REFERENCE

ARTMENT OF MMERCE

BUCATION

NBS TECHNICAL NOTE 728

*»»TI»0« f

U.S.

PARTMENT

OF

OMMERCE

-<k<L

ICO

U5753

y\c. 72.S

l<*7z

Torsional Instabilities

in Composite

and Composite-Reinforced

Aluminum-Alloy

Thin-Walled Cylinders
NATIONAL BUREAU OF STANDARDS

The National Bureau of Standards1 was established by an act of Congress March 3, 1901. The Bureau's overall goal is to strengthen and advance the Nation's science and

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jTal Bureau of Standards

172 -reL 24 1972

160

j

Torsional Instabilities

in Composite

and Composite-Reinforced

Aluminum-Alloy

Thin-Walled Cylinders

Donald E. Marlowe

Engineering Mechanics Section

Institute for Basic Standards

U«0. National Bureau of Standards

Washington, D.C. 20234

*"TedJcu^daJ vUrte via- lit

4** 0F %

o& If ^

O.% v^tlx ^

**»e«uAU of *

U.S. DEPARTMENT OF COMMERCE, Peter G. Peterson, Secretary

NATIONAL BUREAU OF STANDARDS, Lawrence M. Kushner, Acting Director,

Issued June 1972
National Bureau of Standards Technical Note 728

Nat. Bur. Stand. (U.S.), Tech. Note 728, 77 pages (June 1972) CODEN: NBTNAE

For sale by the Superintendent of Documents, U.S. Government Printing Office, Washington, D.C. 20402 (Order by SD Catalog No. C13.46:728). Price 70 cents.
CONTENTS

Page

1. INTRODUCTION 1

2. NOMENCLATURE 2

2.1 Units 2 2.2 Symbols 3

2.3 Notation 6

3. ANALYSIS 8

3.1 Elastic Properties of a Laminated Tube 8

3.2 Torsion Buckling 11

4. TORSION SPECIMENS 12

4.1 Aluminum-Alloy Torsion Specimen 12

4.2 Prepreg Materials 13

4.3 Specimen Designations 13

5. TORSION SPECIMEN PREPARATION 14

5.1 Aluminum-Alloy Tubes 14

5.2 Glass/Epoxy Composite Tubes 14

5.3 Boron/Epoxy Composite Tubes 15

5.4 Glass/Epoxy- and Boron/Epoxy-Reinforced

Aluminum-Alloy Tubes 16

5.5 Volume Fraction Measurements 16

5.6 Profile Measurements 17

6. MATERIAL PROPERTY SPECIMENS AND RESULTS 17

6.1 Material Property Specimens 17

6.2 Results 18

7. TORSION TEST PROCEDURE 18

7.1 Instrumentation of Test Specimens 18

7.2 End Fixtures 19

7.3 Testing Machine 19

7.4 Testing Procedure 19

8. RESULTS FROM TORSION TESTS 20

8.1 Elastic Behavior of Specimens 20

8.2 Torque-Strain Curves 20

8.3 Buckling Strength 20

8.4 Buckle Angle and Buckle Length 21

9. DISCUSSION 21

9.1 Elastic Torsion Behavior 21

9.2 Computed T-y Curves 21

9.3 Buckling Behavior 22

9.4 Post-Buckling Behavior 23

III
CONTENTS-Continued

10. CONCLUSIONS

11. REFERENCES

APPENDIX A MATERIAL PROPERTY TESTS

Page

24

25

66

IV
TORSIONAL INSTABILITIES IN COMPOSITE AND COMPOSITE-REINFORCED

ALUMINUM-ALLOY THIN-WALLED CYLINDERS

Donald E. Marlowe

The elastic buckling strength has been

determined for thin-walled aluminum-alloy

tubes fabricated with and without

unidirectional boron/epoxy and glass/epoxy

composite materials applied as reinforcement

to their outer surfaces. Three boron/epoxy

ply orientations were investigated. The

results of these tests have been compared with

the buckling strengths predicted by two

analytical techniques. It was found that

reinforcement of the metal tubes with an equal

thickness of the composite material increased

the buckling strength about threefold. The

effect on buckling strength of the ply angles

investigated is small when compared with the

overall effect of adding the reinforcement.

The analyses have approximately the same degree of accuracy as that generally

attributed to Donnell's treatment of isotropic

tubes.

Key words: Aircraft structures; boron/epoxy;

composite materials; reinforced aluminum;

stability; thin shells; torsion buckling.

1. INTRODUCTION

The problems associated with increasing the strength or stiffness

of aircraft structural components without increasing the weight of

material significantly have long concerned the design engineer. In

recent years the development of composite materials, such as boron or graphite fiber-reinforced epoxy, or metal-matrix composite material,

has given the designer additional latitude in the solution of these

problems. The use of components fabricated entirely from these

materials requires an extensive revision of conventional aircraft

fabrication techniques. One design concept involves the selective

reinforcement of the metallic part with filament-reinforced composite

materials instead of complete replacement of metallic components with

composite components. Some advantages of this concept are large

weight savings with minimal material useage, retention of current

joining and fastening technology, and maximum joining reliability and

minimum risk along with significant cost-effective weight savings.

Some experimental investigations of the benefits to be expected from

using composite materials in this way have been made (refs. 1, 2).

1
The primary purpose of the study reported herein was to

investigate the elastic buckling strength of a boron/epoxy-reinf orced

aluminum-alloy tubular component loaded in torsion. The strength was demonstrated by the testing of tubes fabricated with and without

reinforcement. Specimens used for this study consisted of 6061-T6

aluminum-alloy tubes reinforced on the external surface with

boron/epoxy, all-boron/epoxy tubes, aluminum-alloy tubes reinforced

with glass /epoxy, all-glass /epoxy tubes, and all-aluminum-alloy tubes.

The aluminum-alloy tubes and the all-composite tubes were designed

with a single diameter to thickness (D/t) ratio and in two lengths

such that the length to diameter (L/D) ratios are one order of

magnitude apart.

This investigation was conducted at the National Bureau of

Standards under the sponsorship and with the financial assistance of

the National Aeronautics and Space Administration, Langley Research

Center.

