STRESS CONCENTRATIONS DUE TO COUNTERSUNK HOLES IN ADHESIVELY BONDED BI-LAYERED ALUMINUM SUBJECTED TO TENSILE LOADING

Transcription

1 STRESS CONCENTRATIONS DUE TO COUNTERSUNK HOLES IN ADHESIVELY BONDED BI-LAYERED ALUMINUM SUBJECTED TO TENSILE LOADING A Thesis by Bhaadwaj Veea Raghavan B.Tech, Jawahalal Nehu Technological Univesiy, 2006 Submied o he Depamen of Aeospace Engineeing and he faculy of he Gaduae School of Wichia Sae Univesiy in paial fulfillmen of he equiemens fo he degee of Mase of Science July 2011

2 Copyigh 2009 by Bhaadwaj Veea Raghavan All Righs Reseved 1

3 STRESS CONCENTRATIONS DUE TO COUNTERSUNK HOLES IN ADHESIVELY BONDED BI-LAYERED ALUMINUM SUBJECTED TO TENSILE LOADING The following faculy membes have examined he final copy of his hesis fo fom and conen, and ecommend ha i be acceped in paial fulfillmen of he equiemen fo he degee of Mase of Science wih a majo in Aeospace Engineeing. Suesh Raju Keshavanaayana, Commiee Chai Chales Yang, Commiee Membe Bob Minaie, Commiee Membe iii

4 DEDICATION To my eaches iv

5 ACKNOWLEDGEMENTS I would like o hank my gaduae adviso D. Raju fo his excellen suppo and guidance houghou my academic caie a Wichia Sae Univesiy. His consan encouagemen and moivaion has helped me owads successful compleion of my hesis. I would like o expess my gaiude o D. Chales Yang and D. Bob Minaie fo being my hesis commiee membes and hei valuable suggesion in my hesis wok. I am exemely gaeful o my paens and my sise fo hei love, encouagemen and consan suppo boh moal and financial houghou my academic caie. I would like o hank all my colleagues, and fiends a my wok place who have povided lively amosphee duing my say a WSU. Special hanks o my fiends Keehi Danu, Manoj Vama Thoakui, Ravi Kian Dukkipai and Floyd Caiado fo hei consan suppo and encouagemen houghou my sudy. v

6 ABSTRACT The adhesively bonded layeed aluminum is used in aicaf sucues o avoid knife edge siuaions when flush head fasenes ae used wih minimum gage skins. Due o he counesunk hole and adhesive bonding, sess flow becomes moe complicaed. Exensive knowledge of he diffeen paamees ha affec he behavio of he bonded joins wih counesunk holes is essenial fo dependable and effecive design. A 3-D finie elemen model was used o esimae he locaion and magniude of sess concenaion unde emoe ension fo he afoemenioned poblem. The influence of he vaious paamees on sess concenaion was invesigaed fo a coune sunk angle of 100º. Diffeen paamees such as aio of young s modulus of adhesive o aluminum, posiion of adhesive laye, counesunk sunk dephs, aio of hickness o adius and aio of widh o adius have been addessed in his sudy. The sess flow vaies significanly when he plaes ae filled wih fasenes of diffeen pe-ension loads. Also he effecs of pe-ension loading wee compaed fo he cases of open hole and fasene filled hole wihou pe-ension fo bonded, monolihic and saigh shank hole. The esuls obained fom he finie elemen analysis fo he monolihic cases have been validaed agains hose epoed in lieaue. vi

7 TABLE OF CONTENTS Chape Page 1. INTRODUCTION Backgound LITERATURE REVIEW Reseach Suvey OBJECTIVE Saemen of Poblem Appoach FINITE ELEMENT MODEL DEVELOPMENT Inoducion Finie Elemen Modeling Developmen of Model Rive Hole Configuaion Bounday Condiions Loading Codiions fo Elasic Plasic Model Maeial Model Elasic Plasic Model Elemen Fomaion Fasene Filled Holes Fomulaion of Conac Beween Plaes and Fasene Loading Condiions fo Fasene Filled Holes Load Seps Applying Pe-Tension Load Fa field Loading Model Validaion...30 vii

8 TABLE OF CONTENTS (coninued) Chape Page 5. STRESS CONCENTRATION IN OPEN HOLES Inoducion Sess Disibuion aound he Hole Effec of Counesunk Angle (2 ) Effec of Raio Young s modulus Adhesive o Aluminum Effec of Thickness o Radius / Raio on Sess Concenaion Vaiaion of Shea Sess in he Adhesive Laye Due o Raio: Effec of Adhesive Locaion on Sess Concenaion Finie Widh Effecs Effec of Counesunk Deph on Sess Concenaion Effec Residual Sesses on Concenaion STRESS CONCETRATION FACTORS IN FASTENER FILLED HOLES Inoducion Sess Disibuion aound he Fasene Filled Hole Effec of Pe Tension Loading in Saigh Shank Holes Effec of Pe Tension Loading in Counesunk Monolihic Holes Effec of Pe Tension Loading Counesunk Adhesively Bonded Holes Compaison of Pe Tension effecs CONCLUSION AND RECOMMDATIONS Conclusion Recommendaions...78 REFERENCES APPENDIX.. 81 viii

9 LIST OF TABLES Table Page Table3. 1: Selecion of Paamees Table 4. 1: Loading Conidions fo Elasic Plasic Model Table 4.2: Popeies of he Maeials used in he simulaions ix

10 LIST OF FIGURES Figue Page Figue Typical Boled Join... 1 Figue 1. 2: Flush Head fasene... 2 Figue 1. 3 :Knife Edge Siuaions... 2 Figue 1. 4 :Layeed Conucion of counesunk fasened join... 4 Figue 3. 1: Cack popagaion in monolihic plaes and meal laminaes [10]...14 Figue 4. 1: Quae symmeic model of bi-layeed plae Figue 4. 2 : Schemaic of counesunk fasene Figue 4. 3: Nomenclaue loading and configuaion of he bonded joins wih Figue 4. 4: Bounday condiions Figue 4. 5 : Sess Sain Diagam Figue 4. 6 : Gadien mesh of he plae Figue 4.7: Convegence of mesh in FE model Figue 4. 8: Pe ension suface of saigh shank fasene Figue 4. 9: Pe ension suface of counesunk shank fasene Figue 4. 10: Pe ension Node x

11 LIST OF FIGURES (coninued) Figue Page Figue 4. 11: Loading condiions of Peension fasene Figue 4. 12: Compaison wih [9] fo C s Figue 4. 13: Compaison wih [9] fo C s Figue 4. 14: Compaison wih [9] fo C s Figue 4. 15: Compaison wih [9] fo C s Figue5. 1: Disibuion of Von-mises sess aound he hole Figue 5. 2: Ou of Plane Defomaion of plae Figue 5.3: Disibuion of Sesses Y -Diecion ( ) aound he hole yy Figue 5. 4 Disibuion of Shea Sess ( xy ) aound he hole Figue 5. 5: Effec of counesunk angle on K (z) Figue 5. 6: Vaiaion Maximum Sess Concenaion wih Counesunk Angle xi

12 LIST OF FIGURES (coninued) Figue Page Figue 5. 7: Effec of E adh E al l on Sess concenaion Figue 5. 8: Vaiaion Maximum Sess Concenaion wih Young's modulus of adhesive Figue 5. 9: Compaison of bonded plaes wih monolihic plaes fo diffeen E adh E al aios.. 43 Figue 5. 10: Effec of on sess concenaion Figue 5. 11: Vaiaion Maximum Sess Concenaion wih / aio Figue 5. 12: Compaison beween Bonded and Monolihic plaes fo maximum sess concenaion...46 Figue 5. 13: Vaiaion of shea sess along cicumfeence of adhesive Figue 5. 14: Effec of adhesive posiion on sess concenaion Figue 5. 15: Vaiaion of maximum sess concenaion due o C a Figue 5. 16: Compaison beween Bonded and monolihic plaes fo diffeen C a Figue 5. 17: Effec of w on sess concenaion Figue 5. 18: Vaiaion of maximum sess concenaion due o w xii

