , ana lys i s , and cont ro l o f mechanica l component s and s t ruc tures . A

smal l i nc rease in the d imen s ions o f pa r t s, t he i r to l e rances , and the i r pa ram ete r va r i a tions can

resu l t i n s ign i f i can t accumula t ions of randomness tha t cou ld propaga te th rough ou t the sys -

t em. In the case of fa s t ene rs , no t on ly a re the i r i n i t i a l pa ramete r va r i a t ions ( such as the i r

loca t ion , type , and appl i ed load) unavoidab le , bu t a l so som e of these va r i a t ions a re func t ions

of t ime i f t he fa s t ene rs a re p l aced in a v ibra t ing envi ronment . Cos t ly fa i lu re and down- t ime

can re su l t i f t he fa s t ene r pa ram ete rs a re w i th in the i r spec i fi ca tions bu t they h ave va lues tha t

cause dras t i c changes in the dynamic re sponse of the en t i re a s sembly .

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

i za t ion / t rans i t ion [9-40] have ra i s ed many fundamenta l ques t ions . The au thors have shown

tha t des ign to l e rances and pa ramete r va r i a t ions in s t ruc tures may resu l t i n d ras t i c changes

in v ibra t ion cha rac te r i s t i c s o f s t ruc tures and may be the cause for an unpred ic t ed fa i lu re o f

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

mented in the des ign proces s and ac t ive cont ro l o f s t ruc tures a re among the i s sues tha t

re sea rche rs have begun to addres s . I t i s ve ry impor tan t tha t a fu l l unders t anding of these

phenomena ( i . e . , l oc i vee r ing /c ros s ing and mode t rans i t ion / loca l i za t ion) i s ga ined so tha t

the i r fu l l po ten t i a l fo r va r ious enginee r ing appl i ca t ions can be explored . In th i s p ro jec t , an

e f for t i s be ing m ade to addres s the abo ve i s sues in fa s t ene r -s t ruc ture sys tems . In pa r t i cu la r ,

fo r the f i r st t ime , the appl i ca t ion of these p hen om ena to fa s t ene rs i s be ing inves tiga ted .

T h i s a s to n i s h in g d y n a m i c b e h a v i o r h a s b e e n r e p o r t e d in m a n y e n g i n e e r in g p r o b l e m s . Ex -

am ples o f such pro b lem s a re f ree v ibra t ions and buc kl ing o f beams , p l a t e s and shel ls , t u rb ine

b lades and compres sor ro tors , e l ec t romagne t i c waves in waveguides , f lu id f low in nonr ig id

conduc tors , po ten t i a l curves and sur face for molecu les , r ings and t i r e s, and l a rge space s t ruc -

t u re s . Be c a u s e o f t h e w i d e s p r e a d a p p l i c at io n a n d i m p o r t a n c e o f th e p h e n o m e n a , t h e a u t h o r

be l i eves tha t the presence and seve r i ty o f these rap id and v io len t changes in the v ibra t ion

charac te ri s ti c s o f s t ruc tures need to b e ex amine d in fa s t ene r -s t ruc ture sys t ems .

I r regula r i ty in pe r iod ic and symmet r i c s t ruc tures has a l so been repor t ed a s the cause of

f requency curve c ros s ing and vee r ing and mode loca l i za t ion and t rans i t ion . Examples o f

such cases a re a symmet r i c r ings due to loca l i zed mass and s t i f fnes s nonuni formi t i e s

[14,17,18,23],

nonuni form t i re s

[23],

di f fe rences in the ind iv idua l b l ades of tu rb ine and

c o m p r e s s o r r o t o r s [22,26], and i r regular i t ies in near ly per iodic s t ructures [10,16] t ha t have

and wi l l have inc reased space appl i ca t ions . In genera l , a l l s t ruc tures can exper i ence dras t i c

changes in the i r dynam ic re sponse i f i r regu la ri t ie s a re w i th in a spec i f i ed range . S uch chan ges

in the i r dyn am ic cha rac te r i st i c s w i ll cau se e i the r rap id fa i lu re o r im pro per func t ion .

Fas tene rs o f a l l t ypes ( such as adhes ives , we lded jo in t s , an d bo l t s and nu t s ) can be a nothe r

source caus ing loca l i za t ion of the modes of v ibra t ion . To the bes t knowledge of the au thor ,

no repor t addres s ing the e f fec t o f fa s t ene rs on the mode loca l i za t ion phenomenon has ap-

C o p y r i g h t b y A S T M I n t l ( a ll r i g h ts r e s e rv e d ) ; F r i M a y 9 1 1 : 4 1 : 0 0 E D T 2 0 1 4

D o w n l o a d e d /p r i n te d b y

Unive r s ida d D e Chi le pur sua n t to L ic e nse Agre e me n t . No fu r the r re produc t ions a u thor iz e d .