2. NOMENCLATURE

2.1 Units

The units used for physical quantities defined in this paper are given in both the U.S. Customary Units and in the International System

of Units (SI) . Conversion factors relating the two systems are given

in reference 3, and those pertinent to the present investigation are presented in the Appendix A3 of reference 3.
2.2 Symbols

A.., i, j = 1, 2, . . . , 6. Component of the in-plane stiffness matrix

J [A] for a laminate. A.. = A... Defined by eq (5). ij Ji

B.., i, j = 1, 2, . . ., 6. Component of the stiffness coupling matrix

-* [B] for a laminate. B. . = B... Defined by eq (5). ij Ji

D Midsurface diameter of tube.

D..j i, j = 1, 2, . . . , 6. Component of the flexural stiffness matrix

J [D] for a laminate. D. . = D... Defined by eq (5).

E

1 1 Young's modulus in the direction of the major in-plane axis of

material orthotropy.

E„„ Young's modulus in the direction of the minor in-plane axis of

material orthotropy.

G.. „ In-plane shear modulus, referred to the principal axes of material

orthotropy.

H Defined by eq (9).

h Thickness of laminate.

ij

>

i, j = x, y. Component of the plate curvature matrix [K] for a laminate. K..EK.. K..=K...

ii i ij Ji

Length of tube.

i, j = x, y. Component of the moment resultant vector [M] for a

J laminate. M. . = M.. M. . = M... Defined by eq (3). ii i ij Ji

N.., i, j = x, y. Component of the stress resultant vector [N] for a

J laminate. N. . = N.. N..=N... Defined by eq (3). ii i iJ Ji

n Number of laminas in a laminate.

Q.., i, j = 1, 2, . . . , 6. Component of the in-plane stiffness matrix

J [Q] for a lamina. Q.. = Q... Defined by eq (1).

Q.., i, j = 1, 2, . . . , 6. Component of the in-plane stiffness matrix

1J [Q] for a lamina, transformed to the plane orthogonal coordinate

system xy. Q.. = Q... Defined by eq (2).

R Midsurface radius of tube.

T Torque

t Thickness
t Nominal thickness of a composite lamina,

c

t. Actual thickness of the kth lamina.

k

u, v, w Displacements in the x, y, z directions, respectively.

x, y, z Orthogonal coordinates, generally in the directions of principal

axes of loading.

Y. . = e. . , i 4 j.

e.., i, j = 1, 2 or i, j =x, y. Component of the strain matrix [e]

ij in the plane orthogonal coordinate system ij . e.. = e..

£ . . = £ . . • IJ J 1

9 Angle between plane orthogonal coordinate systems xy and 12.

v Major in-plane Poisson's ratio.

12

E

v E v -=— Minor in-plane Poisson's ratio.

21 12 E n

E

I EE

11

E TTT ~ G

III 12

E TV

E V IV 12

a. ., i, j = 1, 2 or i, j = x, y. Component of the stress vector [a]

in the plane orthogonal coordinate system ij . a.. = a..

O . . = O . . .

t. . =o.., i 4- j . IJ IJ

ij; E 1 - v v 12 21

Subscripts

a Aluminum alloy,

avg Average.

c Boron/epoxy composite material,

cr Critical,

eff Effective.

4
i,j Coordinates in the general plane orthogonal coordinate system ij

k = 1, 2, . . . , n. Numerical sequence of a specific lamina in a laminate.

m Matrix material of boron/epoxy composite.

s = I, II, III, IV.

x, y Coordinates in the plane orthogonal coordinate system xy.

a = a, c, m Material.

1, 2 Coordinates in the plane orthogonal coordinate system 12.

Superscripts

o Midsurface.

* Reduced.
2.3 Notation

a. Laminate Elasticity

The Hooke's Law relationship for a single ply or lamina in the

principal material coordinate system is given by

or

- — a

1 "

a

2 =

T12

=

_ _

or

°i - Qn e i + Q12 e

2.

°2 = Ql2 e l + Q22 e 2

Tl2 = Q66 Y12

Q11 Q12 Qie

Q12 Q22 Q26

Ql6 Q26 Q66

[a] = IQ] [e]

- — £l

e 2

Y12

_

where

.1 = ^ ' Q

22

= -f- ' Q" " li

Y, 2 \2

and

66 12 i5 26

¥ = 1 - y Y , Y on = Y 22

12 21 21 12 -

E

ll

(1)

The Hooke's Law relationship for an arbitrary rectangular

coordinate system xy lying in the plane of the lamina and making an angle 6 with the principal material coordinate axes is given by (ref,

4):

_ —

a x

°v

=

^xy

_ —

Qn Q12 Qie

Q12 ^22 Q26

Q i6 ^26 Q6 6

x

£ y

Yxy

or [a] [Q] [e]

6
where

11 Q n

cos 4

9 + 2(Q 12 + 2 Q 66 ) sin 2

8 cos 26 + Q sin4

6

22

12

Q sin4

6 + 2 (Q + 2 Q ) sin 2

6 cos 2

9 + Q cos 4

6 11 12 66 22

(Q + Q - 4 Q ) sin2 co S 2 e + q ( sin 4 + cos 4 Q)

11 22 66 12

} = (Q +Q - 2 Q 19 - 2 Q K

) sin 2

6 cos 2

6 +

66 11 22 iZ bb

(sin 9 + cos 9 66

> = (Q - Q - 2 Q ) sin cos j +

16 11 12 66

(Q - Q + 2 Q ) sin 3 9 cos

12 22 66

j = (Q - Q - 2 Q ) sin 3 cos +

26 11 12 66

(Q - Q + 2 Q ) sin cos 3 12 22 66

(2)

The elastic behavior of a laminate or layup of plies is determined by

suitably combining the behaviors of the individual laminas. Consider

a rectangular coordinate system x, y, z where the origin of the system

is in the midplane of the laminate and z is normal to the plane. The

individual laminas are numbered 1, 2, . . . , k, . . ., n beginning

from the most negative value of z. Thus the coordinates which

determine the thickness of the kth lamina are z^ and z stress and moment resultants on the laminate are

k + 1 The

[N] =

xy

J 7. k = 1

dz

xy

[M] =

M

M

M

xy

k = 1

zk

J k + 1

- x^_

z dz,

(3)
Let the midsurface strains in the laminate be represented by

[e°]

and the plate curvatures by

[K]