13 LIST OF FIGURES (coninued) Figue Page Figue 5. 19: Compaison beween Monolihic and bonded plaes Figue 5. 20: Effec of counesunk deph on sess concenaion Figue 5. 21: Vaiaion of maximum sess concenaion due o counesunk deph Figue 5. 22: Compaison beween Bonded and monolihic plaes Figue 5. 23: Nomalized Von-mises vs. Sep Time Figue 5. 24: Von-Mises Sess in Adhesive laye Figue 5. 25: Effec of Residual sesses along he nodal line Figue 6. 1: Von-mises sess aound he hole 62 Figue 6. 2: Ou of Plane defomaion Figue 6. 3: Disibuion of Nomal Sess ( ) aound he hole yy Figue 6. 4: Disibuion of Shea Sess ( xy ) aound he hole Figue 6. 5: Conac Pessue Disibuion In Saigh Shank Holes Figue 6. 6: Conac Pessue Disibuion Counesunk Holes Figue 6. 7: Disibuion of Nomal sess ( ) along he X afe peension loading yy xiii

14 LIST OF FIGURES (coninued) Figue Page Figue 6. 8: Disibuion of Nomal sess ( ) along he X afe fa field loading yy Figue 6. 9: Compaison of yy wih Diffeen peension loads Figue 6. 10: Vaiaion of Nomal Sess along he Z diecion afe Pe Tension loading Figue 6. 11: Vaiaion of Nomal Sess along he Z diecion afe Fa field loading Figue 6. 12: Disibuion of Nomal sess ( ) along he X afe peension loading in yy monolihic plaes Figue 6. 13: Disibuion of Nomal sess ( ) along he X afe fa field loading in monolihic yy plaes Figue 6. 14:Compaison of σyy wih Diffeen peension loads Figue 6. 15: Vaiaion of Nomal Sess along he Z diecion afe Pe Tension loading Figue 6. 16: Vaiaion of Nomal Sess along he Z diecion afe Fa Field loading Figue 6. 17: Disibuion of Nomal sess ( ) along he X afe peension loading in bonded yy plaes Figue 6. 18: Disibuion of Nomal sess ( ) along he X afe fa field loading in bonded yy plaes xiv

15 LIST OF FIGURES (coninued) Figue Page Figue 6. 19: Compaison of yy wih Diffeen peension loads fo bonded plaes Figue Compaison of maximum nomal sess beween bonded, monolihic and saigh shank afe peension loading Figue 6. 21: Compaison of maximum nomal sess beween bonded, monolihic and saigh shank afe Fa field loading xv

16 LIST OF ABBREVATIONS E adh Young s modulus of adhesive E al Young s modulus of aluminum C s Counesunk deph Radius of he hole C a Locaion of he adhesive 2 w Widh of plae 2 h Toal heigh o plae 2 Coune sunk angle Thickness of specimen adh Thickness of adhesive o Applied emoe ension K Maximum Sess concenaion (goss) K z Shea Sess Concenaion yy (z) Hoop s sess xvi

17 LIST OF ABBREVATIONS(Coninued) z Shea sess along θ-z diecion N Numbe of Elemens acoss he Thickness P Pe ension Load X, YandZ Coodinaes xvii

18 CHAPTER 1 INTRODUCTION 1.1 Backgound Joins ae necessay in aicaf sucues o ansfe loads acoss wo o moe membes of a sucual assembly. A complex sucue can be fomed by using diffeen joining pocesses such as fasene joins (also efeeed as boled o iveed joins), welded joins and adhesive joining pocess. Fasene joins ae pefeed ove he ohe joining pocesses because of hei abiliy o ansfe high loads and also faciliae disassembly of sucue fo he puposes of inspecion and epai. The fasene joins ae widely used in ciical sucues such as aicaf wings, fuselage, udde, civil sucues ec. Many of hese mechanical joins fom vial elemens in he sucue which ae mos likely o fail. Thus, i is necessay fo he designe o ecognize he complex sess sae aising in hese joins o ensue safe opeaion of he sucues unde opeaional loads and o minimize he weigh of he sucue. A ypical fasene join is illusaed in figue 1.1. The fasene holds he wo pas (plaes, shees, subsaes, ec) ogehe beween is head and nu, while he shank passes hough he hole in he pas being joined. Figue 1.1. Typical Boled Joins [1] 1

19 Based on he ype of loading, boled joins ae classified ino wo caegoies. In ensile joins, he load acs along he axis of bol. Tension joins ae also called as peloaded o peension joins [1]. When he foces ac pependicula o he axis of he bol, hey ae called shea joins. In shea joins, he loads ae ansfeed beween he joined pas by sheaing (and bending) of he fasene. The load ansfe beween he wo (o moe) pas and he fasene occus hough beaing and in some insances ficion beween he wo pas conibues o he load ansfe pocess. Depending on he specific applicaion, diffeen fasene designs may be used. The wo pimay fasene ypes ae he pouding head and flush head fasene. Wih he pouding head fasenes, he fasene head poudes ou of he join suface as illusaed in figue 1.1. Such pousions may be undesiable in aifame sucues whee an aeodynamic suface is equied. Fo such applicaions, counesunk o flush-head fasenes ae used. Unlike he egula fasene holes, a counesink seas he head of he fasene, heeby poducing a smooh suface. Typical counesunk/flush-head fasenes ae illusaed in figue 1.2. Due o he smalle head size, hese fasenes ae used pimaily in shea loaded joins. Figue 1.2. Flush head fasene [1]. 2

20 The fasene joins suffe fom he sess concenaions aising (in he pas being joined) due o he pesence of he hole. The sess concenaions aise in he pesence of emoe (bypass loads) as well as he beaing loads acing on he hole suface [2]. Unlike he joins using pouding head fasenes whee he full hickness of he pas being joined is available fo beaing load ansfe, he joins using flush head fasenes use a facion of he pa hickness owing o he counesinking of he hole. In sucual applicaions whee he pas ae hin o begin wih, e.g., skins of aifames, he counesinking of he holes could lead o a siuaion emed as knife-edge as illusaed in figue 1.3. Due o he limied hole suface available fo beaing load ansfe, he knife-edge egions ae pone o yielding and educed faigue lives [3] due o elevaed sess levels. Figue 1.3. Knife Edge Siuaion 3

21 The knife-edge scenaio is ofen alleviaed using an adhesively bonded double which adds o he beaing aea as shown in figue 1.3. This configuaion of adhesively bonded layes is efeed o as layeed o laminaed consucion. In addiion, he double(s) could seve as an addiional load pah and could conibue o aleing he sess concenaion a he hole. o y Ø2 Ca h x A B C 2w Cs adh Figue 1.4. Layeed consucion of counesunk fasened Join The evaluaion of sess concenaion aound open-holes wih saigh shanks and counesunk holes has eceived consideable amoun of aenion in open-lieaue [4, 5]. Analyical expessions [2] based on cuve fiing of daa fom expeimens and numeical models ae available fo pedicing he sess concenaion in plain shees wih counesunk holes unde emoe loading. Howeve, he analysis and pedicion of sess concenaion in layeed / laminaed aluminum shees wih counesunk holes ae aely epoed in open-lieaue. Some faigue daa [3] has been epoed fo layeed consucion, highlighing he key diffeence in compaison o he monolihic case. In addiion o he sess concenaion aising due o emoe loads, he layeed consucion pesens added complexiy in ems of he sess disibuion acoss he layes, shea sess 4

22 concenaion in he adhesive, ec. The addiional degees of feedom associaed wih he choice of double hickness and adhesive popeies, adds o he complexiy of he poblem. In he pesen sudy, he sess concenaions in layeed shees wih counesunk holes have been analyzed using non-linea finie elemen analysis. In addiion o he vaiables associaed wih he counesink and he layeed consucion, he effecs of hole filling due o he fasene and he clamp-up loads inoduced duing fasene insallaion, on he esuling sess concenaion has been addessed. 5

