Bonded structures and the optimum design of a joint

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•

.'

TECR ISCHE HOGESCAO l D

n

VUEGTUIG&OUV'lI(lJHt'I

BI UOTHEE

BONDED STRUCTURES AND THE OPTIMUM DESIGN OF A JOINT

by

V. Niranjan

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BONDED STRUCTURES AND THE OPTIMUM DES~GN OF A JOINT

by V. Niranjan

Submitted April 1971

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ACKNOWLEDGEMENT

The author wishes to th ank Dr. G. N. Patterson and Dr. G.K. Korbacher for providing the opportunity to write this tech-nical, note.

Many thanks to Dr. R. C. Tennyson,'for his advice and guidance.

Thanks are also due to Mrs. Dorothy Finlay and Mrs. Barbara Waddellfor patiently typing the manuscript; to Miss Roberta Dunn for the drawingsi to Mr. John McCormack and Mrs. Margaret Stewart for their _help in the publication of this note; and to Mrs. Asta Luik and Miss Nora Burnett for the library services.

The financial support of Fleet Manufacturing Limited, Fort Erie, and the National Research Council, Ottawa, is gratefully acknowledged.

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SUMMARY

The importance of adhesive bonding in spacecraft structures is discussed through its many applications in,

a) the fabrication of heat shieldsfor reentry vehicles, b) solid pr0pèllant rocket motors,

c) saturn structures,

d) the solar panels on.the surveyor

One of the most fundamental ·adhesive joint concepts is the

double strap joint. Results of static and fatigue tests on such

joints are presented.

Two methods of designing such joints for static and fatigue

loading are discussed. The first is a semi-empirical approach

yielding approximate results. The second method is accurate and

computer-oriented. It makes use of a polynomial representation of

data and the theorem of sturm from the theoryof equations, to

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'" d e. E G G a

t

max l o

t

opt N P P max. p (t) n. p 0 r R tI

ti

Tl (J a (J max T a T ave NOTATION

thickness of the adhes~ve layer

error vec1;:or

Young's modulus of·the adherend

shear modulus of the adherend

shear modulus of the adhesive

length of overlap

length ox overlap at which the P vs. l cu~ve obtained

by Szepe shows a· fictitious maximum

a very small length of overlap approaching zero

opt~mum length of overlap

number of fatigue cycles

half of the totalload, carried by the joint at

failure

half the peak load in a fatigue cycle P at a very large length of overlap

P represented as nth degree polynomial in l

P for a joint with overlap

t

o

t ₂/ t

l

=

thickness ratio, lies between 0 and 1

stress ratio - ratio of the minimum stress in.a

fatigue cycle to the maximum

thickness of the thicker adherend, see Fig. 1.

thickness of the thinner adherent, see Fig. 1. P/P

max

tensile strength of the adhesive

maximum tensile stress in the adherent in a fatigue cycle

shear strength of the adhesive

average shear stress in the adhesive

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1. 2. 3. 4 ". 5. 6 • TABLE OF CONTENTS Surnmary Notation INTRODUCTION

SEMI-EMPIRICAL APPROACH TO FIND THE OPTIMUM LENGTH OF OVERLAP

EXTENSION OF THE SEMI-EMPIRICAL APPROACH TO FATIGUE LOADING

EXACT DETERMINATION OF THE OPTIMUM LENGTH OF OVERLAP

A CRITIQUE OF THE SEMI-EMPIRICAL APPROACH CONCLUSIONS REFERENCES APPENDIX A APPENDIX B FIGURES 1 2 3 4 6 6 8

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1. INTRODUCTION

Adhesive bonding is being used extensively in several space-craft structures. This is made possible by the development of ad-hesives capable of withstanding the extreme environmental conditions encountered in space flight.