X

y

Y°

. xy_

K

K

L xyj

Then, for small deflections, the constitutive equations for the

laminate, reference 4, are

where

N" A

I

, B e° = - - - - M B

1

, D K

-

1 _ _

A.

ij

ij

ij

E «ij'k (\ + i-\i

k = j n

2 £ <Vk (z

k + 1 - zk>

k = 1

1 n

3 E. «

±j

)k

(z3 + x - Z 3)

k = 1

(4)

(5)

3. ANALYSIS

3.1 Elastic Properties of a Laminated Tube

a. Elastic Behavior

Consider a laminated, thin-walled, circular tube. The origin of

the coordinate system x, y, z is taken at one end of the tube at the

mid- thickness . Coordinate x is axial, y is circumferential and z is radial, positive outward. The tube is subjected to axisymmetric

torsional loading through clamped ends such that one end is free to
rotate and to extend or contract. The boundary conditions for this

case, reference 5, are

u(0, y) = v(0, y) = w(0, y) = 3w(0, y)

3x

w(L, y) = 3w(L, y) = 3x

u(L, y) = constant

v(L, y) = constant

It is assumed that

N = and N = constant,

x xy

Then, following the analysis of reference 5, if it is further assumed

that

K = K = K =

x y xy

then it may be shown that

N

y

" 0,

that e X ' e y and Y xv are constant, denoting a uniform strain

distribution in the midsurface, and that

u° = po o n

e u x, v x w = e R. x xy y

The expression for the radial displacement w does not satisfy the

boundary conditions but it is claimed (ref. 5) that this is of little

consequence to results obtained at short distances from the

constrained end.

Under these conditions the constitutive equation, eq (4) reduces

to

— — An A 12 A 16 X

= A 12 A22 A 26

e y

hi xyA

16

A

26 He Y°

X

_ _
Letting the effective torsional modulus be

it is easily shown that

Gpff = (t )avg = N

yjy ° xy

Y

° hY

xy xvy

G

e ff

= A66 + All A|

6 - 2A 12 Alfi A?fi + A2? A? R A

2 - A A

( } A

12 AH

A

22

and that the extension-shear coupling factors are

£ x = A

12

A26 " A

22 A

16

Y° A A - A

2

Y xy

A

ll

A22 A

12

£ y _ A

12 A16 " A ll A

26

Yxy

A

11

A22- A

12 (7)

b. Rule of Mixtures

For the kth ply or lamina of a composite laminate, a correction

to the elastic constants must be made where the actual thickness of

the lamina, t, , differs from the nominal thickness, t . In this

k c report a simple rule-of-mixture correction is used, that is

lt -\ - wf + 's-w„ (8)

If a laminate is cured such that the thickness of each composite

lamina exceeds the nominal thickness , then each lamina can be

visualized as an effective laminate consisting of one reinforced ply

having the nominal thickness plus one ply of unreinforced matrix

material where the overall thickness of the combination equals the

actual thickness of the lamina. The values of A.,, eq (5), computed

for this effective laminate are identical to those^obtained using the

10
rule-of-mixtures correction. This correction is entirely valid,

therefore, insofar as eqs (6) and (7) are concerned. This argument

also holds for laminas which have thicknesses which are less than the

nominal one.

This approach is considered to be appropriate for the estimation

of the actual values of E,, and y . The error introduced by this

method of estimating the actual values of G, and E was quite

12 22 small and it will be shown that for these tests, the results were not

significantly affected.

3.2 Torsion Buckling

a. Torsional Buckling of Orthogonal-Anisotropic Cylinders

Hayashi, reference 6, proposed a theory of elastic torsional

buckling in which the critical torques are expressed as a function of

the extensional and bending stiffnesses of the tube.

From eq (4) ,

[N] = ([A] - [B][D_1 ][B])e° + [B][D_1 ][M]

Thus, if the extensional stiffness in the axial direction, A?, , is

defined as the ration N / e° when [M] is identically zero, then it may

be calculated from

.

[A*] = [A] - [B] [D-l] [B].

n a similar way the bending stiffnesses are given by

[D*] = [D] - [B] [A-l] [B]

For a tube of moderate length with clamped ends the critical

shear stress resultant is (ref. 6)

(N

yy ) cr

= 12

^22 [4.6 + A. 8 + 1.67K 372

]

where

A* (A A - A

2

)

i i n 12 12—

12 D*

2 A n A

22

(9)

11
and "moderate length" is defined as & <7.8H.

This theory was derived for specially orthotropic tubes under the

assumption that the tangent of the angle between the buckles and the

tube axis is small compared with unity. Solutions based on this

theory are compared with the experimental results.

b. Buckling of Generally Orthotropic Cylinders

The computer program, "Buckling of Generally Orthotropic

Cylinders", which was developed by Chao (ref. 7) was used to compare

the predicted buckling torques with the experimental results. In the

program, buckling loads are found for a multilayered cylindrical shell

loaded in combinations of torsion, axial compression and lateral

pressure. The theory treats orthotropic layers whose principal

material axes can be oriented in any direction. The shell is assumed

to be anisotropic with discrete longitudinal and rib stiffeners which

are closely spaced. The elastic properties of the stiffeners are then

considered to be smearable in the two directions over the shell. The

program seeks the solution with the lowest buckling strength by

iterating on the number of circumferential buckling waves.

4. TORSION SPECIMENS

Specimens tested in this investigation were intended to show the

advantages to be gained in the elastic buckling behavior of thinwalled aluminum-alloy tubes by reinforcing the external tube surfaces

with boron/ epoxy composite materials. This behavior was determined

for tubes of two lengths with a single ratio of D/t.