23 CHAPTER 2 LITERATURE REVIEW 2.1 Reseach Suvey The ealies sudy on 3-D plain (saigh shank) holes was conduced by Senbeg and Sadowsky [6] in which hey suggesed an analyical soluion fo cylindical hole in an infinie plae of abiay hickness by using modificaion of Riz mehod in elasiciy appoach. A 3- dimensional soluion o he poblem was consideed by supeimposing plane sess soluion on he esidual plane sess. The sess disibuion in his case was found by using he pinciple of supeposiion of plane hydosaic and plane pue sheaing. The esuls obained indicaed ha as he hickness aio (which is defined as aio of hickness o adius) inceases he hoop sess along he hickness shows a dasic ise and asympoically appoaches plain sain value. The change in hoop sess due o he change in he hickness aio was negligible. Hence i can be concluded ha he sess in he diecion of hickness has significan effec on sess concenaion while es of he sess componens ae negligible. Folias and Wang [7] coninued he sudy on 3-D plain holes of abiay hickness by coveing diffeen value of adius o hickness aio. A 3-D plae of abiay hickness 2 h and adius of he hole a is subjeced o a fa field ension of o. The analysis evealed ha, sess concenaion faco vaies acoss hickness and was also a funcion of adius o hickness aio. The analysis also conveyed ha, as he Poisson s aio 0, he sess concenaion faco ends o 3. Fom his sudy hey deduced ha sess concenaion faco deceases as i appoaches he fee suface. Howeve, fo a aio of adius o hickness ha is smalle han 0.2, he vaiaion of sess concenaion is negligible along he hickness and he maximum value occus a he fee suface. The esuls indicae ha as adius o hickness aio ends o zeo, hee exiss a bounday 6

24 laye soluion close o he fee suface. I was hus concluded ha sess concenaion is due o hoop sess which depends on dimensionless paamees such as aio of hickness o adius and funcion of hickness. Howeve he abnomal behavio of sess concenaion faco fo a vey small adius o hickness aio could no be explained. Vey few papes have been published on sess concenaion in he counesunk holes [2, 8, -11]. The fis expeimenal wok was done by Whaley [8] using biefingen coaing on he suface of he plaes o esimae sess concenaion. Two diffeen ses of specimens one wih plain holes and ohe wih counesunk holes subjeced o a faigue loading a 60 cpm wih a maximum sess of 46,700 psi, and esuling lives wee compaed. This evaluaion assised in finding ou he maximum sess concenaion facos fo counesunk holes. Counesink angle of 100 and deph of half he hickness was used in pepaing he specimen wih counesunk holes. The specimens wee coaed wih ype-s phoo sess biefingen plasic. These expeimens poved ha sess concenaion in counesunk holes is highe han he plain holes. The esuls indicaed ha he sess concenaion (which was infeed fom he faigue ess) was maximum a he counesink edge and vaied along he hickness. The maximum sess concenaion fo counesunk holes was 13 o 23 pecen highe han ha of plain (cylindical) holed specimens. The maximum sess concenaion was found o be highes a he counesink edge which is 13 o 23 pecen highe han he values a he fee sufaces which was infeed fom he faigue es. Sess concenaion as funcion of he aio of hickness o adius and hickness as menioned by Folias and Wang [7] wee ignoed in his wok. Cheng [9] used a sess feezing echnique o measue sess concenaion along he hickness of he plae. A oal of 13 diffeen configuaions, by vaying counesunk angle, deph and adius of hole wee invesigaed. A phoo elasic epoxy esin was used as a model specimen 7

25 which is loaded in ension by using dead weighs and fou poin bending by using olles and dead weighs. These specimens along wih a calibaion disk wee passed hough sess feezing cycle in a empeaue conolled funace. Afe he sess feezing cycle he specimens wee halved and he maximum finge ode and hoops sess wee deemined. The esuls confimed ha sess concenaion is highes a he counesink edge when he specimen is loaded in ension. The deviaion in sess along he hickness in counesunk holes was highe han ha of saigh shank holes. Resuls indicaed ha he vaiaion of small change in counesunk angle, deph o hickness aio had no significan effec on sess concenaion. Fom hese expeimens i was obseved ha finie widh had a significan effec on sess concenaion, which was 33% highe han ha of he cylindical hole. In case of bending, i was noed ha he neual plane does no emain a mid hickness of specimen. I was also noed ha in case of bending hoops sess a he fee sufaces wee no equal. The neual plane was shifed slighly below he counesink edge owads he saigh shank poion and he maximum hoops sess occued a he fee edge of he saigh shank poion. In 1993 Young and Lee [10] conduced a paameic sudy of facos effecing sess concenaion in counesunk holes using finie elemen analysis on he 3- dimensional plae subjeced o emoe ension and povided a design equaion fo he sess concenaion. Vaious configuaions wee made by using diffeen design paamees such as hickness o diamee aio, edge disance (widh of plae), counesunk deph and angle. A quae symmeic model of geomey was used in developing a finie elemen model wih gadien mesh which was fine a he suface of he hole. The esuls indicaed ha sess concenaion was maximum a he counesink edge. When compaed wih cylindical holes, he value of sess concenaion a fee sufaces was lowe han ha of plain holes bu highe a he counesink edge. The value of sess 8

26 concenaion inceased wih incease in he hickness o diamee aio (which is also he hickness of plae as he fasene sizes ae of sandad diamees). Similaly, he sess concenaion was also found o incease linealy wih counesunk deph. Fo a small change in counesink angle fom 90 o 100, he auhos obseved ha he change of sess concenaion was negligible. Wih he incease in edge disance (widh of plae) he value of sess concenaion deceased, which is in ageemen wih he S.Venans fee edge effecs. Consideing he above paamees and nomalizing he maximum value of sess concenaion wih ha of he plain holes, i was obseved ha counesunk deph was he only independen paamee affecing elaive sess concenaion. Howeve soluions of Young and Lee wee based on a vey coase model and he equaion developed by hem did no condense o a 2-D plane sess soluion as menioned in he handbooks [4-5]. Lae, his wok was coninued by Shivakuma and Newman [11] in which hey conduced 3-dimennsional sess analysis on vaious configuaions of saigh shank and counesunk holes. Sess concenaion along he hickness was obained fo vaious configuaions such as hickness o diamee aio, counesink deph and angle fo a vey wide plae subjeced ension and bending. In case of saigh shank holes along wih ension and bending, wedge loading was also applied. In case of ension, he sess concenaion was obseved o incease linealy wih he counesunk deph and hickness o adius aio. Simila o Young and Lee s [10] model fo a small change in counesunk angle he vaiaion of maximum sess concenaion was negligible. In case of bending, he sess concenaion was almos unaffeced by counesunk angle and deph. Maximum sess concenaion in ension fo a plae wih counesunk hole was abou 37% highe han he 2-D soluion pesened in he hand books [4-5], wheeas i is 30% highe fo 3-D saigh shank holes. In case of bending, maximum sess concenaion was appoximaely same as ha of 9