A space application where adhesive bonding is of consid-erabIe importance is in the fabrication of heat shields for re-entry vehicles ~]. The first generation of reentry vehicles was exposed

to high heat fluxes for relatively short, exposure times, generally in the order of minutes. Ablative type heat shields consisting of reinforced plastics served to protect the exterior of load. bearing structures for these vehicles. More advanced re-entry vehicles such as the lifting body type are exposed to lower heat fluxes but for considerably longer time periods. A typical·composite heat shield design for these vehicles consists of a structural metallic sheet, a resin-filled honeycomb insulator and a nlyon-phenolic ablator. The ablator to the insulator and the insulator to the sub-structure are bonded with adhesives.

The second application for adhesive bonding is in solid-propellant rocket motors [IJ . In this case there are several layers

of bondin~. The propellant is bonded to the liner, the liner is

bonded to the insulation and the insulation is bonded to the casing. Another application for adhesive bonding is in the saturn· structure [1] . The basic saturn structures are aluminum cylinders closed by hemispherical domes to provide propellant tankage. The cylinder thus formed is divided into two tank volumes by a common bulkhead. The upper volume is filled with liquid hydrogen and the lower volume is filled with liquid oxygen. The bulkhead carries load and also acts as an insulator and a barrier between tanks. It · prevents the liquid oxygen from being frozen by the liquid hydrogene In this application, the honeycomb core is adhesively bonded to the facings of the bulkhead.

A unique application where the adhesive was subjected to all the environmental conditions of space is found on the surveyor [1] • An extremely light weight panel with aluminum honeycomb co re bonded to titanium skins was used for mounting solar cells neces-sary for generating power for the mechanical package docked on the

lunar surface. .

Besides spacecraft structures, adhesive bonding finds many applications in the aircraft industry, automobile industry, construction industry, sports-goods industry and packaging industry. Bonding of orthodontic brackets ~] and femoral head prostheses [3] has also become very common.

There are many instances where adhesive bonding is pre-ferred to other methods of joining structural elements (e.g., riveting and welding) • Following are the points in favour of ad-hesive bonding:

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(a) It permits attachment of metals to plastics and other non-metals.

(b) It permits attachment of dissimilar metals without the normal problem of galvanic corrosion.

(c) Adhesive bonding is known for its excellent fatigue

°strength compared to other joining methods.

(d) Adhesive bonded structures are efficient in their re-sistance to sonic fatigue. Reduction of noise during flight is achieved in flight vehicle structures, due to the damping effect of the adhesive.

One of the most fundamental adhesive joint concepts is the double strap joint [Fig. IJ In the design of such joints, two types of problems exist. The first type deals with the shaping of the adherends to reduce the stress concentrations. The regions at the end of overlap are locations of high stress concentration in the adhesive. Researchers have attempted [4,1

J

to reduce these stress concentrations by bevelling the adherends or by suitably

shaping the adherends. For comparatively thin adherends this method is not effective [5J. This paper deals with the second type of

problem, where the designer has to choose a length of overlap for

, the joint. Thus, given the materials for the adherends and adhesive and the rest of the jointgeometry, how does one choose the length of overlap?

2. SEMI-EMPIRICAL APPROACH TO FIND THE OPTIMUM LENGTH OF OVERLAP

Not withstanding all the assumption involved, Volkersen's equa tion [6

J

(al so d.er i ved by DeBruyne [7

J

and Lunsford [8

J )

and Niles' and Newell's equation [9J (also derived by Demarkles

~O, 11

J )

can be fitted through experimental data satisfactorily.

Volkersen's equation: Tl

=

pip max sinh

bi

(1) r + eosh

b

i

where Niles' and (2 ) where

Szepe's equation [12J (which is based on more severe assumptions than the previous equations) may be given in the following form.

