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THIS OCUMENT S ES T QUALITY AVAILABLE. HE COPY FURNISHED TO DTIC CONTAINED

A IGNIFICANT UMBER F

PAGES HICH O OT REPRODUCE LEGIBLY.

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1 . eport N o. NASA R-14 4899

2. overnment Accession o. 3. ecipient's Catalog o.

4. Title nd ubtitle

BOLTED O I N T S IN RAPHITE-EPOXY OMPOSITES

5. eport Date JUNE 1976

6. erforming Organization Code

7. uthor(s)

L. J. Hart-Smith

8. erforming Organization Report No.

10. Work Unit o. 9. erforming Organization Name nd ddress

Douglas Aircraft Company, McDonnell Douglas Corporation, 3855 Lakewood Blvd, Long Beach, California 90846.

1 1 . Contract or Grant o.

NAS1-13172

12. ponsoring Agency am e nd Address

ational Aeronautics and Space Administration,

Washington, D.C. 20546.

13 . ype of Report nd Period Covered Contractor Report

14. ponsoring Agency ode

15. upplementary otes

1 6 . A b s t r a c t Experimental data generated during a comprehensive investigation of bolted joints in

graphite-epoxy composites ar e presented By interpreting these an d other data, methods ar e provided

f or th e analysis an d design of such joints . (The specimens tested incorporated quasi-isotropic an d

tw o near-quasi-isotropic patterns of th e 0, TT/4, T/ 2 0 , 45, 90) family. Both all-graphite/

epoxy laminates an d hybrid graphite-glass/epoxy laminates were tested.J The tests encompassed a

range of geometries for each laminate pattern to cover th e three basic failure modes net section

tension failure through th e bolt hole, bearing an d shearout . Static tensile an d compressive loads

were applied.

constant bolt

diameter of

6.35 mm (0 .25

in. )

was used

in th e

tests. LThe inter- action of stress concentrations associated with multi-row bolted joints was investigated experi-

mentally by test ing single- and double-row bolted joints and open-hole specimens in tension. Fo r

tension loading, linear interaction was found to exist between th e bearing stress reacted at a given

bolt hole an d th e remaining tension stress running by that hole to be reacted elsewhere. The inter-

action under compressive loading wa s found to be non-linear.J Most of th e joints tested were of

double-lap configuration using regular hexagon-head bolts.^Comparitive tests were run using single

la p bolted joints an d double-lap joints with pin connections (nei ther bolt head nor nut) an d both o

these joint types exhibited lower strengths than were demonstrated by th e corresponding double-lap

joints . The new empirical analysis methods developed here f or single-bolt joints are shown to be

capable of predicting th e behavior of multi-row joints./ The formulation permits further effec t s

(such as different bolt sizes an d environments) to be accounted f or as data become available

1 7 . Ke y Words ( S u g g e s t e d by A u t h o r ( s ) ) Bolted Joints Graphite-Epoxy Composites Stress Concentrations Experimental Results Empirical Analyses

18. Distribution tatement

Unclassified unlimited.

19. ecurity lassif. of this report)

Unclassified

20. ecurity Classif. (of his age)

Unclassified

21. o. f ages

155 22. Price

: For sale by the National Technical nformation Service, Springfield, Virginia 2151

vsA-r.ifi

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FOREWARD

This report wa s prepared by th e Douglas Aircraft Company, McDonnell Doug-

la s Corporation, Long Beach, California under th e terms of Contract NAS1-13172,

Th e test specimens were fabricated at Douglas an d tested at Langley Research Center. Th e program wa s sponsored by th e National Aeronautics an d Space Admin-

istration's Langley Research Center, Hampton, Virginia. Mr. M. B . Dow wa s th e

Contracting Agency's Technical Monitor.

XI i

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CONTENTS

Page

SUMMARY 1

INTRODUCTION

2

SYMBOLS 3

EXPERIMENTAL INVESTIGATION 4

TEST SPECIMENS

Materials

Laminate Pattern Selection

Fabrication Procedures

Configurations

Test Procedures

Failure Modes for Bolted Joints in Composites

TEST RESULTS AND DISCUSSION

DATA INTERPRETATION AND ANALYSIS ,10

BASIC LAMINATE STRENGTHS 1 1

ELASTIC ISOTROPIC STRESS CONCENTRATION FACTORS 1 2 a . oaded Bolt Holes

b . Open Holes

STRESS CONCENTRATION FACTORS FO R COMPOSITES 1 6

a . Loaded Bolt Holes

b . Open Holes

SHEAROUT STRESS CONTOURS 2 2

BEARING STRESS CONTOURS 2 4

COMPRESSION BEARING 26

STRENGTH OF SINGLE-HOLE ( R O W ) BOLTED JOINTS 2 7

STRESS CONCENTRATION INTERACTION (MULTI-ROW BOLTED JOINTS) 2 9

DIFFERENCES BETWEEN PROTRUDING HEAD FASTENERS AND PIN CONNECTIONS 34

COMPARISON BETWEEN SINGLE-LAP AND DOUBLE-LAP JOINTS 35

CONCLUDING REMARKS

REFERENCES

TABLES

ILLUSTRATIONS

99

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TABLES

Table Page

I

aminate Patterns an d Layup Sequences Al

HA IIB * HIA IIIB ensxon-Through-the-Hole Specimens, IV A & IVB All-Graphite Fibers, Epoxy Resin 42-47

VA & VB Tension-Through-the-Hole Specimens, VIA & VIB S-Glass Longitudinal Plies, Graphite Cross Plies, . 48-53 VIIA & VIIB Epoxy Resin

VII L A & VIIIB earin g and Shearout Specimens, Tensile Loading),

All-Graphite Fibers, Epoxy Resin

5Zj- 55

Bearing an d Shearout Specimens, (Tensile Loading), IX A & IX B S-Glass Longitudinal Plies, Graphite Cross Plies, 56-57

Epoxy Resin

X A & XE Bearing an d Shearout Specimens, Compressive Loading), All-Graphite Fibers, Epoxy Resin

58 ~ - 9

Bearing an d Shearout Specimens, Compressive Loading), X IA & XIB S-Glass Longitudinal Plies, Graphite Cross Plies, 60-61

Epoxy Resin

XIIA & XIIB Open-Hole Specimens, Tensile Loading), All-Graphite Fibers, Epoxy Resin ... 62-63

Open-Hole Specimens, (Tensile Loading), XIHA & XIIIB S-Glass Longitudinal Plies, Graphite Cross Plies, 64-65

Epoxy Resin

XIVA & XIVB Interaction Specimens, Tensile Loading), All-Graphite Fibers, Epoxy Resin

...... 66-67

Interaction Specimens, Tensile Loading), X VA & XVB S-Glass Longitudinal Plies, Graphite Cross Plies, 68-69

Epoxy Resin

XVIA XVIB Interaction Specimens, (Compressive Loading), All-Graphite Fibers, Epoxy Resin

.... 70-71

Interaction Specimens, (Compressive Loading), XVIIA & XVIIB S-Glass Longitudinal Plies, Graphite Cross Plies, 72-73

Epoxy Resin

XVIIIA& XVIIIB Pin Connection Specimens

4

XIXA & XIXB Single-Lap Specimens

5

X X

onolayer Properties ............... 6

XXI alculated Laminate Material Mechanical Properties ..... 7 Note: Tables with A suffix are in S.I . Units; Tables with B suffix are in U.S. Customary Units; Tables with neither suffix cover both unit systems.

vi

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XXIIA & XXIIB XXIIIA & XXIIIB Tension-Through-the-Hole Specimens, XXIVA & XXIVB All-Graphite Fibers, Epoxy Resin XXVA & XXVB

XXVIA & XXVIB Filled-Hole Specimens, XXVIIA & XXVIIB (Tensile and Compressive Loading), 86-91 XXVIIIA & XXVIIIB All-Graphite Fibers, Epoxy Resin

XXIXA & XXIXB XXXA & XXXB Bearing and Shearout Specimens, (Tensile Loading) XXXIA & XXXIB All-Graphite Fibers, Epoxy Resin

92 ~98

XXXIIA & XXXIIB

vii

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1 .

2 .

3 . 4 .

5 .

1 0 . 1 1 .

1 2 .

1 3 .

1 4 .