27 he saigh shank plae. Based on he finie elemen esuls, a muli-paamee leas squae fis wee pefomed o obain an equaion fo sess concenaion fo ension, bending and wedge loading. By using he pinciple of supeposiion, ension and wedge loading he esuls fo pin loading in cylindical holes wee obained. A FORTRAN pogam was developed, which included an inepolaion echnique fo deemining sess concenaion fo vaious kinds of loading. The majo dawback of his wok was ha he esuls wee limied o vey wide plaes. Shivakuma e.al [2] coninued hei wok on counesunk holes in which a 3-D finie elemen analysis was pefomed on vaious configuaions of counesunk and saigh shank holes. Vaious counesunk paamees such as, widh o adius aio and hickness o adius aio wee consideed in developing an equaion fo sess concenaion faco. Simila o [10] a quae symmeic model of he geomey was modeled by using appopiae symmey bounday condiions. A emoe ension of o =1 was applied so ha he esuling sesses diecly gave he value of sess concenaion. A vey fine mesh was ceaed a he suface of he hole which gadually became coase away fom he hole. Fom he esuls obained i was concluded ha, fo a small change in counesunk angle he deviaion of maximum sess concenaion can be ignoed. The auhos obseved a monoonous incease in he value of sess concenaion wih counesunk deph and hickness o adius aio. The maximum sess concenaion fo vey hick plaes was obseved o be a he counesunk edge and fo hin plaes i was below (5% of hickness) he counesunk edge in saigh shank poion. Maximum sess concenaion was obseved o decease wih incease in widh of plae. Fo vey wide plaes he sess concenaion emains consan houghou he hickness of he plae. An equaion fo he sess concenaion as a funcion of plae hickness, counesunk deph and widh was developed by using finie elemen esuls. The developed equaion had a maximum eo of 7% when compaed wih finie elemen 10

28 esuls. Hence he equaion obained is accuae enough fo all limiing condiions including he knife edge siuaion. Lancioi and Polese [3] sudied faigue popeies of monolihic and meal laminaed aluminum open-hole (saigh shank) specimens. Thin shees of aluminum wee bonded by using an adhesive o obain he desied hickness, which wee called meal laminaed maeials. Fou diffeen kinds of specimens wee pepaed fo conducing faigue and cack popagaion ess. They ae 1. Monolihic specimens which wee dilled, eamed and de-bued. 2. Monolihic specimens which wee dilled, eamed by sacking en specimens on milling machine and wo aluminum plaes pessed agains he packing. Holes wee no de-bued. 3. Simila o he second case bu pessing is done by placing plasic foil in beween he plaes. Holes wee no de-bued. 4. Meal laminaes wih adhesive bonding used wee dilled, eamed and de-bued. The faigue ess esuls indicaed ha he monolihic specimens wih holes de-bued has a have a longe life compaed o ha of monolihic specimen in which holes wee no de-bued. Fuhe, he life of specimens which wee dilled afe placing a plasic foil wee less due o he lage disconinuiies caused by he plasic foil. Meal laminaes had bee life peiod when compaed o monolihic specimens unde low faigue loads, wheeas boh behaved similaly in case of highe faigue loads. Fo cack popagaion es, a single cone flaw was induced a he edge of hole. In meal laminaed specimens cacks nucleaed ealy bu he popagaion is slow. In monolihic specimens he nucleaion of cack was delayed bu popagaion was vey fas. Faigue cack popagaion lives of meal laminaes wee abou 5 imes highe han ha of monolihic. 11

29 Rawani [11] conduced a paameic sudy of faigue cack gowh behavio in adhesively bonded meallic sucue. The sess inensiy facos wee obained by using a finie elemen model and analyical pedicions wee compaed wih hose of expeimenal values. The finie elemen model consideed each laye as a 2-D dimensional sucue unde plain sess. Adhesive maeial was consideed as a shea sping ahe han elasic coninuum. The simulaions wee caied ou consideing he pesence ellipical de bonds wih mino o majo axis aio of 0.1. The auho concluded ha he use of bile adhesive would decease he cack gowh life of a sucue. Also as he hickness of he adhesive laye inceases, he life of he sucues was obseved o be decease. Due o adhesive bonding and counesunk hole he sess flow becomes moe complicaed. Thee hasn been any wok done on he bonded joins wih counesunk holes in open lieaue which is a pacical design used in aicaf indusy. The pesen sudy has been aken up o give an accuae idea of ensile sess concenaion in adhesively bonded joins wih counesunk holes and he popeies of adhesive affecing he sess concenaion. A compehensive 3-D finie elemen analysis wih vey fine modeling will be conduced on bonded joins wih counesunk holes. A paameic sudy includes aio of hickness o adius, Young s modulus of adhesive o aluminum, posiion of adhesive, counesunk deph o hickness and finie widh effec. The sucue is also affeced by fasene filled holes wih diffeen pe-ension loading. Based on he esuls he sess concenaion in bonded joins will be compaed wih ha of he monolihic plaes. Hence all hese paamees ae o be sudied o design of adhesively bonded join wih counesunk hole. 12

30 CHAPTER 3 OBJECTIVE 3.1 Saemen of poblem The objecive of his wok is o chaaceize he influence of facos effecing he sess concenaion aound fasene holes in adhesively bonded bi-layeed aluminum. Accoding o Lancioi and Polese [3], he cack popagaion ae in bonded aluminum is slow compaed o he monolihic aluminum. In addiion, he bonded aluminum is used o avoid he knife edge siuaions when flush head fasenes ae used wih minimum gage skins as illusaed in figue 3.1 [3]. Counesinking and adhesive bonds complicaes he sess flow and could fuhe incease he local sesses. Theefoe i is vey impoan chaaceize hese local sesses o pedic join sengh and faigue life. Figue 3.1. Cack popagaion in monolihic plaes and meal laminaes [3] 13

31 Disconinuiies inoduced o he counesunk holes changes he load pah. Addiionally, hese joins ae subjeced o vaious ses of loads such as ension, beaing and bending. An accuae sudy demands an invesigaion of sess concenaion facos bonded bi-layeed aluminum wih counesunk holes. Howeve, due o complicaed sess flow in bonded aluminum, i will be moe deimenal o he faigue behavio. Exhausive sudy on vaious paamees such as counesunk deph, hickness o adius aio, widh, maeial popeies of adhesive, locaion of adhesive and counesunk angle effecing he sess concenaion have been sudied. In addiion o hese paamees elasic plasic model fo a paicula configuaion has also been sudied o deemine effecs of esidual sesses on sess concenaion in open holes. In he pesen sudy, he sess fields and specifically sess concenaion facos in monolihic and bi-layeed aluminum shees has been sudied using finie elemen modeling. Boh saigh shank and counesunk holes will be sudied fo compaison. The effecs of he pesence of fasene and associaed clamp-up loads will also be addessed in his sudy. 3.2 Appoach A finie elemen analysis was pefomed o appoximae he posiion and magniude of sess concenaion unde ensile loading fo vaious paamees. To sudy effecs of hese paamees on sess concenaions unde ensile loading, a quae symmeic model of he geomey was modeled wih suiable bounday condiions in ABAQUS. The esuls of he model ae validaed wih he esuls epoed in efeences [2] and [6]. A non linea elasic-plasic analysis wih load incemen mehod has been sudied o find ou he effecs of esidual sesses on sess concenaion. The paamees invesigaed in his sudy ae lised in following able

32 TABLE3.1 SELECTION OF PARAMETERS Type of plae Paamees 1. Counesunk Deph 2. Young s modulus of adhesive 3. Widh o adius aio Open hole 4. Thickness o adius aio 5. Posiion of adhesive 6. Counesunk angle 7. Elasic plasic model Fasene Filled hole Wih pe-ension Saigh Shank hole Counesunk Hole A conac analysis wih beween he fasene and he plae is done o find ou effecs of filled holes on sess concenaion compaed o ha of open holes. The impoan feaue of he 3- D modeling is conac suface beween he plae and he fasene. A compaaive sudy beween he saigh shank hole and counesunk hole was also done. 15

33 CHAPTER 4 FINITE ELEMENT MODEL DEVELOPMENT 4.1 Inoducion This chape discusses in deail he 3D finie elemen model developed o pedic he sess concenaion facos aound he counesunk hole in an adhesively bonded bi-layeed aluminum fo boh open hole and fasene filled holes. The FE model was validaed fo he case of monolihic plaes using he esuls epoed in [2]. 4.2 Finie Elemen Modeling The finie elemen model was assembled using ABAQUS, a commecial finie elemen analysis sofwae.abaqus pe- and pos- pocesso has been used o geneae vaious finie elemen models and o analyze he esuls. 4.3 Developmen of Model The model fo his analysis consiss of wo componens, plaes and fasene which ae shown in he figues 4.1 and 4.2 especively. 16