4.1 Aluminum-Alloy Torsion Specimen

The nominal outer diameter of all specimens is 6 in (15 cm) . The

specimens were tested with gage lengths of 20.0 in (50.8 cm) and 2.00

in (5.08 cm). The all-aluminum-alloy tubes have a nominal wall

thickness of 0.022 in (0.56 mm). The results of tests performed on these tubes were compared with results from similar tubes which had

been reinforced with glass /epoxy or boron/epoxy prepreg on the

aluminum-alloy tube. The thickness of the reinforcement was approximately equal to the thickness of the aluminum-alloy tube.

12
4.2 Prepreg Materials +

The boron/epoxy prepreg used for the reinforcement of the

aluminum-alloy tubes and for the all-composite torsion specimens was supplied by the AVCO Corporation. The boron filaments were nominally

0.004 in (0.1 mm) in diameter. The filament had a guaranteed average

tensile strength of 400,000 lbf/in 2 (28 x 10 8 N/m2

) and an average

tensile modulus of elasticity of between 55 and 60 x 10 6 lbf/in 2 (380

and 414 x 10 N/m ) . It was preimpregnated with Whittaker

Corporation's NAKMCO 5505 RIGIDITE epoxy resin system. The prepreg

was provided in two forms, 0.125-in (0.318-cm) tape and broadgoods.

The filament count for the tape material as reported by the

manufacturer was 26 for the 0.125-in (0.318 cm) tape width; and for

the broadgood material was 208 per inch of width (82 per cm) . The

broadgoods material was supplied with a 0.001 in (0.03 mm) type 104

fiberglass scrim cloth to facilitate handling. This material was

stored at 0°F (-18° C) prior to use. All specimens were fabricated

within seven months after receipt of the boron/epoxy prepreg.

The glass /epoxy prepreg used in the program was 3M Corporation's

SCOTCHPLY E-glass prepreg type 1002. This material has a guaranteed

tensile strength of 160,000 lbf/in 2 (11 x 10 8 N/m2

) and a tensile

modulus of 5.7 x 10 6 lbf/in 2 (39 x 10 9 N/m2 ). It was provided in 0.5

in (1.3 cm) and 6.0 in (15 cm) wide tapes. This material was also

stored at °F (-18° C) prior to use.

4.3 Specimen Designations

The system for designating specimens differentiates between

materials and specimen length, as follows:

AL series - all-aluminum alloy, long length (20 in, 50.8

cm)

AS series - all-aluminum alloy, short length (2 in, 5.08

cm)

BL series - all-b oron/ epoxy , long length

BS series - all-boron/epoxy , short length

GL series - all-glass /epoxy , long length

tCertain materials are identified in this paper by trade name in order

to adequately specify the experimental procedure. In no case does such

identification imply recommendation or endorsement by the National

Bureau of Standards, nor does it imply that the material identified is

necessarily the best available for the purpose.

13
ABL series - boron/epoxy-reinforced aluminum alloy, long

length

ABS series - boron/epoxy-reinforced aluminum alloy, short

length

AGL series - glass /epoxy-reinforced aluminum alloy, long

length

5. TORSION SPECIMEN PREPARATION

5.1 Aluminum-Alloy Tubes

All- aluminum-alloy tubes were machined from a single lot of 6-in

(15-cm) diameter, 0.12-in (0.32-cm) thick, 6061-T6 aluminum-alloy

seamless drawn tubing. The specimens were cut to length, then turned

on a lathe to an outer diameter of 5.950 in (15.11 cm). The

dimensions of these specimens are given in table 1.

The short tube specimen is shown in figure la. The inner surface

of the gage length of the specimen was turned on a lathe to an inner

diameter of 5.906 ± 0.002 in (15.000 ± 0.005 cm).

The long tube specimen is shown in figure lb. The specimen,

after the outer surface was machined, was clamped over its entire

length in a specially made jig. The inner surface of the tube was

then machined to a final diameter of 5.906 ± 0.002 in (15.000 ± 0.005

cm) in a boring mill.

5.2 Glass /Epoxy Composite Tubes

Several glass /epoxy composite tubes were fabricated and tested,

A soft wood mandrel covered with a heat-shrinkable fluorocarbon

plastic tube was used. The mandrel was laminated from four pieces of

redwood. After removal from the press, the wood was allowed to

stabilize for 48 hours before machining. Final finish was obtained

with 280-grit sand paper. A length of type FEP heat-shrinkable,

fluorocarbon tubing was shrunk into place covering the entire surface

of the mandrel (fig. 2)

.

Two techniques were used for laying up the composite tube. For

the tubes with a 90-degree ply-orientation angle, the mandrel was

gripped in the jaws of a lathe and the prepreg tape wound onto the

mandrel (fig. 3). For this purpose, 0.5-in (1.3-cm) tape was used.

The rotation of the mandrel was always in the same direction.

Succeeding plies were applied in the same manner after advancing the

lathe tool holder one-half the width of the tape. This insured that

the tape seams in adjacent plies were staggered. Plies were all

started from the same end of the tube.

14
Tubes with a O-degree ply orientation were laid up using a prepreg tape 6.0 in (15 cm) wide. The seams between the widths of the

tape were staggered in adjacent plies.

After the plies were laid up, a length of the fluorocarbon tubing was shrunk over the laminate, and a thermocouple was embedded between

the two layers of f lourocarbon. The part was then cured usitfg the

prepreg manufacturer's suggested temperature-time cycle.

The dimensions of these tubes are given in table 1.

5.3 Boron/Epoxy Composite Tubes

These specimens were fabricated using the technique? described

above for the manufacture of glass-epoxy tubes. For the majority of

the tubes with a 90-degree ply-orientation angle, boron/epoxy prepreg

tape of 0.125 in (0.32 cm) wide was used (fig. 4). This tape was

applied to the f luorocarbon-covered mandrel, taking ca/e to insure

that the seams between tapes did not coincide in adjacent plies. The

resulting ply angle was 89.5 degrees. One short tube w-th a 90-degree

ply-orientation angle, specimen BS-4, was fabricated Jy rolling a continuous 5-in (13-cm) wide strip of broadgoods material onto the

mandrel until four plies had been built up.

Tubes with a 0-degree ply orientation were laic up with a single

sheet of boron/epoxy prepreg material per ply (fig. 5) . As noted,

this material was supplied with a fiberglass scrim cloth carrier. The

plies were laid on the mandrel with the scrim clot on the outside.