1 5 .

1 6 .

1 7 .

1 8 .

1 9 .

2 0 .

2 1 .

2 2 .

2 3 .

2 4 .

ILLUSTRATIONS

; u r e

Test Specimen and Set-up for Tension-Through-the-Hole Failure Mode .9 Shearout and Bearing (Tensile) Test Specimens 10Q

Compression Bearing Test Specimen and Fixture 1 0 1

Open-Hole Stress-Concentration Test Coupon (Tensile Loading) 102 Stress-Concentration Interaction Test Specimen

(Tensile and Compressive Loading)

Single-Lap Test Specimen and Minimized Eccentricity Test Set-up (Tensxle Loading) .

........ 104 Tension-Through-the-Hole Test Specimens (Graphite/Epoxy) .... 105

Tension-Through-the-Hole Test Specimens (Graphite/Glass/Epoxy) ... 1 0 6 Bearing and Shearout Test Specimens

Stress-Concentration Interaction Test Specimens .... 1 0 8

Open-Hole, Compression Bearing, and Single-Lap Test Specimens 0 o

Load-Introduction Fixture for Compression of Interaction Specimens 110 Lateral Support Fixture for Compression Tests

of Interaction Specimens .....

Modes of Failure for Bolted Joints in Advanced Composites ....'.' 1 1 2 Geometry of Double-Lap Bolted Joint

Elastic Isotropie Stress Concentration Factors for Loaded Bolt Holes with Reference t o Net Section ...........

4

Elastic Isotropie Stress Concentration Factors for Loaded Bolt Holes with Reference t o Bolt Bearing Area T 115 Influence of Joint Geometry on Elastic Strength of Bolted Joints m Isotropie Material Elastic Isotropie Stress Concentration Factors for Open Holes m Strips of Finite Width

Influenced Joint Geometry on Elastic Strength of Finite-Width Strips Containing Open Holes

Stress Concentration Factors at Failure fo r Bolted Joints in Morgan- xte I I / Narmco 1004 Graphite-Epoxy (Quasi-Isotropic Pattern) 18

Stress Concentration Factors at Failure fo r Bolted Joints in Morgan- ite I I / Narmco 1004 Graphite-Epoxy (Orthotropic Pattern) 119 Stress Concentration Factors a t Failure for Bolted Joints in Thornel

300 / Narmco 5208 Graphite-Epoxy (Quasi-Isotropic Pattern) 20

Stress Concentration Factors at Failure for Bolted Joints in Thornel 300 / Narmeo 5208 Graphite-Epoxy (Orthotropic Patterns) ... 1 2 1

Vlll

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25. nfluence of Jo in t Geometry on Predicted Tensile Strengths of Bolted Joints in Composites 122

26. nfluence of Jo in t Geometry on Net-Section Tension Strengths (Predicted Empirically) for Graphite Epoxies 123

27. et-Section Failure Stresses for Thornel 300 / Narmco 5208 Graphite-

Epoxy an d S-1014 / Thornel 300 / Narmco 5208 Glass-Graphite- Epoxy Composite Strips Containing Open Holes 124

28. ssessment of Scale Effect and Influence of Fiber Pattern on Stress Concentrations at Filled (Unloaded) Holes in Modmor II / Narmco 1004 Graphite-Epoxy Composite Under Tensile Loading 125

29. nfluence of Fiber Pattern on Tensile Strength of Modmor II / Narmco 1004 Graphite-Epoxy Composite Strips Containing Filled (Unloaded) Holes 126

30. nfluence of Fiber Pattern on Compressive Strength of Modmor II / Narmco 1004 Graphite-Epoxy Composite Strips Containing Filled (Unloaded) Holes 127

31. hearout Stress Contours for Various Laminate Patterns of Modmor II / Narmco 1004 Graphite-Epoxy Composites 128

32. hearout Stress Contours for Various Laminate Patterns of Modmor II / Thornel 75S / Narmco 1004 Graphite-Epoxy 129

33. hearout Stress Contours for Various Laminate Patterns of AVCO 5505 Boron-Epoxy Composite 129

34. earing Stress Contours for Various Laminate Patterns of Modmor II / Narmco 1004 Graphite-Epoxy Composite 130

35. earing Stress Contours for Various Laminate Patterns of Modmor II / Thornel 75S / Narmco 1004 Graphite- Epoxy 131

36.

earing Stress Contours for Various Laminate Patterns of Avco 5505 Boron-Epoxy Composite 131

37. earing Stress as Function of Edge Distance to Bolt Diameter Ratio for Thornel 30 0 / Narmco 5208 Graphite-Epoxy 2 38. earing Stress as Function of Edge Distance to Bolt Diameter Ratio for S-1014 / Thornel 300 / Narmco 5208 Glass-Graphite-Epoxy . 133

39. ypical Tensile-Bearing Failures of Bolted Joints in Graphite-Epoxy an d Glass-Graphite-Epoxy Composites 134

40. ompressive-Bearing Stresses for Thornel 300 / Narmco 5208 Graphite- Epoxy an d S-1014 / Thornel 30 0 / Narmco 5208 Glass-Graphite- Epoxy 5

41. ypical Failures of Bolted Joints under Compressive Bearing in Graphite-Epoxy an d Glass-Graphite-Epoxy Composites 136

42. tress Concentration Factors in Bearing an d Tension as Functions of Joint Geometry for Graphite-Epoxies 137

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4 3 . Non-Dimensionalized Joint Strengths and Failure Modes as Functions of Joint Geometry for Graphite-Epoxies I 3 3

Comparison Between Predicted and Observed Joint Strengths fo r Thornel 300 / Narmco 5208 Graphite-Epoxy

139

Comparison Between Predicted and Observed Joint Strengths fo r S-1014 / Thornel 300 / Narmco 5208 Glass-Graphite-Epoxy ....... 140

Inter-Relationship Between Failure Modes a s a Function of Bolted Joxnt Geometry fo r Graphite-Epoxy Composites 141

Calculated Interactions Between Bearing and Tension Loads on Two-Row Bolted Joints in Graphite-Epoxy Composites .......... 1 4 2

4 4 .

4 5 .

4 6 .

4 7 .

4 8 -

54- 5 9 .

6 0 .

6 1 .

6 2 .

Experimental Interactions Between Bearing and Tension Loads on 5 3 - Two-Row Bolted Composite Joints 143

Experimental Interactions Between Bearing and Compression Loads on Two-Row Bolted Composite Joints

4 z ,

Comparison Between Bearing Strengths for Pin-Loading and R-gular

(Torqued) Bolts .....

1 4 5

Bearing Damage at Bolt Holes in Graphite-Epoxy Composites .... 146

Comparison Between Bolt Bearing Strengths i n Sinele- and Donbl Shear for Graphite-Epoxy Laminates ........ 1 4 7

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BOLTED JOINTS IN GRAPHITE-EPOXY COMPOSITES

By L . J . Hart-Smith

Douglas Aircraft Company, McDonnell Douglas Corporation

SUMMARY

The objectives of this report ar e to present the data generated during a

comprehensive experimental investigation of bolted joints in graphite-epoxy

composites and, by interpreting these an d other data, to provide methods for

th e analysis an d design of such joints. Th e specimens tested incorporated

quasi-isotropic an d two near quasi-isotropic patterns of the 0, TT/4, r / 2

(0, 45, 90) family. Both all-graphite/epoxy laminates an d hybrid graphite- glass/epoxy laminates were tested.

The tests encompassed a range of geometries for each laminate pattern to

cover th e three basic failure modes - ne t section tension failure through the

bolt hole, bearing, an d shearout. A constant bolt diameter of 6.35 mm (0.25

inch) was used in th e tests. The interaction of stress concentrations assoc-

iated with multi-row bolted joints wa s investigated experimentally by testing

single- an d double-row bolted joints an d open-hole specimens in tension. For

tensile loading a linear interaction wa s found to exist between th e bearing

stress reacted at a given hole an d th e remaining tension stress running by that

hole to be reacted elsewhere. Th e interaction under compressive loading was

found to be non-linear. Most of the joints tested were of double-lap config-

uration using regular hexagon head bolts. Comparative tests were ru n using

single-lap bolted joints an d double-lap joints with pin connections (neither

bolt head no r nut) an d both of these joint types exhibited lower strengths than

were demonstrated by the corresponding double-lap joints.