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6 S T R U C T U R A L NT E GRIT Y OF F AS TE NERS

peared in the open l i t e ra ture . There i s a need to s tudy the re l a t ionsh ip be tween fas t ene r

p a r a m e t e r s a n d t h e a b o v e - m e n t i o n e d v i b r a ti o n p h e n o m e n a .

The purpose of th i s p ro jec t i s t o e s t ab l i sh the feas ib i l i t y o f u t i l i z ing and incorpora t ing

t h e s e v i b r a ti o n p h e n o m e n a i n a s y s t e m a t ic w a y i n t h e p r e d i c t io n m o d e l a n d d e s ig n p r o c e d u r e

of fa s t ene rs. Othe r g oa l s o f the prop osed re sea rch a re to inves t iga te the adv antages tha t such

d y n a m i c c h a r a c te r is ti c s m a y h a v e o n i m p r o v i n g t h e p e r f o r m a n c e o f f a s t en e r s a n d , t h e re f o re ,

o f the hos t s t ruc ture , and on be t t e r p red ic t ing the l i f e cyc les o f bo th fa s t ene rs and the hos t

structure.

Fas tene r pa ram ete rs such as to l e rances , i r regu la ri t ie s , m a te r i a l nonuni formi t i e s , l oca t ions ,

and s t a t i c /ope ra t iona l loads wi l l be s tud ied . F i r s t , t he ro le and cont r ibu t ion of such pa ram-

e te r s to the abo ve-m ent ioned d ynam ic cha rac te r i s ti c s w i l l be iden ti f ied an d c l a s s if ied . Next ,

a m e thod olog y wi l l be deve loped to in t egra te these fac tors in the s t ruc ture - fas tene r com pute r

m o d e l a n d d e s i g n p r o c e d u re .

The feas ib i li t y o f th i s con cept i s be ing es t ab l ished b y d emo ns t ra t ing a few c las si ca l cases

in the f i rs t phase o f the pro jec t. Ex tended re sea rch and the fu l l deve lop me nt o f the com pute r

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

of th i s p ro jec t w i l l r e su l t i n a more prec i se l i f e p red ic t ion and des ign of a i rc ra f t f a s t ene rs

a n d , p e r h a p s , in d e v e l o p i n g m o r e e f f e c ti v e m e t h o d s o f c o n t r o ll in g t h e d y n a m i c r e s p o n s e o f

s t ruc ture -fas t ene r sys t ems . Such adva ncem ent s in the f i e ld o f fa s t ene r mode l ing , l i f e p red ic -

t ion, and des ign wi l l increase the qual i ty of U.S . a i r , sea , an0 ground vehic les , and thus give

the Uni t ed S ta t e s a be t t e r change in g loba l compe t i t ion .

W h a t I s L o c a l i z e d V i b r a ti o n ?

Lo c a l i z a t i o n o f m o d e s o f v i b r a t i o n h a s b e e n o b s e r v e d a n d r e p o r t e d s i n c e 1 9 5 8 a n d h a s

rece ived ex tens ive a t t en tion in s t ruc tura l v ibra t ions dur ing the l a s t t en yea rs . Th e prev iou s ly

repor t ed s tud ies were co nce rned w i th the bas i c unders t anding of these a s ton i sh ing phen om -

ena , reasons for the i r occur rence in s t ruc tures , and the pa ramete rs tha t con t ro l them. The

purpose of th i s p ro jec t i s t o inves t iga te the feas ib i l i t y o f incorpora t ing these phenomena in

a pred ic t ion m ode l and des ign o f fa s t ene rs in a i rc ra f t s truc tures .

Severa l v ibra t ion cha rac te r i st i c s we re repor t ed by the au tho r and o the r re sea rche rs [9 -4 0] .

Tw o types of curves were used to p resen t the re su l t s o f such s tud ies: l oc i (o r f requency

curves ) and mode shapes . Examples o f typ ica l f requency curves a re shown in F ig . 1 . These

curves ( loc i) r epresen t the na tura l f requen c ies o f the s t ruc ture ve rsus s e l ec ted pa ram ete r ( s) .

A t ce r t a in va lues o f the pa ramete r , t he f requency curves c ros s (CC poin t shown in F ig . 1 ) .

In th i s case , t he s t ruc ture has two mode shapes a t a s ing le f requency . When two f requency

curves come c lose bu t do no t c ros s , t hey vee r away (VA) or vee r toge the r (VT) . The l a t t e r

i s know n as c urve vee r ing or loc i v

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