Tubes with a 45-degree ply orientation were aid up using strips

of boron/epoxy prepreg material. Because of the iif ficulty of

wrapping wide sheets of material at 45 degree anles , the broadgoods

were slit into 3-in (8-cm) wide strips (fig. 6) . Care was taken to

insure that the seams of strips in adjacent layrs of prepreg did not

coincide.

After four plies of prepreg had been buil up, a layer of release

cloth was placed over the laminate (fig. 7). A layer of 0.004-in

(0.01-cm) fiberglass bleeder cloth was placec" over the release cloth

and sealed at the seam with mylar tape (fig. 8) . A station of

fluorocarbon tubing was then shrunk over thf laminate (fig. 9) , a thermocouple was embedded between the two layers of fluoi0carDon ancj the part was cured using the temperature-t:me cycle recommended by the

prepreg manufacturer. The dimensions of tie boron/epox> specimens are given in table 1.

Specimen BL-2A was salvaged from specimen BL-2 after ihe latter

tube had been tested and had failed locally near one end so *~-hat a 15-

in (38-cm) specimen could be recovered.

15
5.4 Glass/Epoxy- and Boron/Epoxy-Reinforced Aluminum-Alloy Tubes

The aluminum-alloy tubes which were intended for testing as reinforced tubes were chemically cleaned immediately prior to the

l^y-up process. The tubes were vapor degreased in trichlorethylene,

washed in a sodium hydroxide solution , deoxidized and rinsed in hot

water. They were dried in a forced air jet.

The composite layup techniques for these tubes were the same as those for the ill-composite tubes where the aluminum tube served as a non-removable nandrel. Specimens ABL-1, ABL-2 and ABL-3, the first

reinforced aluminum tubes fabricated, were cured without the bleeder

cloth under the heat-shrinkable tubing. The dimensions of these

specimens are shown in table 2.

5.5 Volume Fraction Measurements

After all meclanical testing had been completed, a sample of

boron/epoxy materia, was removed from fifteen tubes. A

photomicrograph of i cross-section of each sample was used to

determine volume fractions of epoxy and boron. These measurements

were made using the ferid-intersection technique commonly used in

sterology (ref. 8). ^he results of these measurements are shown in

table 3. Typical photomicrographs used are shown in figure 10.

As discussed abovL during the fabrication of the specimens,

three combinations of teinf orcement material and fabrication

techniques resulted in ttiree groups of specimens based on the volume

fraction measurements. Specimens were fabricated from broadgoods

material containing fiberglass scrim cloth both with and without the use of a fiberglass bleeW cloth in the curing cycle. Specimens were

also wound from narrow ta\e without scrim cloth but with a fiberglass

bleeder cloth. These thrfo layup techniques resulted in tubes with

differing ratios of boron \ilament to epoxy matrix. The tubes

fabricated with broadgoods Material having a scrim cloth, but without

a bleeder cloth, have a borVi fiber fraction of approximately 34

percent. Specimens using tlfe same broadgoods material, and also using

a bleeder cloth, have a boro\ fiber fraction of about 43 percent. The

tape wound, 90 degree specim&s fabricated without scrim cloth, but

with a bleeder clotb, have a Won volume fraction of about 55

percent. It should be recallei at this point that the fiberglass

scrim cloth constJ- tutes about V) percent of the thickness of a finished laminate. This alone Vends to a somewhat thicker laminate

and a lower boron /raction.

16
5.6 Profile Measurements

Surface imperfection measurements were made on seven aluminumalloy tubes. Five of these were tested with boron/epoxy

reinforcement. To make these measurements, the tube was supported at

its ends in the jaws of a lathe. A dial gage graduated in 0.0001 in

(0.00025 cm) per division was mounted in the tool holder and moved to

trace a path along a generator line of the tube. Measurements were

taken at 1-in (2.5-cm) intervals along the gage length of the tube

(fig. 11) and along five generator lines equally spaced around the

circumference of the tube. The results of the measurements are shown

in figure 12.

Elevations, or radial displacements from the straight generator

line, are measured relative to the elevation at the left end of the

No. 1 profile, i.e., relative to the first elevation point measured.

For example, the generator profiles for tube AL-3, figure 12a,

indicate a maximum radial displacement, from the first point on the

No. 1 profile, of 0.007 in (0.018 cm) at a location 15 in (39 cm) from

the left end of the tube. It would also be possible, with these

measurements, to indicate the amount of out-of-roundness of the tube

at any station along its length.

When these tubes were instrumented for test, the strain gage

rosettes were centered over the profile lines.

Figure 12 also indicates the profile on which the first

indication of gage reversal was observed. Gage reversal is defined as

a change in direction of a strain increment during a torque increment

experienced by either of the 45-degree gages of a three-gage

rosette. Where multiple profiles are indicated, gage reversal

occurred simultaneously in more than one rosette. The ABS-series

tubes failed catastrophically and an indication of buckling prior to

gross failure was generally not available. Correlation between the

surface imperfections and the location of the first buckle indication

was not evident from this work.

6. MATERIAL PROPERTY SPECIMENS AND RESULTS

6.1 Material Property Specimens

Material property tests for the determination of longitudinal

elastic modulus, transverse elastic modulus and Poisson's ratio were

.nade on all materials used in this program. The preparation of and

testing procedure for these specimens are described in the Appendix to

this report.

17
6.2 Results

The average material properties measured on the aluminum-alloy,

boron/epoxy, and glass /epoxy materials are shown in table 4. These

values of E^ , E 2 2» an^ v i2 were corrected for thickness variation

using equation 8 when they were used for calculation with the two

analytical methods of buckling analysis described in Section 3 above.

7. TORSION TEST, PROCEDURE

7.1 Instrumentation of Test Specimens

a. Strain Gages

Each of the twenty-nine tubular test specimens was gaged at the

midlength of the specimen. Five 45-degree rosette foil strain gages

having a gage length of 0.25 in (0.63 cm) were equally spaced around

the specimen. These rosettes were oriented to measure strains in the

axial direction and at 45 degrees to the axial direction. Tubes in

the AL, GL, BL and BS series were gaged on the outer surfaces (fig.