The new empirical analysis methods developed here for single-bolt joints

ar e shown to be capable of predicting the behavior of multi-row joints. These

methods are formulated to account for further effects (such as different bolt

diameters an d different environments) as data become available.

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investigation employed a single bolt diameter, 6.35 mm (0.25 in .), throughout.

Therefore th e specific strength values derived do no t account for th e known

sensitivity to scale effect for bolts of other sizes. The analysis techniques

developed permit straightforward extension to account for such effects as

operating temperature an d bolt diameter, as well as to other composite material systems, once the appropriate test data have been generated.

While a considerable body of information about experiments on bolted

joints in composite structures can be found in the literature, there appears to

be no other comparable analytical investigation. The analyses which have been

reported are mostly of finite elements and, as such, apply to specific situ-

ations which are covered in greater depth than is possible with th e empirical

methods developed here, but which do n o t . lend themselves to such comprehensive

parametric studies as th e empirical methods permit.

Th e significance of th e material presented in this report is that empir-

ical analysis methods have been developed for bolted joints in graphite-epoxy

composites and that these methods cover a range of geometries, fiber patterns

an d material combinations of practical interest so that efficient joints ca n be

designed. The methods are applicable to both single- an d multiple-bolt joints

an d ar e capable of extension to account for other factors an d new material

systems as data become available. Th e test program employed here ca n serve as

a model to account for such variables as new composite materials, larger bolt

diameters, an d different operating environments.

Th e units used for physical quantities in this report are given both in

U.S. Customary Units an d in th e International System of Units (SI) (ref. 1).

SYMBOLS

C

onstant

d

ol t diameter

e

dg e distance from middle of bolt

F , aterial allowable bearing strength F tu material allowable tensile ultimate strength 1^ , k f c interaction coefficients (defined in equation 26)

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c

omposite stress concentration factor at failure,

with respect t o bearing stress

lastic isotropic stress concentration factor,

with respect t o bearing stress

ktc composite stress concentration factor at failure,

with respect t o net section tension stress k te elastic isotropic stress concentration factor,

with respect t o net section tension stress P load

t aminate thickness w pecimen width G

oefficient (defined in equation 2 )

0 " , a

aminate tensile stress

laminate bearing stress T

s laminate in-plane shear stress

EXPERIMENTAL INVESTIGATION

This section of the report explains the c h o i c e , of materials and fiber

patterns employed in this program, describes the test specimens, the test pro-

cedures, and the characteristic failure modes, and presents a compilation of

the test results. These results are interpreted in the succeeding section.

The test results are classified here according t o failure mode.

TEST SPECIMENS

Materials

The laminates from which the bolted joint specimens were fabricated were

made of the Thornel 300 / Narmco 5208 graphite-epoxy composite. his material

was selected because of its widespread use throughout the U.S. composites in-

dustry a t the start of this program. t i s a high-strength material of inter- mediate modulus and has been found t o have such a mix of properties a s t o make

i t attractive for aerospace applications. bout half of the specimens had the

longitudinal plies replaced by S-1014 glass fibers impregnated with the same

Narmco 5208 resin. All cross plies (^/4 and TT/2) were graphite. The compos-

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s

was checked on scrap material before the specimens were drilled. Those speci-

mens with bonded aluminum doublers were set up in a milling machine to trim

the metal doublers with a fly-cutter so that they were parallel t o the opposite

face of the composite laminate and so that the composite laminate was located

centrally within the doublers. This machining was done t o ensure that the loads were applied properly.

Configurations

The test specimens and fixtures used in this program are shown in fieure

1 t o 1 3 . Each test specimen i s explained below. Bolts of 6.35 mm (0.25 in.) were used throughout the tests.

m=te M l L s S e c i ^ s.- The test specimens illustrated in figures 7

and 8 were proportioned t o induce failure by tension through the bolt noil A range of values of each of the geometric ratios d/w and e/w was covered with

the objective of testing a t a variety of stress concentration factors. Speci-

mens of three widths ( 3S 4 and 6 times the bolt diameter), each having two or

three edge distances were tested for each of the six laminates. The bolts we^e

loaded in double shear. A total of 3 6 specimens was tested in this part of the

investigation, with each specimen providing four or six data points.

Beaj n roul The test specimens shown i n figures 2

and 9 were of sufficient width ( 1 0 bolt diameters) t o preclude tension failures

for the laminate patterns tested. Double-shear tests were performed at edge

distances of two, four, six and eight bolt diameters t o encompass both shearout

faxlures, in which the proximity of the end of the specimen was sufficient t o

Ixmxt the joint strength, and bearing failures, in which all boundaries of the

specimen were sufficiently far removed t o permit the maximum strength possible

t o be developed. Twelve specimens, each with four test holes, were used t o

assess the resistance t o shearout and bearing under tension loads.

Figures 3 and 1 1 depict the specimen and test fixture used for applying

a compressive bearing load. Twelve of these specimens were tested. The bolts were loaded in double shear.

OE^h^^e^imens.- Figures 4 and 1 1 show the test specimens which were used t o measure the strengths of each laminate in a strip containing an open

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hole. The strip width was four times the bolt diameter. Twelve of these spec-

imens were tested, each having the same geometry and providing two data points per specimen.

Multi-bolt interaction specimens . - Figures 5 and 1 0 show the two-row

bolted joint specimens employed t o investigate the interaction between stress

concentrations when some of the total load i s reacted by any given bolt while

the remainder of the load passes by t o be reacted at the other bolt hole(s).

Both tensile and compressive loads were applied. Forty eight such specimens

were tested, twenty four each in tension and compression. The selection of

two bolts and uniformly thick laminates in this specimen was to ensure that

the load reacted at each bolt would be known even though the load paths were

redundant. With this design, the load must be shared equally between the two

bolts. The bolt holes were drilled right through the three laminates simult- aneously t o ensure that the bolts were a precision fi t in the holes. Indeed,

the bolts were selected on a hole-by-hole basis to improve the fit. Figures

1 2 and 1 3 illustrate the fixtures employed to load these specimens in compres-

sion. The fixture in figure 1 3 provided lateral support fo r the compression specimens.

Pin-joint specimens . - Two quasi-isotropic specimens of the type shown

fo r bearing and shearout in figure 2 were tested with the load transferred by

a simple pin, instead of the conventional mechanical fasteners, t o quantify

just how much additional load transfer i s accomplished because of the bolt head and nut.

Single-lap shear specimens . - Four quasi-isotropic all-graphite specimens

were made and tested in tension a s shown in figure 7 . The special test fixture

was designed to eliminate the laminate bending usually associated with single- shear single-row bolted joints.

Test Procedures

The bolts used throughout the tests were NAS 464-4 6.35 mm (0.25 in.)

titanium alloy heat treated t o 1100-1240 MPascal (160-180 ksi). New bolts were

used for each test t o preclude the possibility of accumulated bolt distortion

affecting the results. The bolts were torqued to 2. 8 N. m ( 2 5 in-lb), which i s

the normal tightening torque fo r such bolts in composite applications.

7

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strength attained, pattern 3 being slightly stronger than pattern 2 which wa s

stronger than pattern 1 . Th e patterns 6 , 5 an d 4 were ranked similarly. Th e

holes caused failures at stresses significantly below th e ultimate laminate

strengths for each pattern an d material combination.

Multi-bolt i nte r action specimens (tables X IV to XVII) . - Th e most signif- icant finding of th e investigation of th e two-row bolted joints is that th e

strengths were no t very much higher than those of a single-row joint in an

all-graphite specimen of th e same width (four bolt diameters). Th e failure

mode, ne t tension, wa s th e same in each case. This similarity of failure loads

means that the combination of the stress concentration induced by th e load to

the second bolt bypassing th e first bolt and th e stress concentration caused

by the load in th e f irst bolt itself is nearly as bad as that induced by react-

ing the entire load at a single bolt hole. Th e two-hole graphite-glass epoxy

specimens exhibited higher strengths than for th e single-hole specimens by as

much as f if ty percent, demonstrating again an advantage for the graphite-glass

combination over th e all-graphite reinforced composite. Th e compression loads

sustained by these interaction specimens were consistently higher than for tensile loading.