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~~---~---, Szepe's.equation: 11

=

pip _max (3) where G

a

=

~ (1 1 ) 3dE

t

-

2t 2 1

Equations [IJ and ~J are shown graphically in Fig.2. Since true joint,behaviour is represented qualitatively by Volkersen's forrnula, what is the meaning of

t

shown in Szepe's curve? The'

max

first contribution of t~is paper-is in,answering this question~

Af ter a considerable exercise in.algebra, i t.can be shown, that a length corresponding to _.

t

_max,Volkersen's equation always givesa constant value of 11 (for a constant r) irrespective of the materials used for· the joint (Appendix A). Thus

t

gives us the length at

max

which ,P

=

11P ,where 11 is a constant between 0.9 andO.98 [Fig. 3J. max

Beyond a certain value of

t

,

anincrease in overlap does not give us a worthwhileincrease in the load carried by the joint. If we define this length of overlap as the optimum length of overlap

t t ' (this occurs inthe range of 11 of 0.9 to 0.98) the value of tOP determined from Szepe's equation givesn àn estimate of t t.

T

mh~x _~s_correl _at~on' b _etween n d n ' • • op h

N an N t ~s very ~mportant s~nce t e

max op

value of t can be easily evaluated from max. where. P

₌

max, P

₌

0

t

= max 2P

t

max 0 P o load carried by a of overlap load carried by a

t , t

-70 o 0 (4)

specimen with a very large length

specimen with a length of overlap

Thus, this semi-empirical approach provides us with an estimate of the value of topt' u$ing just two experimental point~ on t~e P vs.

,

t

curve.

3. EXTENSION OF 'THE SEMI-EMPIRICAL APPROACH TO FATIGUE LOADING Fatiguecurves [13J for double-strap joint$ of various lengths of overlap are presented in Fig. 4. The adherends are of 2024-T3 alloy, with tI

=

0.064", r

=

0.5, and the adhesive is a nitrile epoxy (FM-123-2). The fatigue testsweredone, at a stress of 0.1; From these.fatigue curves one could cross-plot P vs.

t

for various endurances as shown, in Fig. 5, .where P is the maximum

semi-load in the fatigue cycle. The semi-empirical approach des-cribed in-Sec. 2 was applied to theseP vs •. t curves for constant values of the endurance N, and i t. was found~ that the results yielded a conservative estimate of the optimum length of overlap (Fig. 6). Thus, the values of

to

t .obtained from the semi-empirical approach should be sufficient

i~

the preliminary stage of design of a bonded

3

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---~---joint subjected to fatigue loads. The design for statie loads is a special case of the design for fatigue loads, where the endurance is 1/4 cycle.

4. EXACT DETERMINATION OF THE OPTIMUM LENGTH OF OVERLAP

I t was shown above that two data points on the P vs.

t

curve were sufficient for determining the optimum length of over-lap at a given endurance approximately. Experience shows that about 5 to 7 properly spaced data points on the P vs. t curve are

needed fordetermining the optimum length accurately. It was found

that these data points can be represented analytically by means of a polynomial as given below.

n n 1

P (t)

=

a t + alt - + •.• + a lt + a ,( n < 4)

n 0 n- n - (5 )

4.1 To Determine the Coeff icients a , al ... , a _o _n [Appendix B ] Since P

=

0 , at

t

=

0 , a n

=

0

If the data points are given by PI' t l i P

2, t 2i ••• i Pm,tmi

the error vector may be given as e = [P

l- Pn(t1) P2- Pn(t2)·· .Pm- Pn(tm)

J

= [el e

2 .•••.•.•• em]

(6 )

The Lp norm of the error vector [ 14,15

J

is gi ven by

m

Lp(e) = [

I

(ei)pJ lip (7)

i=l

The coefficients a ,al, ... ,a _o _n-1 of the polynomial are obtained so as to minimize the L norm of the error vector for a, p of 2 (by minimizing the Euclldean norm of the error vector). This gives us the best polynomial (least squares polynomial) representation of the experimental data.