13). On the ABL, AGL, ABS and AS series specimens, the gages were

mounted on the inner surfaces (fig. 14) . Specimen AL-1, the first

tube tested, had gages in locations other then those mentioned above.

This specimen was instrumented in three belts of three rosette gages

each. These belts were located at 0.25, 0.50 and 0.75 of the length

(fig. 15). In addition, single gages were mounted near one end to

measure the end effects due to the end caps.

In addition to the above gage locations, several specimens were

tested with additional strain gages in an attempt to detect the

earliest indication of buckling and to check uniformity of strain

distribution. Specimens AS-1 and AGL-1 each had five single-element

gages mounted on the same belt as the five rosette gages and spaced

between them. These gages were oriented at 45 degrees, in the

direction of the maximum compressive stress. Several reinforced

aluminum-alloy specimens had one rosette gage mounted on the outside

of the tube back-to-back with a similar gage on the inner surface.

On tubes where the surface waviness profiles had been measured,

the rosette gages were centered on the generators along which the

measurements had been made. All gages were mounted using a cynoacrylate contact cement. Each gage was sealed from atmospheric

damage with a polyurethane coating.

b. Twist Measurements

Twist measurements were made on all specimens with the exception

of Specimen AL-1. Measurements of total twist were made at each end

of the gage length of the specimen. The difference between the two

18
measurements determined the net twist on the specimen. These

measurements were made using the reflected light from two mirrors

bonded to the specimen at the ends of the gage length. The light source and angle sensor was a Tuckerman optical strain gage

autocollimator. The autocollimator provided a source of plane,

parallel light which was reflected from the mirrors and read manually

on the scale of the autocollimator (fig. 16) . The smallest angle of

twist which could be resolved using this troptometer was one milliradian.

7.2 End Fixtures

The end fixtures used for each specimen are shown in figure 17.

These close-fitting end plugs were bonded to the inner surface of each

end of the tube specimen. There are approximately 27 in (174 cm ) of

bonded area at each end of the tube. Three epoxy systems were used at

different times during the program for this purpose. The first of

these is a room temperature-curing epoxy which was used where low

torsional loads were expected. The other two epoxy systems required

an elevated temperature cure cycle. This was achieved by the use of

infrared radiant lamps or close-fitting heater collars in the area to

be cured (figs. 18 and 19). The end plugs for tubes in the AL, GL,

BL, and BS series were bonded to the tubes with the specimens mounted

in the testing machine, after lead wires were attached to the strain

gages. All other specimens had one end plug attached before lead

wires were attached to the strain gages. The second end plug was

attached when the specimen was placed in the testing machine.

7.3 Testing Machine

The torsion testing machine which was used for these tests was calibrated with dead weight and a lever arm just prior to the first

torsion test.

The load errors of the testing machine over the range of loads used in

these tests did not exceed one percent. The alinement of the testing

machine was verified during the calibration procedure. It was observed that the axes of rotation of the two machine heads were

coincident within 0.001 in (0.003 cm). The maximum axial force

introduced into the specimen, resulting from machine friction in the

sliding spindle of the loading head, was measured to be 45 lbf (200 N)

,

7.4 Testing Procedure

After a specimen was bonded to its end plugs in the testing

machine, the strain gage leads were wired to the strain measurement

circuits and the mirrors and autocollimators of the troptometer were

alined. Loads were applied at a constant rate in each load increment.

Loading was stopped periodically and load was maintained while strain

and twist measurements were recorded. The magnitude of the load

19
increment between successive sets of readings was decided on the basis

of the specimen behavior during the previous increment. The direction

of loading was generally the same for all specimens. This was chosen

so as to cause a tensile stress in the filaments for tubes fabricated

with a 45-degree ply-orientation angle. Thus, the specimens with a 90-degree filament orientation were loaded in the direction which

"tightened" the wrap of fibers on the tube. The exceptions to this

direction are as follows: the specimen pairs ABL-2 and ABL-4 were

loaded in opposite directions and specimens AS-1 and AS-2 were loaded

in the direction of ABL-2, which was opposite to all other specimens.

8. RESULTS FROM TORSION TESTS

8.1 Elastic Behavior of Specimens

The elastic properties of the tubes tested are shown in table 5.

e + e° x y

This table gives the values of G

£££ and 2Y

° » ^e avera8e of the

xy

extension shear coupling factors, which were predicted by the analysis

and measured during tests. The experimental moduli and average

coupling factors shown were determined from the data of the first four

torque increments applied in the linear elastic range of each test.

8.2 Torque-Strain Curves

The torque-strain curves for all tubes tested are shown in figure

20a thru 20i. The shear strains computed from the rosette

measurements at the center of the specimen and averaged over the five

rosettes, and the strains computed from the twist measurements of the

mirror-auto collimator troptometer, are both shown.

8.3 Buckling Strength

The maximum torques and the torques at which gage reversal

occurred are summarized in table 6. Included in this table are the

values of buckling torque predicted by the Chao and Hayashi analyses

used and the ratios of torque at strain reversal to predicted torque

for the two analytical programs. The elastic material properties used

in the analyses to predict the buckling are those presented in table

4. In the case of the Chao program, these were adjusted for thickness

variations from the nominal. The values of G used in the Chao

12

program are the averages of Ge£f measured on the AL, BL, and GL

specimens, respectively, corrected for variations from nominal ply

thickness using the rule of mixtures (eq. 8).

Photographs of typical failed specimens are shown in figures 21a

through 2 In.

20
The all-boron/ epoxy composite tubes which were fabricated with a 90-degree ply orientation failed by matrix shear between adjacent

filaments. The failure torques are shown in table 5.

8.4 Buckle Angle and Buckle Length

Measurements were made on the tested specimens of the angle

between the axis of the tube and the line of maximum buckle depth.

Measurements were also made of the length of tube which showed skin

distortions due to the buckle pattern. The results of these

measurements are shown in table 7. Also shown are the buckle counts

predicted by the Chao analysis and from experiment.