Pin-connection test_Sec i mens (table XVIII) . - The bearing strengths devel-

oped by pi n loading of th e holes in th e quasi-isotropic all-graphite laminates

were only about half as high as for the same specimens with conventional bolts.

Single-lap test speci mens (table XIX). - Th e bearing strengths at failure

with single shear bolts were about 69 0 MPascal (100 ksi) or about twenty per-

cent lower than for double shear. This results applies when the bolt is able

to deflect du e to th e local eccentricity in load path but the basic laminate is

relieved from th e gross bending moment usually associated with single-lap joints

by the special fixture shown in figure 6 .

DATA INTERPRETATION AND ANALYSIS METHODS

This section of th e report begins with a listing of the basic laminate

strengths which have been computed to serve as a basis for th e establishment

of stress concentration factors at failure. Th e purpose of the succeeding

analyses for each of th e characteristic failure modes is to generate methods

10

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an d understanding which will permit the generalization of specific test data

to joint geometries for which test data ar e no t available. ac h of th e basic

failure modes (tension-through-the-hole, shearout, an d bearing) is then assess-

ed in turn. The test data from th e present investigation are supplemented

where appropriate by other results, given in th e appendices where th e source references ar e identif ied. The analysis for tension failures is in tw o parts.

Th e first is for the elastic isotropic stress concentration factors and serves

as the basis for al l such analyses. Correlation factors between such elastic

isotropic stress concentration factors an d those observed at failure in comp-

osites are then established from test data. An isotropic elastic stress concen-

tration reference is used for both quasi-isotropic laminates an d orthotropic

laminates in which the material axes coincide with th e load an d geometric axes

because, for th e specific area of interest, such orthotropy could be represented

by a proportionality constant. The values of such correlation factors between

th e stress concentration factors are found to depend on both th e composite

material an d the fiber pattern. The joint geometries at which transitions

between failure modes occur are, likewise, found to be a function of both th e

composite material an d f iber pattern. Th e various analyses for each individual

failure mode for single bolted joints ar e then integrated into a method for

preparing design charts covering the entire range of possible geometries an d

depicting over which regime each mode of failure prevails.

Th e data interpretation an d analysis section then proceeds to address th e

problem of load sharing at multi-row bolted joints. Th e test data generated on

two-row bolted joints ar e combined with those for single-row bolted joints an d

open holes, for each of the si x laminates, to explain a linear interaction

theory for those cases in which the failure mode is ne t tension. For wider

bolt spacings, the failure ca n be bearing. A technique is proposed for account-

in g for a transition between bearing an d tension failures in such cases.

BASIC LAMINATE STRENGTHS

The basic laminate strengths for the materials tested in this investi-

gation have been computed using the monolayer data in table XX. Th e computer

program used to compute laminate properties in terms of such experimentally

1 1

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derived monolayer data employs a modified Hill's criterion to establish th e

load level at which some ply f irst becomes critical. Because of th e much higher

elongation of the glass fibers than th e graphite fibers, an initial failure in

a cross ply need no t denote th e maximum load capacity of th e laminate. Indeed,

th e original computations for th e strength of th e hybrid graphite-glass/epoxy laminates predicted failures at lower loads than the 0 (0) glass f ibers alone

could carry. Therefore, th e program w as modified to predict failure at th e

second f iber failure instead of th e f irst in th e event that, after th e cross

plies (TT/4) 45) had failed, the remaining f ibers could withstand a higher

load than that at which th e initial failure wa s predicted. (I t is believed

that th e failure of th e ir /4 (45) graphite f ibers prior to th e failure of th e

0 (0) glass f ibers is responsible for th e preponderance of bearing failures

for the hybrid laminates rather than th e tension failures demonstrated by th e

all-graphite laminates having th e same joint geometries).

Th e average failure strengths an d moduli predicted for each of th e six

laminates used in this program ar e given in table XXI. These strengths serve

as th e basis for the calculated stress concentration factors in composites at failure.

ELASTIC ISOTROPIC STRESS CONCENTRATION FACTORS

a . Loaded Bolt Holes

Th e experimental data of Frocht an d Hill (ref. 2), along with th e theor-

etical investigations cited below, provide a means of establishing an empirical

equation fo r th e stress concentrations at lightly loaded bolt holes. Such an

equation applies within th e elastic regime for Isotropie materials. At higher

load levels the ductile materials, such as aluminum alloys, yield locally to

reduce the stress concentrations at bolt holes. Composites, likewise, exhibit

lower stress concentrations at failure than would be predicted from linear

elastic theory. However, because of th e more limited extensibility of compos-

ites in comparison with that of ductile metals, the stress concentration factors

at failure for composites are much higher than for ductile metals. Consequently

it is incorrect to perform stress analyses on bolted joints in f iber-reinforced

composites by assuming that th e net sections of th e members being joined ar e

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uniformly stressed at the yield stress ( o r at any other uniform stress, for

that matter), as i s commonly assumed fo r metal practice. The objective of this

section i s t o develop the basis of analyses for bolted joints in graphite-

epoxy composite laminates in such a form that the stress concentration factors

at failure can be accounted for.

The elastic isotropic stress concentration factor at a loaded bolt hole

i s given here by the equation

k = 2 + T- l ) 1 . 5 W* I \\ 9

1 )

' t e * T W xl i>J ( w / d + 1 )

in which the parameter 8 is defined as

0 = 1. 5 - 0.5/(e/w) for /w < 1 ( 2 )

0=1

or /w > 1

The various geometric parameters are identified in figure 1 5 . The maximum

stress in the plate, adjacent to the bolt hole on the diameter perpendicular

t o the load direction, i s given by

o = k . , P ^

3 ) max te t( w -d)

In this and all other mention of stress concentration factors in this report,

the stress concentration factor is evaluated with respect t o the net rather

than gross section. Equations ( 1 ) and ( 2 ) lose their physical significance fo r d - > w and for e - > d/2. For values of e not much greater than d/2 the crit-

ical stress condition i s one of shearout or cleavage rather than of tension

through the hole and it i s necessary to account fo r these different failure

modes separately to identify which i s more critical fo r a particular geometry.

For the limiting case in which d/ w - > 0 (and e i s not so small as t o make shear-

out or cleavage critical) the failure mode will be in bearing but, even s o ,

equation ( 1 ) correctly characterizes the tension stress in the laminate next

t o the loaded bolt hole.

Equation ( 1 ) above can be re-expressed with respect to the bearing area,

instead of the net tension area, so that

, _ ax _ te _ . 2

. 5 0 ,*be P/td ~ (w/d - 1 ) " l (w/d - 1 ) (w/d +1) J 1 3

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Equations ( 1 ) and ( 4 ) are derived as follows. The lifting value of unity for

kbe in an infinite plate i s adopted from figure 7 of reference 2 in which i t i s

attributed to theoretical investigations by Bickley r e f . 3 ) and by Knight

( r e f . 4 ) . The lifting value k^ = 2 as the hole diameter approaches the width

of a fmite strip i s also based on theory. Koiter ( r e f . 5 ) computed this lim- iting value fo r a large open hole in a narrow strip. Since there is no contact

on the sides of a loose or net fit bolt hole, nothing in his analysis would be

changed by reacting the load a t one end by a bolt instead of the entire section

Therefore the same value should apply here also. The equations were also made

t o produce values of k^ = ^ = 2. 5 for d/ w = 0. 5 and e/w > 1 t o comply with

the other of Knight's theoretical computations. In addition t o these discrete

points, the equations were selected t o conform with the general trend of the

experimental data of Frocht and Hill in figures 5 t o 7 of reference 2 . The

final constraints imposed on equations ( 1 ) and ( 4 ) are the physically necessary

ones that k^ i s a monotonically increasing function of d/w and that d ( l c ) /

d(d/w) = 0 a s d/ w . 0 . Likewise, k^ i s a monotonically decreasing function of

d/w. The form of the function 0 in equation ( 2 ) i s such that, fo r an infinitely

wide plate containing a loaded bolt hole within a finite distance of the edge of the plate,

be+f/ft) as l.o

5)

This relation satisfies the obvious requirements that k ^ for e/d + 0

because the bolt would pull straight out of the half hole at the end of the

laminate with no resistance and that the effect of the e/d ratio should become

increasingly small as the value of that ratio becomes progressively larger.