34 Figue 4.1. Quae symmeic model of bi-layeed plae Figue 4.2. Schemaic of counesunk fasene 17

35 4.4 Open Hole Configuaion The configuaion of a counesunk plae of heigh 2 h and widh 2 w, wih a fasene hole is shown in figue 4.3. Le he hickness of he plae be, adius of hole shank be is assumed o be in [2] and he same adius is also used in he pesen analysis, he deph of saigh shank bec, hickness of adhesive be adh and counesunk deph bec s. A pacical counesunk angle of 100 º was used in a majoiy of he simulaions, alhough he effec of counesink angle is discussed in he pesen sudy. The effec of counesink angle was sudied by vaying he counesunk angle fom 60 o 110. The aio was found o be he main paamee in evaluaing sess fom heoeical analysis. This paamee is vaied fom 0.5,1, 2 ill 4. Commonly used cases in he aicaf indusy [3] ae fom The cases such as 0.5 o 2. The counesunk deph C s is vaied as 0.25, 0.5 and C s =0 and C s = ae ignoed as hey ae epesening he cases of saigh shank hole and knife edge siuaion. Finie widh effecs ae sudied by consideing half widh w = 3,4, 6 and15. The cases of 3 o 6 ae pacically used in aicaf indusy. In Senbeg and Sadowsky s case, he soluion was developed fo a case of infinie widh plae [6]. Accoding o S.Venans pinciple of dissipaion of localized sesses, hee will be a finie widh beyond which he sesses can be consideed o appoach ha in a case of an infinie widh plae. Fuhe, he aio of Young s modulus of adhesive o aluminum is also consideed o be key paamee fo deemining he sess concenaion in bonded joins. I is vaied fo E adh E aol =0.02, 0.05, 0.08, and 0.1. When he aio of young s modulus of adhesive inceases he siuaion ends o become a case of monolihic plae. Pacical adhesives used in he indusy esul in a aio of 0.1 o 0.2. The posiion of he adhesive is also a key paamee affecing sess 18

36 concenaion. The posiion of adhesive is vaied fo C a = 0.2, 0.4, 0.5 and 0.7. Commonly a case of 0.5 is used in aicaf indusy as ohe cases like 0.2 and 0.4 ae pacically difficul o use. The above paamees ae vaied o cay ou diffeen ses of simulaion. 19

37 σ 0 σ adh C a C s z 2α σ adh σ 0 a) y-z plane b) x-y plane Figue 4.3. Schemaic of he poblem showing he geomeic vaiables. 20

38 4.5 Bounday Condiions The figue 4.4 shows he bounday and loading condiions of he mechanical model fo bilayeed aluminum. U2=0 σ 0 U 1 =0 Figue 4.4 Bounday condiions A quae symmeic model of he geomey was modeled by applying suiable bounday condiions x-symmeic (u 1 =0) and y-symmeic (u 2 =0) in x =0 and y =0 planes especively. The sudy was conduced fo an aveage fa field sess of o =1000 psi. To obain unifom sains in boh adhesive and plae, he sess in aluminum and adhesive laye ae popoional o hei Young s modulii. Howeve, he aveage sess is sill 1000 psi. 21

39 4.5.1 Loading Condiions fo Elasic-Plasic Model The invesigaion was conduced fo o =10, 15, 20 and 25 ksi and sess along he nodal line A-B-C wee aken which gave he sess concenaion K (z). A consan counesink angle of 100º was used in all simulaions. The hickness of adhesive was mainained consan fo all simulaion as adh =0.005in. A nonlinea elasic-plasic analysis was conduced by load incemenal mehod fo calculaing esidual sesses. Fo calculaing he esidual sesses ampliude of he load is defined as shown in he Table 4.1. TABLE4.1: LOADING CONDITIONS FOR ELASTIC -PLASTIC MODEL Toal Time Seps Load faco The configuaion of he model used fo he elasic-plasic analysis was C s =0.5, C a =0.5, E adh E aol =0.05, =0.5, w =15 and h =15. 22

40 4.6 Maeial Model Fo he open hole simulaions, boh he plae and adhesive ae assumed o be linea elasic. The maeial is assumed is o be isoopic Hookean which can be used in combinaion wih diffeen kinds of elemens. The sess-sain cuve of he elasic model is epesened by Hooke s law as shown in equaion 4.1. E (4.1) 0.2 Figue 4.5. Sess Sain diagam Whee σ epesens he uniaxial sess and he epesens he sain induced due o he applied sess. The plaes ae assumed o have popeies of Al-2024-T3 which is used in aicaf indusy. The adhesive is also assumed o be isoopic-hookean maeial. To invesigae he effecs of young s modulus of adhesive on sess concenaion, i is assumed o be vaying paamee. 23

41 4.6.1 Elasic Plasic model The maeial behavio in assumed o be linealy elasic unil i eaches he yield sess σ y. When he applied sess eaches beyond he yield sess, maeial expeiences wok hadening, which in un esuls in boh elasic and plasic defomaion. The maeial is assumed o have popeies of Al 2024-T3 and undego isoopic hadening. The Table 4.2 liss all he popeies of he maeial used in his pesen sudy. TABLE4. 2 PROPERTIES OF THE MATERIALS USED IN THE SIMULATIONS [13] Maeial Popeies Elasic Modulus msi Aluminum(Al ) (Boh Plaes and fasene) Poisson s aio=0.3 Yield Sess -50 ksi wih 0% Elongaion Yield Sess -65 ksi Wih 15 % Elongaion Adhesive Elasic Modulus vaying paamee Poisson s Raio -0.3[3] 4.7 Elemen Fomaion Diffeen meshing echniques wee applied o mesh he plaes and adhesive used in he simulaions. The figue 4.6 shows he ypical finie elemen mesh of he componens used in he analysis. The geomey of plaes has been paiioned ino wo halves so ha he desied mesh is obained. Gadien mesh was used becuase he sess a he hole face is anicipaed o be highes, a fine mesh is ceaed a he hole face (o accuaely deemine he local sesses) which 24

42 pogessively becomes coase away fom he hole. An 8- node hexahedon elemen (in ABAQUS C3D8R) wih educed inegaion and houglass conol was used in he simulaion fo boh he plae and adhesive maeial. Linea geomeic ode of he elemen was used fo boh plae and adhesive in all simulaions. Figue 4.6. Gadien mesh of he plae 25

43 K(max) The es of convegence was caied ou on one of he models wih fine uning of mesh and numbe of elemens acoss he hickness (N) and nea hole was done o ensue if he soluion will convege as shown in figue 4.7. Based on his convegence sudy 50 elemens wee used acoss he hickness fo he simulaion as he cuve sas conveging fom ha poin Cs/=0.5,Ca/=0.5 Eadh/Eal=0.1,w/=15 Bonded Numbe of elemens along he hickness Figue 4.7. Convegence of soluion wih diffeen mesh size 4.8 Fasene Filled Holes A non linea conac analysis beween he plaes (wih boh cicula, counesunk hole) and fasene, o find ou he effecs of pe-ension on sess concenaion by vaying he maximum pe-ension load. The configuaion of he model used fo saigh shank hole used is =0.5, w =15, h =15, =0.077 in. The configuaion of he model used fo he counesunk holes was C s =0.5, C a =0.5, E adh E aol =0.05, =0.5, w =15 and h =15. 26