4.2 To Determine the Optimum Length of Overlap

Since we have defined the optimum length of overlap in Sec. 2 as that value of

t

at which P = TlP (where Tl

=

a constant

max in the range 0.9 to 0.98), we can write,

on

n-l-Tl.P _max = a.KJ + a P. + ••• + a t

0 opt 1 ropt n-l opt ₍₈₎

The smallest positive root of this equation gives us the optimum length of overlap. This can be obtained by using the theorem of Sturm in the theory of equations [16J

4.3 Results

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results shown in Fig. 5 could be represented analytically by P = 2343.02t + 21007.88t 2_ 49086.29 t 3

+

29233.63 t 4 (9) (N = 1/4 cycle, 0

S

t.:s

0.75") P = 3955.6U - 2224.19

t

2 + 157.47

t

3 (10) (N = 10 4 cycles, 0 <t< 0.75") P = 3445.14t - 2393.9t 2 (11) 5 (N = 10 cycles,

o

< t < 0.75" )

-

-P

=

2317.03t + 3162.07 t2

-

14615.27t 3 + 10867.27 t 4 (12 ) 6 (N

=

10 cycles, 0 <

t

< 0.75")

Using the method of Sturmian sequences [16J with 11 =.0.98, the optimum lengths of overlap were computed to be

toPt

=

0.49", N = 1/4 cycle t = 0.72", N

₌

104 cycle _{( 13)} opt t

₌

0.64", N = 105 cycle opt t

₌

0.42", N = 106 cycle opt

These values of

t

are shown in Fig.6 by the lower curve. opt

4.4 Motivation for Using Polynomials

(a) Narning the graphical representation of Eq. (1) as the hyperbolic curve, i t is very difficult to obtain the least squares hyperbolic curve that represents the ex~

perimental data. On the other hand, i t is very simple to obtain the least squares polynomial for the data. (b) As we have seen.,polynomials have provided us with a

way of determining t t accurately without resorting

h' op

to grap 1cal means.

(c) If we are ready to put up with minor inaccuracies, the least squares polynomial can be replaced by a poly-nomial of lower degree by using the Chebyshev econo-mization procedure, thereby simplifying the analytical representation of the data.

(d) From Eq. (1) , as

t

--7 0 0 P bt 0 0 = Pmax r+l 5 (14 )

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b

=

P o /;0 (r+l) Pmax (14 )

Thus with two data points P a n d P , Eq. (1) is determined. max 0

A comparison of such a curve with the polynomial fit is shown in Fig. 7. The polynomial is seen to give a better fit through the data.

Ce) This method is well suited for computing purposes. 5. A CRITIQUE OF THE SEMI-EMPIRICAL APPROACH

The semi-empirical approach described in Sec. 2 may be criticized on the following grounds. It assumes (a) the adhesive to be elastic up to failure, (b) the normal stresses in the adhesive to be negligible, (c) all the failures to be occurring in the ad-hesvie, and (d) the adherend to be in its elastic range. There are also other minor assumptions.

We may attempt to correct the theory for some of these.

assumptions. For example, we may take into account the normal stresses in the adhesive in an approximate way. This gives us (making use of the Hill's criterion for failure under combined stresses) an expression for Pas,

P

=

2(1 + r) - 2 ti

[~

( r + cO:h t i ) + T sinh b/; a (15)

This equation is Seen to be very much more complicated than Eq. [2J . Further sophistication can be introduced into the theory by considering the inelastic behaviour of ·the adhesive and adherend. These sophistications are practically of no value due to the fact that the adhesive properties in a joint (in thin film form) cannot be determined accurately [ 17,18

J

even in the elastic range, leave alone the inelastic range. The difficulties are principally due to

(a) adhesive properties in thin film form being entirely different from the adhesive properties in bulk form, and

(b) the difficulty in obtaining a uniform stress state in the adhesive.

In the face of these difficulties one is justified in the use of the semi-empirical method in spite of its assumptions, due to its practical advantages and simplicity.

6. CONCLUSION

The principal results of this paper are summarized as follows:

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(1) A new semi-empirica1 approach to estimate the optimum 1ength of overlap of a double strap joint subjected to statie and fatigue loads was shown to yie1d usefu1 re-su1ts for pre1irninary design ca1cu1ations.

(2) The po1ynomia1 approach is shown to yie1d accurate va1ues

of the optimum 1ength for both statie and fatigue loads.

(3) The optimum 1ength of overlap is seen to be fatigue 1ife

dependent.