This constant 3/4 was deduced here largely by curve fitting the Frocht and Hill

data (ref. 2 ) for e/ w * 1/3 and e/ w * 1/2 fo r moderate rather than small values of d/ w because no more appropriate data i s yet available.

Figures 1 6 and 1 7 depict equations ( 1 ) and ( 4 ) . The experimental data of

and reported by, Frocht and Hill r e f . 2 ) are included in these figures. The dominant influence i s clearly the d/ w term in both equations while the e/ w or e/d term has but a minor influence.

In order to adapt the equations above for single loaded bolt holes t o the

situation prevailing at multi-row bolted joints, it i s necessary t o understand

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the stress trajectories in the immediate vicinity of the bolt hole. Bickley

( r e f . 3 ) has performed analytical studies on the elastic Isotropie stress con-

centrations around loaded bolt holes. These investigations have established

that the hoop tension stress adjacent to the bearing perimeter of the bolt

i s of the order of the average bolt bearing stress P/dt from a t o c and on to the mirror image of a on diameter bb in figure 1 5 . The bearing stress varies

from about 2P/dt in the middle of the contact area (point c in figure 1 5 ) t o

zero on the edges (point a and opposite) fo r a loose or net fi t bolt.

In order to derive expressions fo r the ratio of the strengths of bolted

joints t o the strength of the basic laminate containing the joint, i t i s nec-

essary t o rearrange equation ( 1 ) t o read

o tw P

" 2 + 1.56

6)

W / \ W / \ w /

Equation ( 6 ) permits an assessment of the influence of the joint geometry on

the joint strength and i s plotted nondimensionally in figure 1 8 . I t can be

seen that, for a given maximum stress in the plate, the load carried is maxi-

mized when

d/w = 0.40

7 )

This corresponds with a bolt pitch of approximately 2. 5 bolt diameters which, on the basis of this interpretation of the stress concentrations at loaded bolt

holes in elastic isotropic materials, would appear t o be the optimum bolt pitch.

(The customary bolt pitch of 4d established fo r ductile metals has been estab-

lished largely on the basis of ultimate static strength). Figure 1 8 indicates

that the bolted joint strength i s fairly insensitive t o minor variations about

the optimum location and that the maximum possible joint efficiency fo r a

brittle elastic isotropic material barely exceeds 20 per cent.

b . Open Holes

The stress concentration factor at the net section of a strip containing

an unloaded hole is needed for the assessment of the interaction of stress con-

centrations at multi-row bolted joints in loaded plates. The equation proposed

here for a hole in a strip is

1 5

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figures 2.4 .2-15 to -17) in terms of an allowable net-section design strength

supposedly applicable for al l joint geometries. It is suggested here that the

considerable scatter shown in those diagrams should be explained in terms of

the influence of joint geometry on the net-section failure stress. therwise,

th e us e of those data in th e form presented in reference 9 will lead to some designs which are excessively conservative an d to others which ar e dangerously

unconservative.

In references 10 an d 11 it is suggested that a linear relationship exists

between the elastic isotropic stress concentration factors for low load levels

an d the stress concentrations at failure of bolted composite joints of the same

geometry. The basis of this linear relationship is illustrated in f igures 21

and 22 which have been replotted from reference 12 using the stress concentra-

tion equations ( 1 ) an d (2). Th e stress concentration factors k were evalu- tc

ated with respect to experimentally determined laminate strengths. Th e straight

lines have been constrained to pass through th e point (1,1), for which there is

no stress concentration at an y load level, with a slope evaluated by minimiz-

ation of the squares of th e deviations between individual points an d the lines.

A straight l ine is employed because th e degree of scatter does not justify an y

more complex representation. The test data on which f igures 21 an d 22 ar e

based are recorded in tables XXII to X XV of the appendix.

The open-hole data have been included with th e loaded-hole data to show

that, at least as far as th e ne t section through th e bolt hole is concerned, th e

origin of th e stress concentration is no t important. Much th e same proportional

reduction in stress concentration at failure of th e composite is shown for both

th e loaded an d unloaded holes. Therefore, it is reasonable to assume that two

bolted joints having different geometries but the same elastic isotropic stress

concentrations (by compensating differences in th e d/ w an d e/ w ratios) would

experience similar stress concentrations at failure also.

The justification offered for plotting measured orthotropic stress concen-

tration factors at failure of the non-isotropic material in figure 22 against

calculated elastic isotropic stress concentration factors is as follows. When

attention is confined to only th e net section through the bolt hole perpendic-

ular to the load direction an d th e axes of material orthotropy are th e same as

th e geometric axes of the joint (length and width), the difference between th e

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elastic Isotropie stress concentration factors and the corresponding elastic

orthotropic stress concentration factors i s merely a proportionality constant.

This constant can be just a s conveniently accounted fo r in the slope of the

line in figure 2 2 , without having t o evaluate the constant, a s by determining

its value and rescaling the abscissa of such a figure.

Test data for the present program, from tables I I t o I V , are depicted in

figures 2 3 and 2 4 , showing how the stress concentrations a t failure compare

with the calculated elastic isotropic stress concentrations. The equations

used t o characterize the stress concentrations are a s follows:

Quasi-isotropic Thornel 300 / Narmco 5208 ( 0 , TT/4, T/2, -TT/4)

k tc " - 7 3 + - 2 7 1 0 )

Orthotropic Thornel 300 / Narmco 5208 (0, rr/4, v/2, 0, -TT/4, TT/2, 0, TT/4) S & (0, TT/4, 0, -TT/4, TT/2, r/4 5 0, -TT/4)

s k tc= 0-60+0.41 k t

11)

The similarity of the results fo r patterns 2 and 3 results from the similar

elastic moduli and strengths (see table XXI). The hybrid glass-graphite/epoxy

laminates did not fail in tension for this p r o g r a m , s o no stress concentration

values could be calculated. The equations corresponding with equations ( 1 0 )

and ( 1 1 ) fo r the Morganite I I / Narmco 1004 system, for which the results are

presented i n figures 2 1 and 2 2 are a s follows:

Quasi-isotropic Morganite I I / Narmco 1004 ( 0 , TT/4, TT/2, -TT/4) c

k tc " 0-75 +0.25 k te

12)

Orthotropic Morganite I I / Narmco 1004 ( 0 , TT/4, 0 , -TT/4)

k tc = ' 5 4 + - 4 k te

1 3 )

These equations ( 1 2 ) and ( 1 3 ) should not be expected t o apply also t o the sim-

ilar Modmor I I / Narmco 1004 graphite epoxy (Narmco 5206) material because of a

significant change in interlaminar shear strength between the two systems.

Figures 2 3 and 2 4 include test data for bearing failures a s well a s the

tension failures respresented by equations ( 1 0 ) and ( 1 1 ) . The reason why these

data contribute confidence t o the coefficients i n equations ( 1 0 ) and ( 1 1 ) i s a s

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follows. If a joint specimen fails in bearing rather than tension, the com-

puted value of k would necessarily be higher than that which would have been tc

exhibited during a tension failure. Therefore, those data in figures 23 and 2 4

pertaining to bearing failures should lie consistently above the lines denoting

equations ( 1 0 ) and ( 1 1 ) . This i s seen to be s o . Furthermore, an examination of figures 23 and 24 shows that the transition between tension and bearing

failures for these composite laminates occurs fo r joint geometries having k

values of about 5. 5 and that the bearing data diverge progressively more from

the lines plotted for tension failures with still greater values of the stress

concentration factor k (The data plotted in figures 2 1 and 22 are complete.

Bearing and tension results for that investigation were indistinguishible).

In equations ( 1 0 ) to ( 1 3 ) the net-section strength i s related t o the

material and geometric properties of the joint in terms of the equation

( w - d)tF p = u

14) k tc

The application of the concepts described above i s explained as follows.

An elastic isotropic stress concentration factor i s evaluated for any specific

geometry under consideration, using equations ( 1 ) and ( 2 ) . Then, for the par-

ticular material system being assessed, the corresponding stress-concentration

factor in the composite laminate a t failure i s evaluated by means of an equation

such a s equation ( 1 0 ) . This design method does not require the testing of each and every joint geometry being assessed. The test data from selected geometries

can thus be generalized to other geometries, which were not tested, by working

in terms of the stress concentrations. As more data become available, the

coefficients in equations ( 1 0 ) to ( 1 3 ) and the like can be expanded t o account

for such effects as different environments and different bolt diameters.