44 4.8.1 Definiion of Conac beween Plae and Fasene A geneal suface-o-suface conac ineacion [12] is made beween he plae and fasene. The conac suface connecing he plae and fasene is chosen as ficionless sliding ineface. The funcion of his conac ineacion is o avoid peneaion of elemens of boh componens. Ficionless conac is chosen o simplify he poblem, on he sess concenaion. Newon s ieaive echnique along wih adapive sabilizaion [12] is used fo solving his poblem Loading condiions fo Fasene filled holes The pe-ension secion will allow he conacing sufaces o inefee wih each ohe, i.e., he op and boom half of he bol may ovelap wihou a conac being deeced. If hee ae no shees beween he bol head and he nu, he wo halves of he bol simply ovelap each ohe wihou any pe-ension being geneaed as shown in he figue 4.8 and 4.9. Howeve, when a shee is pesen beween he head and nu, i will ge squeezed and esis he ovelapping of he wo pas of he bol and hus geneae he pe-ension. This pe-ension-load may be locked by fixing he conol node displacemen shown in figue Load Seps The invesigaion was conduced fo vaious pe-ension loads 50,100,150,200 lbs in he fasene and fa field ension of o = 1000 psi in plaes as shown in he figue Apply Pe-ension Load Pe-ension load is applied on he fasene in he fis sep of analysis which has auomaic sabilizaion fo aaining load equilibium on an inenal bol suface. In his sep he fa field ension in he plaes is zeo. 27

45 Pe Tension Suface Figue 4.8. Pe-ension suface of saigh shank fasene Pe Tension Suface Figue 4.9. Pe-ension suface of counesunk shank fasene 28

46 Pe Tension Node Figue Pe-ension Node Figue Loading condiions of Pe-ension fasene 29

47 Fa field Loading The sep 2 sas afe he sep 1 is compleed. In his sep, he bol defomaion is fixed a he value which is obained a he end of fis sep. The ovelap beween he head and nu is fixed. Howeve he lengh of he bol can change. 4.9 Model Validaion A deailed evaluaion of pesen finie elemen model wih available daa was done o validae he accuacy of model. The numbe elemens used acoss he hickness wee 50. The finie elemen model developed in his sudy has been validaed by compaing he esuls of finie elemen model esuls epoed in [2] and [6]. A monolihic plae was modeled wih same configuaion as in [6] and analyzed wih he same bounday condiions. The vaiaion of sess concenaion wih he hickness pe ef [6] was also sudied in he analysis. The configuaion of model used fo validaion was = 0.5. w =15 and h =15 and he hole adius is 0.077in.The esuls summaized ae shown in figues 4.12 o

48 Figue Compaison wih [2] fo C s =1 Figue Compaison wih [2] fo C s =

49 Figue Compaison wih [2] fo C s =0.5 Figue Compaison wih [2] fo 32 C s =0.75

50 The maginal diffeences beween he esuls of pesen simulaion in compaison wih [2] ae due o he diffeen mesh used. Fom he Figues i is also eviden ha he sess concenaion vaies along he hickness as suggesed by [6]. The diffeences noiced among hese wo appoaches ae aibued o he numeical eos associaed wih finie elemen analysis. 33

51 CHAPTER 5 STRESS CONCETRATION FACTORS IN PLATES WITH OPEN HOLE 5.1 Inoducion This chape gives a deailed oveview of he sess fields compued using finie elemen model fo open counesunk holes. FE analysis has been conduced fo a vaiey of configuaions E by vaying he aio of Young s modulus of adhesive o aluminum ( 2, posiion of adhesive bondline ( C a ), aio of C s, aio of hickness o adius ( adh E al ), counesunk angle ) and aio of widh o adius ( w ). In all he simulaions he disance of he loading edge fom he hole has been fixed such ha h =15. A consan adhesive hickness of 0.005inches was used fo all analyses. 5.2 Coodinae sysem and Sess Disibuion aound he Hole In he counesunk hole, hee ae hee egions whee he sess gadien is high nea he wo fee sufaces and a he counesink edge. Fom [7] i is obseved ha he sess concenaion vaies along he hickness fo 3-D configuaions. The disibuion of von-mises sess aound he hole suface and along he hickness diecions is shown in he figue 5.1. I indicaes ha he highes sess gadien is locaed a he counesunk edge. The counesunk holes make he poblem asymmeical abou he hickness which esuls in a sess disibuion ha is asymmeical acoss he hickness, esuling in ou-of-plane displacemen/bending as shown in figue 5.2. The disibuion of ( ) he along Y -diecion and shea sess τ θz componen developed in he egion of he hole ae shown in he figues 5.3 and 5.4. yy 34

52 Figue 5.1. Disibuion of von-mises sess aound he hole Figue 5.2. Ou of Plane Defomaion of plae 35

53 Figue 5.3. Disibuion of Sess in Y -Diecion ( ) aound he hole yy Figue 5.4. Disibuion of Shea Sess (τ θz ) aound he hole 36

54 5.3 Effec of Counesunk Angle (2 ) The effec of counesunk angle on he sess concenaion aound he hole in his wok is sudied by aleing he half counesunk angle fo quae symmeic model. In his sudy, he counesunk angle is vaied fom 60º o 110º o deemine he effecs of counesunk angle on sess concenaion. Vaiaion of K was found o be elaively negligible wih he small change in counesunk angle ove he ange of angles invesigaed. This was confimed by vaying he counesunk angle fo wo diffeen configuaions of 1 and 0.5, while keeping he ohe paamees h w 15 E, adh 0. 1, C 0. 5 E s and C a 0. 5 and =0.077 in consan fo boh configuaions. al The sess concenaion faco K (z) inceases monoonically wih incease in he value of 2 as shown in figues 5.5a and 5.5b. The eason fo monoonic incease is due o unineuped channeling of load pah in he egion of he counesink edge. Maximum value of K is obseved a counesink edge and i deceases owads he maeial sufaces whee he sess concenaion is lowe. Decease of K in counesunk poion (B-C) is much fase han ha of he saigh shank poion (A-B). The minimum sess concenaion is found a counesunk fee suface (C). The change in maximum sess concenaion fo change in α fom 90º o 100º and 100º o 110º is abou 1.6%, which is shown in Figue 5.6. Hence he vaiaion of K is negligible fo small change in counesunk angle. A consan counesunk angle of 100º is used in all following simulaions because i is commonly used in aicaf indusy. The vaiaion in he value of K fo monolihic plaes is slighly lowe han ha of Sivakuma and Newman [11]. The esuls ae in ageemen wih he esuls fom [11], bu ae 37

55 opposie o he end obained by Young and Lee s model [10]. This may be due o he use of coase mesh by Young and Lee [10]. Figue 5.5 (a). Effec of counesunk angle on K (z) Figue 5.5 (b). Effec of counesunk angle on K (z) 38

56 K(max) /= /= Counesunk angle Figue 5.6. Vaiaion of Maximum Sess Concenaion wih Counesunk Angle 5.4. Effec of Raio of Young s modulus of he adhesive o aluminum The effec of Young s modulus of adhesive on he sess concenaion aound he hole in his wok is sudied by aleing he aio of Young s modulus of he adhesive o aluminum (popeies ae shown in Table 4.2). Simulaions wee caied ou fo modulus aios of 0.02, 0.05, 0.08 and 0.1 fo a fixed geomeic configuaion of C s 0. 5, C a 0. 5, 1 and w 15. The hickness of he adhesive was mainained consan a in. The esuls fom he analysis ae pesened in he figues 5.7 and 5.8. Thee is a diffeence of 2.4% in he m ax i m u m sess concenaion when E adh E al 0.02 is E compaed wih adh E The diffeence deceases o less han 1% when adh E E al al is E compaed wih adh The value of K (z) E is obseved o be monoonically deceasing al 39

57 wih inceasing aio of E adh E al. As he Young s modulus of adhesive inceases, he siuaion ends owads monolihic case. The compaaive sudy is shown in he figue 5.9. Fo a aio of E adh E al 0.07, he value of K is nealy he same as ha of monolihic plaes. Fo smalle aios E of adh E al he value of K is highe in case of bonded plaes compaed o ha of E monolihic plaes, wheeas fo highe aios of adh 0. 07, i is less han ha of he E monolihic plae. The eason fo highe vaiaion in al K is due o disconinuiy in he load pah because of bonding. Wih highe Young s modulus, hee is a educion in sess value. One can expec ha he sess aound he hole o be educed when siffe adhesives ae used. Based on hese esuls i may be concluded ha K in adhesively bonded plaes is highe han hei monolihic counepas, and is a funcion of he aio of Young s modulus of adhesive o aluminum (shee). 40