9. DISCUSSION

9.1 Elastic Torsion Behavior

The results shown in table 5 indicate good agreement between the

predicted and experimental values of G ff (eq 6) and the extensionshear coupling factors (eq 7) . This agreement tends to justify the

assumptions made in the elastic analysis, i.e., the axial force on the

tube and the plate curvatures are zero (Nv = 0, K . • = 0).

The agreement between the two methods of measuring shear strain

(fig. 20) shows that y was essentially uniform over the tube length.

In reference 5, Whitney and Halpin observe that the radial

displacement, w = £°R, does not satisfy the boundary conditions of the

clamped specimen. They claim that this is of little consequence in

results obtained at short distances from the ends. This assertion

appears justified by the agreement between the shear strains measured

over the entire gage length and those measured at the center of the

specimen. This assertion appears to be valid for both long and short

specimens

.

9.2 Computed T-y Curves

The torque-shear strain behavior of the short reinf orced-tube

specimens, Series ABS , as can be seen from figure 20e. suggests that

in all of these specimens the shear yield strength of the aluminum

alloy had been exceeded before buckling occurred. An attempt was made

to calculate the torque-shear strain relationship using data available

from the all-aluminum-alloy and the all-boron/epoxy specimens. For

this calculation it was assumed that the shear strain in the aluminum

alloy is equal to the shear strain in the boron/epoxy. The fraction

of the total torque carried by each of the components is then a function of the cross-sectional area and the shear stress-strain

relationship of the material. These calculated curves are given in

figure 22. In the case of tubes reinforced with 0-degree and 90-degree

21
boron/epoxy plies, (figs. 22a, 22c), the differences between the

calculated and experimental yield stresses are believed to be related

to residual fabrication stresses in the specimen and overaging in the

aluminum alloy due to the composite cure cycle. The residual stresses

are caused by the differences in thermal expansion between the

aluminum alloy and the boron/epoxy. In the case of the 45-degree

reinforced tube, figure 22b, the large difference between the elastic

slopes is a result of the coupling between shear and extension that

exists in tubes reinforced with this orientation. In figure 22c, the

boron stress-strain data was extrapolated to produce the dashed

portion of the curve shown. As can be seen from table 5, the

extension-shear coupling factor for these specimens is large when

compared to factors for the other configurations tested. As the

specimen is twisted, the aluminum-aHoy tube does not allow the

boron/epoxy laminas to extend or contract freely. As a result, the

shear strain is constrained and the boron/epoxy laminas are stiffer

than they would be if they acted alone. Also, the specimen is stiffer

than the tubes where the coupling factor is approximately zero. Similar behavior would be expected for all ply orientations other than

and 90 degrees.

9.3 Buckling Behavior

A comparison of results for predicted and experimental buckling

strengths from table 6 indicates fair agreement. The two analyses

appear equally capable or incapable of predicting buckling behavior

for these particular layups. However, Hayashi is not suitable for

more complex layups and does not account for effects of stacking

sequence, direction of loading, etc. Except for the ABS series tubes

which yielded and the tubes where the material sheared before buckling

occurred, both analyses have approximately the same degree of accuracy

as that generally attributed to Donnell's treatment of isotropic

tubes. It should be noted that presently available theories do not

account for the effects of variation in surface imperfections on torsional buckling strength, as do theories of compression buckling of

imperfect shells (ref. 9). There is some evidence, however, (ref. 10)

that the long tubes tested in this program were insensitive to surface

imperfections.

Further examination of table 6 indicates some other differences

in the three behaviors (two predictions and one experimental) for the

reinforced tubes. For the long tubes (ABL series), the Chao program

predicts that the 90-degree orientation is strongest, followed by the

45-degree and the 0-degree orientations, in that order. The Hayashi

theory predicts that the 90-degree orientation is strongest, followed

by the 0-degree and the 45-degree orientations. Experimentally, the

45-degree orientation is the strongest, followed by the 90-degree and

the 0-degree orientations. Similar differences can be seen in the

short tubes (ABS series) where the order from strongest to weakest for

the Chao theory is 45, 0, 90 degrees; for the Hayashi theory it is 90,

45, degrees; and from the experiments 45, 90 degrees. The

22
experimental differences between these three orientations, however,

are small relative to the increase in strength resulting from adding

reinforcement. For the ABL series, for example, the buckling strength

increases more than three-fold as a result of adding reinforcement

while the differences between the three ply orientations is only about

17 percent.

The principal source of error in the two existing theories of

torsion buckling used in this program is believed to be in the

assumptions made concerning buckle pattern. If, the buckle angle is

defined as the angle between the X axis of the tube and the line on the surface of minimum radial distance from the tube axis, then both

of these analyses assume small buckle angles. This assumption is

explicit in the Hayashi equations and is implicit in the Chao analysis

where the prediction of skin buckling is governed by Donnell's

approximations. From table 7 it can be seen that this assumption is

generally not valid. In the case of isotropic tubes, the buckling

strength is apparently not sensitive to this parameter. In the case

of strongly orthotropic tubes, however, the buckling strength should

be very sensitive to buckle angle. Table 7 also shows the buckle

length relative to the tube length. These specimens have lengths in

the region where the buckling behavior, as shown by the Hayashi

analysis, is influenced by the end conditions. As a result, it was expected that the buckling behavior in the two lengths of specimens

tested would be similar, i.e., that the buckles would extend the full

length of the specimen. This was true only for the short tube length.

The two methods of analysis predicted only the elastic buckling

strengths of the configurations tested. However the all-composite

tubes, except for specimens BL-1, BL-3 and GL-1, failed by shear of

the epoxy matrix. The differences in behavior of specimens BS-2 and

BS-4 are noteworthy. Specimen BS-2 was tape wound, as were most of

the 90-degree ply tubes. BS-4, however, was fabricated by rolling one continuous strip of broadgoods material onto a mandrel. This

broadgoods material was supplied by the manufacturer with a 0.001-in

(0.003-cm) fiberglass scrim cloth. The narrow tape did not have the

scrim cloth. The apparent effect of the scrim cloth was to increase

the material shear strength of the laminate by more than 40 percent.