Composite materials have been shown in figures 2 1 and 2 3 t o exhibit lower

stress concentrations at failure than linear elastic theory would predict.

Therefore, it i s appropriate t o redefine equation ( 6 ) as follows, fo r composite materials.

L_ = i i) / k

is) w / tc

F tw tu

1 9

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Equation (15) is plotted in figure 25, in which th e relationship between k 3nd k te is of the form

C

(k tc - 1 ) = CONSTANT x (k^ - 1 )

16)

Th e values of th e constant shown in figure 25 are 0, 0.1, 0.2, 0 4 6 8

an d 1 . Three features in figure 25 are noted. Th e first is that the siller

values of th e constant ar e associated with higher joint strengths for a given

common laminate strength because k is less than k The second feature

xs that th e opt value of d/ w changes as th e stress concentrations decrease close to the lifting ful ly-plas t ic case, whereas the optimum d/w ratio is

0.40 for a perfectly-elastic Isotropie material, that optimum, is closer to 0 30

for th e quasi-isotropic co f f iposites tested in this program since the constant in

equat ion (16) is, in that case, given by equation ( 8 ) as 0.27. Th e optimum for

the two orthotropic laminate patterns tested in the present program is, likewise

found to be at d/ w * 0.35. This shows that the optimum Joint geometry (domin-

ated by the d/ w ratio) is a function of both th e material system an d f iber pat-

tern. The third feature of figure 25 is that the stress concentration relief

exhxbxted by th e graphite-epoxy laminates is sufficient to double the optimum

ooltec joint strength for th e quasi-isotropic laminates tested (with respect to

predxetions for a brittle elastic Isotropie material) from just over 20 percent

of the basic material strength to 42 percent. Th e radial lines from the origin

m fxgure 25 denote lines of constant bearing strength F The predominant-

failure mode for small d/w ratios is usually bearing, rather than tension so

the tension strengths predicted in that portion of figure 25 can no t usually

be realized. (Bearing failures ar e discussed in a later section of this report)

Because figure 25 is plotted in non-dimensionalized form, it does no t provide a

convenient quantitative comparison between the potential strengths of th e differ-

en t laminate patterns tested during the present program. Figures 26 have been

prepared to afford such a comparison, taking into account the different basic

laminate strengths for the all-graphite composites.

b. Open Holes

Th e test data from the present investigation, pertaining to tension fail-

ures at unloaded holes, are recorded in tables XII an d XIII an d are illustrated

in figure 27. Th e results for th e all-graphite laminates al l represent tension-

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through-the-hole failures. However, none of those coupons with glass f ibers

show an y evidence of tension failure. All of this latter group show classical

shearout failues in th e 0 (0) direction originating at th e sides of th e holes.

It is not possible to make deductions about th e tensile failure of graphite-

glass hybrid laminates at stress concentrations on th e basis of these data. Th e stress concentration factors for the present all-graphite specimens have

been calculated to li e in the range 1. 5 to 2. 0 at failure an d ar e significantly

lower than th e stress concentration factors calculated for loaded bolt holes

in equivalent specimens. These results ar e shown in the lower left corners of

figures 23 an d 24, using equation ( 8 ) to compute the elastic isotropic stress

concentration factors k . Figure 21, likewise, includes open-hole results in

the lower left corner an d these ar e seen to be compatible with th e line plotted

to fi t the loaded hole results.

The results of th e present investigation ar e supplemented by some previ-

ously unpublished tests on filled (but unloaded) holes in th e Modmor II / Narmco

1004 graphite-epoxy encompassing a far wider range of f iber patterns than wa s

tested here. These results (see tables XXVI to XXVII I of this report), obtain-

ed by th e contractor, are illustrated in f igures 28 to 30 to show the influence

of f iber pattern, hole size, and direction of loading (tension or compression)

on th e strength of graphite-epoxy laminates. Th e test specimen used for both

th e specimens with the holes an d th e basic laminate control specimens wa s a

honeycomb sandwich beam under four-point loading. The holes tested were of 6.35

mm (0.25 in.) diameter in 38.1 mm (1.5 in.) wide strips an d 25.4 mm (1.0 in.)

diameter in 50.8 mm (2.0 in.). The holes were filled with net-fit pins. Figure

28 presents the tensile test results for both size holes plotted in terms of the

ratio of th e stress concentration factors observed at failure to the elastic

orthotropic stress concentration factors as calculated using equations from

reference 9 . It is clear both that there is significant stress concentration

relief, between lo w stresses an d failure, in al l cases an d that the larger holes

are associated with consistently greater stress concentrations at failure.

There is also a clear indication that the maximum relief is achieved with lam-

inates which contain either f ew or many 0 (0) plies. Figure 28 cannot be used

to determine th e absolute strength of a laminate with a hole in it because of

th e variable orthotropic reference strengths. This limitation is overcome in

2 1

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figure 29, in which th e net-section strength for th e 6.35 mm (0.25 in.) holes

is depicted on an absolute basis. Th e strength increases essentially monoton-

ically with the percentage of 0 (0) plies. Figure 30 presents the corres-

ponding data for compressive instead of tensile load. Th e test specimens were

honeycomb sandwich beams with 6 .35 mm (0.25 in.) holes in the 38.1 mm (1 .5 in . ) wide facings, just as for th e tensile tests. An examination of figures 29, for

tensile loading, an d 30, for compressive loading, shows that the strength of

laminates with unloaded f i l led holes is lower when loaded in compression than in

tension. Since th e pins filling the holes were no t an interference fit, on e

should assume that the same results would apply also for open holes. Compressive

tests were no t conducted for the 25.4 mm (1.0 in.) holes.

A direct comparison between the present, an d prior test results is possible

only for the quasi-isotropic all-graphite pattern. In this case, the present stress concentration factors ranged from 1. 5 to 1. 7 while, in the prior tests,

the factors ranged from 1. 5 to 1.6. The results are thus seen to be comparable,

with the small difference possibly attributable to the different tests specimen

geometries. Test data from th e present program are included in figure 29.

SHEAROUT STRESS CONTOURS

When the edge distance between a loaded bolt an d th e edge of a composite

laminate is small, or th e f iber pattern is deficient in cross plies (u/4 and/or

rll (45 and/or 90)), the predominant mode of failure is either shearout or

cleavage (fig. 14). Just as in the preceding case of tension through-the-hole

failures, the characteristic shearout an d cleavage modes of failure are strongly

influenced by the joint geometry, f iber pattern, an d composite material of which the joint is made.

Figure 31 shows previously unpublished shearout stress contours, as a

function of f iber pattern, which were obtained during an earlier investigation,

by th e contractor, on Modmor II / Narmco 1004 graphite-epoxy laminates. These data ar e given in tables X X I X to XXXII of this report. Al l such specimens

tested had 6.35 mm (0.25 in.) diameter bolts, an edge distance of 12.7 mm (0 .5

in.), an d a width at least as great as 38.5 mm (2 .5 in.). That geometry had

been selected in anticipation of consistent shearout or cleavage failures. Yet,

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despite an edge distance ratio e/d (fig. 15) as lo w as 2 an d a w /d ratio at

least as great as 10, al l of those f iber patterns containing less than 50 per-

cent 0 (0) plies failed consistently in tension through-the-hole rather than

by shearout. Failures were by shearout in th e upper portion of the triangle,

an d it ca n be seen that the reduction of cross plies is associated with a

consistent loss of shearout strength.

Figure 32 illustrates the corresponding shearout stress contours for mixed

graphite-epoxy laminates. These laminates were made from Modmor II f ibers in

th e 0 (0) an d TT/2 90) directions, an d Thornel 75S f ibers in th e i r / 4 (45)

directions, with Narmco 1004 epoxy. The results share on e characteristic with

those in f igure 31 inasmuch as the highest shearout strength is demonstrated

for intermediate amounts of i r / 4 (45) fibers, with lower strengths for those

laminates containing either few or many such fibers. Th e major difference

between f igures 31 an d 32 is that, in th e latter, al l failures were in shearout.