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1. Niranjan, . V •. 2~ Smith, D. C. 3. Charnley, J. 4. Cherry, -B. W. · Harr:L~on"N. L. 5. Hamel, .. D. R. 6. Volkersen, O. 7. De Bruyne, N. A'. 8. Lunsford, -L. R. 9. Niles, A. S. Newell, . J. S. · 10. Demarklesj L. ·R. 11. Segerlind, L.J. , 12. Szepe, .F •. 13. Niranjan, V. Hamel, . D. R • . Yang" C.A. 14. Rice, J.R. REFE:RE·NCES

Bond~d-Joints - A review for Engineers~

UTIAS-Review No.28, September 1970.

A New Dental·Cement, British Dental

Journal, Nov 5, 1968.

Acryl,ic Cement .. in Orthopaedic Surgery,

E & S Livingstone,.1970.

The Optimum Profile for·a Lap. Joint,

J. of Adhesion, April 1970.'

Bonded Joints - Increasing Fatigue

Strength' by Bevelling, UTIAS T. N. 159,

1970 •.

Die Nietkraft Verteilung in Zugea~

spruchten Nietverbindungen mit Konstanten·

Laschenqu~rschnittenl · Luftfahrtforschung, .

Vol. 15, 1938. .

Strength of Gl~ed- Joints, Aircraft Eng.

April ·1944.

Stress Ana~ysis of Bonded Joints· - In

Struct~ral Adhesives Bonding, edited by

Bodnar , M. J .• , .. Int~rscience Publisbers,

1966 •

. Airplane Structures, Vol. I. John

Wi~ey & Sons,1954.

Investigéltion of the-Use of a, Rubber·

Analog in Study of Stress Distribution

in Riveted. and çemented .;roints. NACA

T~N. 3413, Novetnber, .1955.

On the Shear Stress,in Bonded.Joints,

J . . of Appl ied Meçhanic s, March 1968.

Strength of· Adhesive7Bonded Lap Joints

With RE;spect to Change of Temperature·.

and Fatigue, Expt·. Mechanics, May 1966.

Statie and Fatigue . StrE;I:lgth,of FM .... 123-2

Adhesive, in Double', Strap Joints of

Va~ious ~engthsof Overlap, UTIAS TN 160, Aug. 1970.

The Approximation· of ·F~nctions, Vol. 1,

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11 15. Froberg, C.E. 16. Uspensky, J.V. 17. Kutscha, D. Hofer, K. E. 18. Rutherford, J. L. Boss1er, _ F. C. Hughes, E. J.

Introduction to Numerical Ana1ysis, Addison~Wesley Publishing Co., 1969. Theory of Equations, McGraw-Hi11 Book Co., 1948.

The Feasibi1ity of Joining Advanced Cornposite F1ight Vehic1e Structures, AFML-TR-68-391, January, 1969.

On Measuring the Properties of Adhesives

in Bonded-Joints, Vol. 14, 14th. Nationa1

Symposium and Exhibit, SAMPE, Nov, 1968.

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APPENDIX· A: Interpretation of '~x In Szepe's Theory

By differentiating Eq. 3 and equating d~/~ to zero, we ·get -1/2

,gmax . - (0:) . . . (Al)

Using the definition of b in·eq. 1, one can show tha~

,g

=

1 [3 (1+r.)

j/2

max.

b

.

(1",:,r/2)

J

substituting i,= P, _max in.eq, •. 1,

where TJ = cp (r) = sinh f.(r) cosh f(r)

+

r f (r) =. [

(f=;i1) ]

1/2 (A2) (A3)

Equation A3 is p10tted in Fig.3. This figure tells us that·

(for a given thickness ratio. r) i, given·by Szepe's equation,. in reality represents a 1ength of ov~~!ap at which P =~.P _max, where

~ is a constant indep~ndent of the adherends or the adhesive used for the joint.