58 K (z) Eadh/Eal=0.1 Eadh/Eal=0.02 Eadh/Eal=0.05 Eadh/Eal= z/ Figue 5.7. Effec of E adh E al on sess concenaion K E adh /E al Figue 5.8. Vaiaion Maximum Sess Concenaion wih Young's modulus of adhesive. 41

59 Bondedplaes Monolihic[8] 3.8 K E adh /E al Figue 5.9. Compaison of sess concenaions bonded plaes wih monolihic plaes fo diffeen E adh aios. E 5.5. Effec of Thickness o Radius Raio on Sess Concenaion al The effec of shee hickness o adius aio on he sess concenaion aound he hole in his wok is sudied by vaying he hickness of he plaes, while holding he hole adius a in. In his sudy, he hickness of he plaes is vaied fom 0.5 o 4 o deemine he effecs of hickness o adius aio on sess concenaion. Values of = 0.5, 1 and 2 epesen he pacical ange of holes used in aicaf indusy and > 2 is used fo hick plaes. The vaiaion coves fom hin plaes o hick plaes. Simulaions wee caied ou fo diffeen hickness aio = 0.5, 1, 2 and 4, fo fixed values of E adh E al = 0.1, C s = 0.5, C a = 0.5 and w = 15. The hickness of he adhesive bondline was mainained consan a in. The vaiaion of K (z) wih he hickness o adius aio is shown in figue Wih 42

60 incease in aio he value of K inceases monoonically. Fo smalle aios 1, he value of K is obseved o be a he counesink edge. A he counesunk edge he K value appeas o have a maximum value of 3.47 fo he case of A simila end was obseved in saigh shank holes in [7]. Thee is diffeence of 1 6% in he maximum sess concenaion beween 4 and 0. 5 is shown in figue These esuls ae in ageemen wih he end epoed by Senbeg and Sadowsky [6]. A compaison beween monolihic and bonded plaes is shown in figue The sess concenaion in case of bonded plaes is lowe han monolihic plaes fo highe adhesive modulus. The diffeence beween maximum sess concenaions fo hinne plaes 0.5 is abou less han 1% wheeas he diffeence beween maximum sess concenaions fo hicke plaes is aound 4% when compaed wih monolihic. This implies ha fo hin plaes sess concenaion does no vay much beween he bonded o monolihic plaes. 43

61 Figue 5.1. Effec of / on sess concenaion K / Figue 5.2. Vaiaion Maximum Sess Concenaion wih / aio 44

62 K Bonded Plaes Monolihic [8] / Figue 5.3. Compaison beween Bonded and Monolihic plaes fo maximum sess concenaion E fo adh C =0.1 and s = 0.5 E al Vaiaion of Shea Sess in he Adhesive Laye Due o Raio The shea sess z inceases wih an incease in value of as shown in figue Values of z a x along he cicumfeence (i.e. fom = 0 o 90 ) of mid hickness of he adhesive laye wee obained fom finie elemen esuls. As shown in figue 5.13, he shea sess z along he cicumfeence of adhesive was found o be minimum a x and y and i is maximum a an angle of 45º fom x 0. The shea sess z is an impoan faco in invesigaion of sess concenaion facos in laminaed plaes. The cack iniiaion in he bonded plaes is due o he de-bonding a he ineface of adhesive and plaes whee he maximum sess concenaion occus [3]. The eason fo ealie cack iniiaion in [3] is aibued o shea sess z which is absen in he monolihic 45

63 plaes. Alhough he cack iniiaes ealie, due o he bonding beween he plaes, he cack akes a longe ime o popagae. The diffeence beween maximum shea sess fo hinne plaes 0.5 is abou less han 90% compaed o ha of he hicke plaes 4. This is shown in figue This huge vaiaion suggess ha cack iniiaion a bond line beween adhesive and aluminum is ealie in hicke plaes compaed o ha of hinne plaes σ θz /=0.5 /=1 /=2 /=4 E adh /E al =0.1,C s /=0.5 C a /=0.5,w/=15 θ Figue 5.4. Vaiaion of shea sess along cicumfeence of adhesive 46

64 5.6 Effec of Bondline Locaion on Sess Concenaion The effec of adhesive locaion on he sess concenaion aound he hole has been sudied by vaying he l o c a i o n of he adhesive. In his sudy, he locaion of he adhesive is vaied fom 0.2 o 0.8, o deemine he effecs of he adhesive locaion on sess concenaion. Simulaions wee caied ou fo diffeen aios of C a 0.2, 0.5, 0.7 and 0.8 fo a fixed configuaion of C s 0.5, E adh E al 0.5 and w 15 and hickness of he adhesive 0.1, was mainained consan a in. The vaiaion of K (z) acoss he hickness is shown in figue The sess concenaion value is highes a he counesink edge fo all Ca values. Thee is a diffeence of 4 % in he maximum sess concenaion beween C a 0.5 and C a 0.2 is shown in figue The diffeence in he maximum sess concenaion fo small vaiaion of C a fom 0.8 o 0.7 is less han 1%. The sess concenaion value inceases in he saigh shank poion and is highes a he counesink edge. The sess concenaion deceases apidly in he counesink egion. When he adhesive laye is locaed in he counesunk secion away fom he counesunk edge, he value of K is obseved o be lowes. The value of adhesive laye is posiioned nex o he coune sunk edge. K is highes when he A compaison beween monolihic and bonded plaes fo diffeen posiion of adhesives is shown in figue The sess concenaion is highes when he adhesive is posiioned nex o he counesink edge in saigh shank poion. The eason fo maximum value of K a his locaion is due o disconinuiy of load pah a he counesink edge due o he adhesive. 47

65 K(z) Ca/=0.8 Ca/=0.6 Ca/=0.5 Ca/=0.2 Monolihic Cs/=0.5 Eadh/Eal=0.05 /=0.5 w/= Figue 5.5. Effec of adhesive posiion on sess concenaion z/ K C a / Figue 5.6. Vaiaion of maximum sess concenaion due o C a 48

66 K Bonded Monolihic[8] C a / Figue 5.7. Compaison beween Bonded and monolihic plaes fo diffeen C a 5.7 Finie Widh Effecs The effec of widh o adius aio on he sess concenaion aound he hole in his wok is sudied by vaying he widh of he plaes. In his sudy, he widh of he plaes was vaied fom 3 o 15 o deemine he effecs of widh o adius aio on sess concenaion. Values of w 3, 4, 6 and 15 epesen he diffeen widh of plaes coveed in his sudy. The case of w 3 epesens he classical case of sess concenaion in saigh shank holes. Similaly he case of w 15 epesens he infinie widh poblem. Simulaions wee caied ou fo diffeen modulus aio w 3, 4, 6 and 15 fo diffeen configuaions 0.5 and 1 wih paamees emaining consan E adh E al C 0.1, s C 0.5 and a 0.5. The hickness of he adhesive was mainained consan a in. 49

67 The vaiaion of K (z) wih w aio is shown in figue The K (z) value deceases monoonically wih an incease in he widh of he plae. These esuls wee in concuence wih he expeimenal esuls of [6]. The maximum K occus a he cenal egion and declines owads he fee suface. The fee edge phenomenon, which is a esul of he non-zeo Poisson s aio has been explained by [6]. The value of K (z) is highes in he saigh poion slighly below he counesunk edge. The ae of incease in K deceases as w aio inceases above 5. Thee is diffeence of 17% in he maximum sess concenaion beween w 3 and w 15 is shown in figue The diffeence in he maximum sess concenaion fo he vaiaion of fom 6 o 15 is less han 3%. A compaison beween monolihic and bonded plaes is shown in figue The sess concenaion in case of bonded plaes is lowe han monolihic plaes. The diffeence in he maximum sess concenaion fo bonded and monolihic is 5%. Disconinuiy due o bonding is he eason fo he diffeence in he value of K beween monolihic and bonded specimens. w 50