This difference between figures 31 an d 32 illustrates th e sensitivity of th e

strength and behavior of bolted joints in composites to th e particular composite

material as well as to the joint geometry and f iber pattern. Th e data from

which figure 32 wa s prepared are recorded in reference 13.

Figure 33, replotted from reference 13, presents the corresponding shear-

ou t stress contours for AVCO 5505 boron-epoxy, 0. 1 mm (0.004 in.) fibers. This

diagram is included in a report on graphite-epoxy to emphasize the point that

th e nature of the data presented in f igures 31 an d 32 is characteristic of the

particular materials system being assessed. In comparison with figures 31 and

32 for graphite-epoxies, the boron-epoxy data shares th e characteristic of lower

strengths for f ew an d many TT/4 45) fibers. There is a transition between

shearout and tension failures, but at a different location than in f igure 31. The

The data for these tests ar e recorded in reference 13.

The shearout stresses in f igures 31 to 33 were calculated by the custom-

ary formula

TS = P / [2t(e - f )]

17)

The value so calculated is not, in general, a material property alone since it

is known from prior testing to be a function of th e e/ d ratio (ref. 14) an d

possibly th e w/d ratio also. Such shearout stresses are meaningful as a measure

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of aoxnt strength, even if th e failure mode is in bearing or tension (as is the

ease for many of th e failures of the specimens tested to produce f igures 31 to

33), provided that the specimen geometry is identified to prevent unwarranted

extrapolation. In every test on which f igures 31 to 33 are based, the w/d

ratxo wa s at least eight an d sometimes as high as twelve to eliminate an y influence from that parameter.

The shearout test data for th e present investigation are reported in

tables VIII an d IX. Equation (17) wa s used to compute the shearout stresses

Th e value of w/ d used for these specimens was sufficiently high that its value

should have very little effect on the results. It should be noted that, in

tables VIII an d IX , shearout failure occurred only for e/ d values as low as two

Fo r greater edge distances, th e failure wa s always bearing an d occurred at a

higher

load,

The shearout stresses developed in this test program for e/ d ratios of

the order of two ar e either as good as or better than those which have been

attained in prior investigations (compare, for example, tables VIII an d IX with

figure 31). Th e stresses are, however, significantly less than the in-plane

shear strengths of th e laminates tested (see table XXI). This confirms the

presence of significant stress concentrations in th e shear distribution reacting

the bolt load, as has been observed in prior investigations.

In concluding this section, it should be noted that very f ew shearout

failures were experienced during this program. This is th e result of

consciously restricting th e f iber patterns to be favorable for efficient bolted

joints an d essentially free from premature failure by shearout (see figure 31).

This investigation confirmed that earlier assessment. Shearout failures at large

edge distances in composite laminates are associated with unsuitable f iber

patterns for bolted joints. The failure loads of bolted composite joints failing

in shearout has been found by prior testing to be either independent of , or only

weakly dependent upon, th e e/ d ratio (see ref. 14).

BEARING STRESS CONTOURS

In most cases in which both th e edge distance an d panel width (o r bolt

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pitch) are large in comparison with th e bolt diameter, the dominant failure mode

is bearing. Such damage is localized an d is usually not associated with catas-

trophic failure of a composite structure. The initiation of such a failure ma y

be caused by compressive bearing at the base of the bolt hole or by tension or

shearout at th e sides of the hole.

Figure 34 presents some previously unpublished test results from a system-

atic survey of the bearing strength of Modmor II / Narmco 1004 graphite-epoxy

laminates of various fiber patterns. These data were obtained from th e same

test specimens as used for the shearout tests shown in figure 31, but with a

greater edge distance. Tw o important features ar e evident in figure 34. Th e

first is th e large plateau at th e peak bearing stress in the vicinity of th e

quasi-isotropic pattern (25% 0 , 50% TT/4, 5% 7 r / 2 ) . Th e second important feat-

ur e in figure 34 is th e change in failure mode from bearing to shearout, in

spite of th e large edge distances an d widths, for those laminate patterns con-

taining more than about f if ty to sixty percent of 0 (0) plies. Figures 35 an d

36 (replotted from reference 13) contain bearing data corresponding with th e

shearout data for the mixed-graphite an d boron/epoxy laminates for which th e

shearout results are presented in f igures 32 an d 33. The shape an d location of

th e transitions in failure modes differs between each of f igures 34 to 36 and,

therefore, such behavior cannot be projected from on e material for which test

data exist to another for which they do not. Joint geometries known to be

associated with bearing failures for on e composite material are sometimes assoc- iated with tension or shearout failures for other composites, even if th e joint

geometries are identical. The test data from which figure 34 has been prepared

are recorded in tables XXIX to XXXII of this report.

Th e test data from th e present investigation are reported in tables VIII

an d IX an d illustrated in figures 37 an d 38. A photograph of typical failure

modes is provided in figure 39. An edge distance ratio e/ d as great as four is

necessary to develop th e full bearing strength of these laminates. Th e solid

symbols in

figures 37

an d 38

denote

bearing

failures, while

th e

open

symbols signify tension failures, at less than th e potential bearing strength. Th e

solid lines show average strengths of bearing failures for th e range of e/ d

ratios over which each line extends. Th e chain lines refer to the predictions

of equation (5).

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In comparing th e data in figures 37 an d 38 with those shown in figure 34,

two things are clear. First, th e present data are consistent with the exist-

ence of a plateau of maximum bearing strength for th e same f iber pattern domain

as was demonstrated in figure 34. However, the strengths of th e laminates

tested during th e present investigation [891-908 MPascal (129-131 ksi) for th e all-graphite laminates an d 834-850 MPascal (119-122 ksi) for the graphite-glass

hybrid laminates] are significantly lower than those shown in figure 34 [965-

1000 MPascal (140-145 ksi)] an d considerably lower than those bearing stresses

[1172-1241 MPascal (170-180 ksi)] associated with th e net-tension failures in

the tests on which f igures 21 an d 22 are based (see tables XXII to XXV of this

report). Second, th e data in figures 37 an d 38 suggest that, for al l practi-

ca l purposes, the same maximum bearing strength wa s developed fo r both material

systems and al l three fiber patterns tested in the present program. These

results highlight the need for data generated specifically for the composite material of interest.

COMPRESSION BEARING

Tables X an d XI record th e measurements made on compression bearing

specimens during th e present investigation. Th e results are summarized in fig-

ur e 40 , showing average bearing strengths of 866 MPascal (126 ksi) for the all-

graphite laminates an d 1209 MPascal (175 ksi) for the hybrid graphite-glass

laminates. In comparison with tension bearing (see f igures 37 an d 38), it is

apparent that there is a slight increase in bearing strength for the all-

graphite laminates when the bolt load is reacted by compression rather than by

tension, bu t for th e hybrid laminates, there is a pronounced increase in

bearing strength.

Figure 41 illustrates sample compression bearing failure modes an d it is

evident that these look very similar to those in figure 39 fo r tension bearing.

Th e logitudinal stresses in the f ibers adjacent to th e hole diameter perpendic- ular to th e load changes sign between tensile an d compressive bearing, ye t the

failure modes an d loads exhibited are much th e same for both cases. Therefore,

it is concluded that th e longitudinal stress di d no t play a major role in the

bearing failures observed during the present investigation. With the elimin-

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I f , fo r sufficiently small values of d/w, the net-tension analysis were t o

predict lower stress concentration factors than given by equation ( 2 2 ) , these

lower values could not be realized because of a failure i n bearing. This

failure mode transition i s shown in figure 4 2 , based on experimental data,

where bearing failures dominate up t o some value of d/w, with tension failures for greater values of d/w. Instead of k^ continuing t o decrease with decreas-

ing d/w according t o a tension calculation, k^ i s not permitted t o decrease

below the value calculated using equation ( 2 2 ) for bearing failures. Figure 43

presents strengths for the three patterns of Thornel 300 / Narmco 5208 graphite-

epoxy composite using data generated in the present investigation and for

the two patterns of Morganite I I / Narmco 1004 graphite-epoxy composite. All

such data are recorded in the tables o f this report and the specific locations

are cited in the text above fo r each failure mode. The composite stress con-

centration factors a t failure are computed as follows. From equation ( 1 6 ) ,

k tc = l + C k te ~ 1}

2 3 )

and, from equation ( 1 9 ) ,

\c t c l 2 4 )

while, from quations (1) and (2),

\ - 2 + f-1 ~ 1-5 C (f l)/(f + 1 )

25,

These equations enable the stress concentration factor

^c = Mt' C> f)

2 6 )

t o be evaluated and i t i s these computations which are shown in figures 4 2 and

4 3 , using the values of C given by equations ( 1 0 ) t o ( 1 3 ) . Figures 42 and 4 3 apply only for e/ w > 1 .