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APPENDIX B: polynomial Curve Fitting

The problem outlined -here- is to fit the polynomial given by Eq. 1, through a set of ~ exp~rirnental points (PI' i ₁) , (P_{2 '} i

2), ••• , (P , i ). The nurnber of experimental points m sfioula be

con-m rn

siderably larger than the degree n 'of the polynomial.

f

n-l

P (0) =a . . +a

1 0 . + •••• +a li

n k O k . n- (BI)

For the m experimental points,eq. 1 gives us the following matrix equation in 1 in 2 n m n-l i l

... · . .

tI

n-l i ₂ i ₂

...

Equation 2, may be abbreviated as,

a n-l

(B2)

(B3)

A rneasure of error E, in representing the· experimental data

by eq~ 1 is, I E = ([P n J - [P J ) T ([ P n J - [ PJ ) where [PJ = PI P 2 P m (B4)

Now, the coefficient vector [aJ is evaluated so as to minimize E. From Eqs. 3 and 4,

E(a)

=

E

=

([iJ [aJ - [PJ)T ([iJ [aJ- [PJ) E(a+v)

=

([iJ .[a+vJ- [PJ)T ([iJ [a+vJ- [PJ) D(v)

=

E(a+v) - E(a)

If D(v) is positive definite, E(a) would be minimized. This condition leads us to tbe normal equations

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(BS)

The coefficient vector [aJ can now be evaluated as,

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P----1

cover plate

1--....-.2P

p - - - t

_{cover plate}

Not. that t.

<

ti

p -...

ma in ploft

2 ti 2 P

p---I

Figure 1. NOMENCLATURE

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TJa

P/P_{max .}

1.0

~-

TJ

sin h bi } Vol kersen

= r+ cash bi [ Ga(t,+t.)