68 Figue 5.8. Effec of w/ on sess concenaion K w/ Figue 5.9. Vaiaion of maximum sess concenaion due o w/ 51

69 K Bonded Monolihic[8] w/ Figue Compaison beween Monolihic and bonded plaes 5.8 Effec of Counesunk Deph on Sess Concenaion The effec of counesunk deph on he sess concenaion aound he hole was sudied by vaying he counesunk deph. In his sudy, he counesunk deph vaied fom 0.25 o 1 o deemine he effecs of counesunk deph on sess concenaion. The counesunk deph of zeo is a case of saigh shank hole wheeas he counesunk deph of 1 epesens he knife edge siuaion. This vaiaion coves hin doubles o hick doubles. Simulaions wee caied ou fo diffeen aios of C s 0.25, 0.5, 0.75 and 1 fo wo diffeen configuaions of 1 and 0.5 wih ohe paamees E adh E al C 0.1, a 0.5 and w 15 held consan. The hickness of he adhesive was mainained consan a in. The vaiaion of K (z) along z fo vaying counesunk dephs is shown in figue Fo hinne plaes maximum sess concenaion occus a he counesunk edge and as hickness 52

70 inceases, maximum sess concenaion is slighly away fom he counesunk edge in saigh shank poion. The value ofk inceases monoonically wih incease in C s. The knife-edge siuaion is also shown in figue The end was also noed by [2]. Thee is a diffeence of 14% in he maximum sess concenaion beween C s = 3 and C s = 15 is shown in figue The diffeence in he maximum sess concenaion fo vaiaion of C s fom 6 o 15 is less han 3%. Thee is a diffeence of 22% in maximum sess concenaion of knife edge siuaion and saigh hole classical poblem K 3 and 17% fo poblem saigh shank hole wih finie hickness. Thee is a significan diffeence in he value of K beween monolihic and bonded plaes as shown in Figue The sess concenaion in case of bonded plaes is lowe han monolihic plaes. The diffeence in he maximum sess concenaion fo bonded and monolihic is 3.5% 53

71 K (z) Cs/=1 Cs/=0.75 Cs/=0.5 Cs/=0.25 S Shank Hole z/ Figue Effec of counesunk deph on sess concenaion K C s / Figue Vaiaion of maximum sess concenaion due o counesunk deph 54

72 K Bonded Monolihic[8] C S / Figue Compaison beween Bonded and monolihic plaes 5.9 Effec Residual Sesses on Sess Concenaion A nonlinea elasic-plasic analysis was conduced by load incemenal mehod o sudy he effecs of esidual sesses on he sess concenaion aound he hole. In his sudy, he maximum emoe sess was vaied fom 10 o 25 ksi o deemine he effecs of esidual sesses on sess concenaion. The loading condiions and maeial model ae shown in Tables 4.1 and 4.2. Simulaions wee caied ou fo diffeen emoe sess levels, o 10, 15, 20 and 25 fo a paicula configuaion of 0.5, E adh E al 0.05, C a = 0.5, C s = 0.5 and w = 15. Nomalized von-mises sess is ploed agains he oal ime fo all load cases. Fom he figue 5.23 i is eviden ha nomalized von-mises is maximum fo max 10ksi. As he load eaches he maximum value duing he analysis, von-mises sess also eaches he maximum value hen i sas deceasing he as he load is deceasing. The plaes will be wihin he elasic egion when subjeced o a load of 10ksi. Theefoe he esidual sesses in such plaes ae almos zeo. Wheeas, he plaes ae subjeced o loads such as 15ksi, 20ksi and 25ksi will go beyond he 55

73 elasic egion ino he plasic egion. In his case, he compessive esidual sesses ae developed. Theefoe, von-mises sess inceases duing he las seps of analysis. von-mises sess in adhesive laye inceases wih an incease in maximum load which is shown in figue Fo he cases, 10ksi and 15 ksi von-mises sess is almos zeo a end of las sep, wheeas fo he 20ksi and 25ksi some esidual sesses wee developed. This is due o he incease in he esidual compessive sess developed in he plaes wih he incease in he load. The nomalized value of yy is ploed agains he aio z which is shown in he figue The value of yy almos emains consan in saigh shank and i is maximum in counesunk egion (appoximaely 10% of hickness away fom counesunk edge). Similaly fo he cases of max = 10 ksi and 15 ksi, he plaes ae wihin he elasic egion and fo max = 20 ksi and 25 ksi compessive sesses ae developed. Fom he esuls i is eviden ha he lage plasic defomaion occus along he nodal line A-B-C. Due o he sess concenaion, he sesses incease appoximaely 3.5 imes he applied maximum load which causes a lage plasic defomaion in he plaes. When he maximum load is inceased he esidual sesses developed also inceases. Fo he maximum load of 10ksi he plaes ae sessed wihin he elasic egion since he maximum sess developed is less han he yield sess. 56

74 4 3.5 C s /=0.5,/=0.5, E adh /E al =0.05C a /=0.5 3 σ vonmises /σ max ksi 15 ksi 20 ksi 25 ksi Sep TIme Figue Nomalized von-mises vs. Sep Time ksi σ vonmises ksi 20 ksi 25 ksi Sep ime Figue von-mises Sess in Adhesive laye 57

75 σ yy /σ max ksi 15 ksi 20 ksi 25 ksi Figue Effec of Residual sesses along he nodal line 58

76 CHAPTER 6 STRESS CONCETRATION FACTORS IN FASTENER FILLED HOLE 6.1 Inoducion In his chape, a deailed oveview of he sess fields compued using finie elemen model fo fasene filled counesunk holes is pesened. The invesigaion was conduced fo peension loads of 50, 100, 150 and 200 lbs in he fasene and fa-field ension of 1000 psi in plaes. A non-linea conac analysis was pefomed in wo diffeen seps wih he fis sep of applying pe-ension load and second sep applying he fa-field load as descibed peviously in chape 4 (see figue 4.10). A compaaive sudy beween he saigh shank, monolihic counesunk and bonded counesunk plaes was conduced. Also, he esuls wee compaed wih he case of open hole and fasene filled hole wihou pe-ension. 6.2 Sess Disibuion aound he Fasene Filled Hole The von-mises sess as developed in he egion of he hole is shown in he figue 6.1. The ou of plane defomaion of he plaes wih fasene is shown in figue 6.2, when boh he pe-ension and fa-field load ae applied. The disibuion of he nomal sess along Y-diecion yy componen is shown in he Figue 6.3. Shea sess componen developed aound he hole ae shown in he Figue 6.4. As shown in he figue, he sesses in he egion of hole ae high, which evenually lead o commencemen of failue. The pe-ension load poduces compessive sess in ou-of-plane diecion in he plae. The angenial sesses developed in he viciniy of hole ae compessive in naue boh afe peload and fa-field load. This is because of he Poisson s effec, due o which o 59

77 maeial aound he hole (away fom he clamp-up egion) esiss he expansion in he adial diecion. The conac pessue is developed due o pe-ension and conac beween he fasene and plae. The pe-ension loads ae applied in he fasene as shown in figues 4.7 and 4.8. Due o naue of he pe-ension loading, he fasene elongaes in axial diecion because of which he flanges of he fasene exe compessive foces on plaes. Conac pessue is vey high neae o he fee sufaces in saigh shank holes, wheeas conac pessue in he case of counesunk holes is seen in he counesunk egion and no a he fee suface z 1. This is shown in figues 6.5 and

78 Figue 6.1. von-mises sess aound he hole (psi) Figue 6.2. Ou of Plane defomaion (in) 61

79 Figue 6.3. Disibuion of Nomal Sess ( ) aound he hole (psi) yy Figue 6.4. Disibuion of Shea Sess ( ) aound he hole (psi) xy 62

80 Figue 6.5. Conac Pessue Disibuion In Saigh Shank Holes (psi) Figue 6.6. Conac Pessue Disibuion Counesunk Holes (psi) 63