Figures 44 and 4 5 show the relationship between joint strength and lam-

inate width t o bolt diameter ratio, for all six laminate patterns i n the present investigation and the two laminate patterns for the other graphite-epoxy identi-

fied above. The experimental data are included on these plots. No tension

failures were observed for the glass-graphite fiber reinforced laminates tested

in this program, so the transitions between bearing and tension failures cannot

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skin, for example) or along a bolt seam aligned with th e dominant load (as at

a wing spar cap, for instance). In such more complex load situations, it is

necessary to characterize both th e bolt load an d also th e general stress f ield

in which th e particular bolt under consideration is located. Th e stress con-

centrations from each source will obviously interact an d analyses which do

no t take this into account would no t be meaningful. Th e f irst interaction data

for bolted joints in composites appear in reference 15. Th e first attempt to

explain such interactions analytically, and to account for them during design,

is in reference 16. Additional experimental work is reported in reference 17,

using essentially th e same two-bolt interaction specimen as used in the present

investigation. However, the laminate patterns in reference 17 are different

from those used in the present, investigation, so a comparison is no t possible.

Th e interpretation (ref. 16) of th e original data (ref. 15) suggested a linear interaction between tension an d bearing stresses of th e form

Gmax = k b Cb + k t t - F t u

27)

in which Ftu wa s th e basic laminate strength,' a f a the bolt bearing stress at the

hole under consideration, an d a f c the net-section tension stress caused by the

lemainder of th e load (not reacted at that bolt). Th e proportionality constants

^ an d k t account for both th e specimen geometry an d an y stress concentration

relief of which th e material is capable. This summation ma y be looked upon as

the su m of the contribution due to the load reacted at a bolt hole an d that du e

to the portion of the total load running by that hole an d reacted elsewhere.

Th e data generated during th e present investigation confirm th e validity of

equation (27) for the all-graphite laminates subject to tension loads, for which

the failures were in net-section tension. Fo r th e hybrid glass-graphite lamin-

ates, the failure mode changed from tension to bearing and this requires that

the interaction (27) appears to be subject to the same cut-off as defined in

equation (22) for single-row bolted joints. Thus, equation (27) should be re-arranged to read

= (F t u - k t V ' \ S F b r

2 8 )

to cover both tensile an d bearing failures.

Before proceeding with th e discussion of the present test results on this

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topic, i t is appropriate to demonstrate what can be predicted on the basis of

the single-hole equations, developed above, when used in conjunction with

equation ( 2 7 ) or ( 2 8 ) . The expressions fo r k , at a loaded bolt hole and k t

an unloaded hole can be evaluated in terms of the elastic isotropic factors

k , and k and the correlation factor C between stress concentration factors

observed in composites at failure and those in truly isotropic elastic material

specimens of the same geometry. Equation ( 1 6 ) reads

k = 1 + C ( k - 1 ) tc e i n which, fo r a loaded hole, equation ( 1 ) reads k = 2 + te f " l> 1-5 WT J

( 2 9 )

( 3 0 )

( i n which 0 is defined in equation ( 2 ) and usually has the value unity) and,

for an unloaded hole, equation ( 8 ) reads

te 2+1 _ d)3

( 3 1 )

Now, from equation ( 4 ) ,

\ 5 . This is

consistent with th e present investigation of tension through-the-hole failures, in which it wa s seen that bearing failures occurred for w/d ^ 6 while tension

failures occurred for w/d 4 , for th e quasi-isotropic graphite epoxy. Th e

transitional value of w/d at which bearing failures first occur, an d th e value

of th e bearing cut-off F /F are both functions of the composite material an d

f iber pattern. Plots of th e type of figure 47 for multi-row bolted joints

could be prepared similarly from single-hole data for any composite material

for which tests ha d established th e values of C an d F F br u*

Th e interaction test data generated during this program are recorded in tables XIV to XVII an d shown in figures 48 to 59. The linear interaction for

tensile loading of the all-graphite laminates is particularly clear for al l

three patterns (see figs. 48 to 50). Th e graphite-glass hybrid laminates

exhibit a non-linear interaction in th e manner that follows from figure 47

because, for such laminates in a joint geometry for which w/d = 4 , the failure

of single loaded holes wa s observed to be in bearing rather than tension. The

diagrams for the all-graphite laminates, figures 48 to 50, contain also th e

theoretical predictions based on the single-hole data discussed above. It is

evident that th e agreement is good but could be improved by a higher value of

k t in equation (26). Th e reason for this is apparent from figures 23 an d 24

which show that th e mean theoretical values for k (given by equations (10)

an d (11)) are significantly less than those observed experimentally for open

holes. Th e us e of an upper bound estimate for k instead of a linear mean tc

value constrained to pass through th e points (1,1) in figures 23 an d 24 would

permit an improvement in predicting th e test data in figures 48 to 50. Th e

corresponding lines in figures 51 to 53 permit th e use of equations (26) to

(33) in reverse to compute values of C in equation (29) for the graphite/glass hybrid laminates. Th e values so computed are as follows:

Pattern 4 : C = 0.51, Pattern 5: C = 0.48, Pattern 6 : C = 0.61 (34)

Th e actual computation of these values wa s performed as follows, using the two-

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ro w loaded hole data. For w/d = 4, equation (31) gives k =2.42 for an open

hole, while equation (30) gives k fc e = 4.10 for a loaded hole. Since th e fail-

ures were in tension an d each bolt accepts an equal load, th e failure condition

can be expressed in th e form

Ftu = ( 1 + 3.10C)(4)v + ( 1 + 1.42C)a t

35)

from which C can be determined. (The quantity a, d / (w - d) is equal to th e

net-section tension stress at th e bolt hole, du e to th e bearing load).

A point of special significance about the tension/bearing interaction test

results is that, for the all-graphite laminates tested, th e use of two bolts in

series di d no t increase th e load carried much above that which a single bolt

alone would be expected to have carried in a laminate of that thickness (twice

that on which th e single-bolt tests were performed). That this should be so

can be deduced from f igures 48 to 50, regardless of the relative proportion of

bearing an d tension loads, provided that th e linear interaction for tension

failures applies. For th e quasi-isotropic pattern, with w/d = 4, the tension

load capacity of the ne t section is practically identical with the bearing load

capacity on a single bolt. Therefore, any ratio of loads shared between bear-

ing and tension in a multi-row joint of that w/ d ratio made from' that composite

material an d laminate must inevitably be associated with essentially the same

total load capacity per unit laminate thickness. The orthotropic patterns 2

an d 3 carry slightly more load in net tension for w/d = 4 than in bearing, so

the mult-row bolted joints would be slightly stronger than a single-row for

those materials, fiber pattern an d geometry combinations. Figure 47 suggests

that, even fo r other w/d ratios, provided that th e failures are by tension at

the ne t section, th e use of multi-row bolted joints offers no significant

strength increase over a single-row joint of the same material an d geometry.

Only in that regime of joint geometries as is associated with bearing failures

for single-row bolted joints is there to be found an y major increase in joint

strength by th e use of multi-row bolt patterns. Furthermore, even in such cases, it appears that still higher strengths could be attained by a single ro w

of bolts closer together. However, this latter approach would mean accepting

potentially catastrophic tension failures in conjunction with such higher loads.

The analysis methods developed in this section permit a rational investigation

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of alternative joint design configurations without an extensive test program.

These methods can establish whether or not a candidate design i s either suit-

able or optimum for a given requirement and can minimize the amount of any testing necessary.

The interaction between compression and bearing in mult-row bolted joints

depends on a fundamentally different mechanism than that discussed above fo r

tensile loading. In the case of the compression of a laminate containing an

unfilled hole, there i s a stress concentration just a s with tensile loading of

the same specimen. When the hole i s filled with a net-fit bolt, however