]t

where b· dE t, t. 2./ä·1

'--- TJ

= --""'---I

+

all Ga I I where aa 3dE

(t; -

2t, ) Szepe I_max. o.o~

____________________

~~~

__________________________

~

o

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70

65

60

55

50

45

40

35 -

"ii ~

30

.c G

S

25

20

15

10 ---....

...

,

"

_"

ti

- - - -

----....

1-0'25

-....

...

'o~.

_ _ _ _ •

1-0'125"

---0 ________ _

-0_

10°

₁₀

6

APPROXIMATE BOUNDARY ABOVE WHICH NO GLUE FAILURES CAN OCCUR APPROXIMATE BOUNDARY BELOW WHICH NO METAL FAILURES CAN OCCUR

_._---

_{-_._.-}

_{THE REG ION BETWEEN THESE TWO LlNES IS A REG ION OF MIXED FAILURES}

FIG. 4

Comparison of the S-N 'curves _{lengths of} _overlap_with _{the plain}for joints _{metal specimens.}of various

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P (Ibs)

0.1

Min. Stress in Fatique Cyele 11 0.1

STRESS RATIO 11 Max. Stre .. in FatlQue Cyele

N 11

t

Cyele (Statie) _ . J f ) 0

-

---N. 106 Cyeles

-0.2 0.3 0.4 0.5 0.6 0.7

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I_opt

(inches)

1.00

0.80

0.60 o

Semi - Empirical Approach

A

Experiment

Stress Ratio

=

0.1

o.oo-+----.----.---~--__.,

log N

3

4

5

6

7

Figure 6. OPTIMUM OVERLAP VS FATIGUE LIFE

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P(lbs)

2400

2000

1600

1200

o

_o.

-I

N =tCYCle - - - Fit by Eye - - - - Polynomial Fit _ . - Hyperbolic Fit ~~

-_.

~ ~

J/~

fl

.

-ó

/.~

~./

0.2

0.3

0.4

0.5

0.6

0.7

0.8 1 ( inches)

(25)

UTIAS TECHNICAL NOTE NO. 164

Institute for Aerospace Studies, University of T oronto

Bonded 'Structures and the Optimum Design of a Joint

Niranjan, V. 9 pages 7 figures

1. Double Strap Joint 2. l'M-123-2 Adhesive 3. Nitrile Epoxy Adhesive

4. Fatigue of Joints 5. Design of Joints 6. Semi Experimental Method

1. Niranjan, V. II. urIAS Tech. Note No.l64

The importance of adheslve banding in spacecraf't structures ls dlscussed through

lts ,'/II8Il.y appllcatlons ln, (a) the fabricatlon of heat shields for reentry vehicles,

(b) soUd propellant racket motors, (c) saturn structures, and (d) the solar panels

on the surveyor. One of the most fundamental &dhesive joint concepts is the double

strap joint. Results of statie and fatigue testB on such joints are presented. Two methods of designing such joints for statie and fatigue lo&ding are discussed. The first is a semi-empirical approach yielding approximate results • The second method is accurate and computer-oriented. It makes use of a polynomial representa-tion of data end the tbeorem of sturm from the theory of equatlons, to determine

the optimum length of overlap for the joint.

~

Available copies of this report are limited. Return this card to UTIAS, if you require a copy.

UTIAS TECHNICAL NOTE NO. 164

Bonded Structures and th. Optimum Design of a Joint Niranjan, V. 9 pages 7 figures

1. Double Strap Joint 2. l'M-123-2 Adhesive 3. Nitrile Epoxy Adhesive

4. l'atigue of Joints 5. Design of Joints 6. Semi Experimental Method

1. Niranjan, V. Ir. urIAS Tech. Note No.l64

The importance of adhesive bonding in spaeecraft struetures is discussed through

its many applications in, (a) the fabrication of heat shields for reentry vehicles, (b) solid propellant rocket motors, (c) saturn structures, and (d) the solar panels on the surveyor. One of the most fundamental adhesive joint concepts is the double

strap joint. Results of statie and fatigue tests on such joints are presented.

Two methods of designing such joints for statie and fatigue loading are discussed. The first is a semi-empirical approach yielding approximate results. The second method is accurate and computer-oriented. It makes use of a polynornial

representa-tion of data 8Dd the theorem of sturm from the theory of equations, to determine

the optimum length of overlap for the joint.

~

"'" ,

"I

Available copies of this report are limited~ Return this card to UTIAS, if you require a copy.

UTIAS TECIlNICAL NOTE NO. 164

Bonded Structures and the Optimum Design of a Joint Niranjan, V. 9 pages 7 figures

1. Double Strap Joint 2. l'M-123-2 Adhesive 3. Nitrile Epoxy Adhesive 4. Fatigue of Joints 5. Design of Joints 6. Semi Experimental Method

1. Niranjan, V. II. urIAS Tech. Note No.l64

The importance of adhesive handing in spacecraft structures la dlscussed through

its many applications in, (a) the fabrication of heat shields for reentry vehicles,

(b) BoUd propellant rocket motors, (c) saturn structures, and (d) the solar panels

Two methods of designing such joints for statie and fatigue lo&ding are discussed. The first is a semi-empirical approach yielding approximate results • The second

method is accurate and computer-oriented. It makes use of a polynomial representa

-tion of data end the theorem of sturm from the theory of equations, to determine

the optimum length of overlap for the joint.

~

Available copies of th is report are limited. Return this card to UTIAS, if you require a copy. urIAS TECIlNICAL NOTE NO. 164

Bonded structures and the Optimum Design of a Joint Niranjan, V. 9 pages 7 figures

1. Double Strap Joint 2. l'M-123-2 Adhesive 3. Nitrile Epoxy Adhesive 4. Fatigue of Joints 5. Design of Joints 6., Semi Experimental Method

r. Niranjan, V. Ilo urIAS Tech. Note No.l64

The importance of &dhesive bonding in spacecraft structures is discussed through its many applications in, (a) the fabrication of heat shields for reentry vehicles,

(b) solid propellant rocket motorB, (c) saturn structures, and (d) the solar panels

Two methods of designing such joints for statie and fatigue loading are discussed.

The first is a semi-empirical approach yielding approximate results. The seeond

methcxi is accurate and computer-oriented. It makes use of a polynomial representa

-ti on of data end the theorem of sturm from the theory of equations, to determine

the optimum length of overlap for the joint.

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