9.4 Post-Buckling Behavior

As shown in figure 20, only a few tubes were tested beyond

initial buckling. In general it was not possible to determine the

average strains in the specimen after buckling because the high

localized strains which occurred at buckling destroyed many of the

rosette gages and also caused the range of the troptometers to be

exceeded. In such cases no further strain readings were obtained.

Unreinforced specimen AL-3 and reinforced specimen ABL-3 were tested

into the post buckling region and their behaviors are shown in figure

20a and 20d. As a reinforced tube buckled, the stiff boron/epoxy

laminate was unable to conform to the buckled shape of the aluminum

23
tube. This resulted in large areas of delamination between the

laminate and the aluminum. At the sharp edges of a buckle this also

caused many broken boron filaments. As a result, the load-carrying

capacity of the reinforced tube was reduced by approximately 50

percent. Additional loading of the specimen would have served little

purpose except to increase the delaminated areas of the tube. It may

be possible in future testing of reinforced tubes to prevent much of

this premature delamination by introducing a layer of epoxy adhesive

between the metal tube and the composite laminate.

10. CONCLUSIONS

Based on the work covered by this report, the following

conclusions are drawn:

1) Laminate analysis adequately predicts the elastic

behavior of composite-reinforced aluminum-alloy torsion

tubes

.

2) Existing buckling theories for anisotropic tubes have

approximately the same degree of reliability as Donnell's

equations for isotropic tubes for predictions of elastic

b uckl ing to rques

.

3) The 0.001-in (0.003-cm) fiberglass scrim cloth supplied

by the manufacturer with the boron/epoxy broadgoods

material contributes significantly to the material shear

strength of the cured laminate.

4) The post-buckling properties of boron/epoxy reinforced

tubes are seriously degraded by delaminations of the

reinforcement at buckling. The use of an additional layer

of adhesive between the aluminum tube and boron/epoxy

composite may improve the post buckling behavior.

5) Buckling strength increases as a result of adding

reinforcement, but the differences in strength between the

three reinforcement orientations tested (0, 45 and 90

degrees) are small relative to the overall effect of adding

reinforcement. Other more optimum tube layups may show

significant improvements in buckling strength.

Mr. R. E. Snyder and Mr. G. F. Sushinsky gave valuable assistance

in the fabrication and testing of these specimens.

24
11. REFERENCES

1. Zender, George W. and Dexter, H. Benson: Compressive Properties

and Column Efficiency of Metals Reinforced on the Surface with

Bonded Filaments. NASA TN D-4878, 1968.

2. Dexter, H. Benson: Compressive and Column Strengths of Aluminum

Tubing with Various Amounts of Unidirectional Boron/Epoxy

Reinforcement. NASA TN D-5938, 1970.

3. ASTM Designation E380-70, Standard Metric Practice Guide,

American Society of Testing and Materials, Philadelphia,

Pennsylvania.

4. Ashton, J. E. , Halpin, J. C. and Petit, P. H. : Primer on Composite Materials: Analysis. Technomic Publishing Co.,

Stamford, Connecticut, 1969.

5. Whitney, J. M. and Halpin, J. C: Analysis of Laminated

Anisotropic Tubes Under Combined Loading. Journal Composite

Materials, Vol. 2, No. 3, pp. 360-367, July 1968.

6. Hayashi, T.: Torsional Buckling of Orthogonal-Anisotropic

Cylinders. Proc. 8th Int. Cong, on Theo. and Applied Mechanics,

pp. 189-190, 1953.

Chao, Tung-Lai: Minimum Weight Design of Stiffened Fiber

Composite Cylinders. AFML TR 69-251, September, 1969.

Underwood, E. E. : Stereology, The Quantitative Evalution of

Micros tructures. Journal of Microscopy, Vol 89, Part 2, pp. 161-

180, April 1969.

Arbocz, J. and Babcock, Jr., C. D. , Experimental Investigation of

the Effect of General Imperfections on the Buckling of

Cylindrical Shells. NASA CR-1163, September 1968.

10. Stern, M. , Some Recent Advances in the Investigation of Shell

Buckling. AIAA Journal, Vol 6, No. 12, pp. 2339-2345, December

1968.

25
Table 1 - Dimensions of Aluminum Alloy and All Composite Material

Torsion Specimens

Material

type and

specimen No. Gage length

Mid surface

diameter

Average

thickness

Filament

orientation (a) xn cm in cm in cm deg

Aluminum

AL-1 20.0 50.8 5.928 15.057 0.022 0.056 _ AL-2 20.0 50.8 5.918 15.032 .032 .081 - AL-3 20.0 50.8 5.928 15.057 .021 .053 - AS-1 2.00 5.08 5.928 15.057 .022 .056 - AS2

2.00 5.08 5.928 15.057 .022 .056 - AS3

2.00 5.08 5.905

Glass

14.999

/epoxy

.045 .114

GL-1 20.0 50.8 6.040 15.342 0.021 0.053

GL-2 20.0 50.8 6.040

Boron

15.342

/epoxy

.021 .053 90

BL-1 20.0 50.8 6.104 15.504 0.022 0.056

BS-1 2.00 5.08 6.074 15.428 .023 .058

BS-1A 2.00 5.08 6.074 15.428 .023 .058

BS-1B 2.00 5.08 6.074 15.403 .023 .058

BL-3 20.0 50.8 6.064 15.403 .023 .058 45

BS-3 2.00 5.08 6.058 15.387 .023 .058 45

BL-2 20.0 50.8 6.060 15.392 .018 .046 90

BL-2A 15.0 38.1 6.060 15.392 .018 .046 90

BS-2 2.00 5.08 6.030 15.316 .018 .046 90

BS-A 2.0 5.08 6.008 15.260 .022 .056 90

(a) Filament orientation is measured with respect to the X axis,

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27
Table 3 - Results of Volume Fraction Measurements

Ply Boron/epoxy

Volume fraction

Tube Epoxy + scrim

No. angle thi ckness Boron + void

Degrees in cm percent percent

ABL-1 0.025 0.064 32.7 67.3

ABL-3 0.025 0.064 36.4 63.6

ABL-2 90 0.022 0.056 52.8 47.2

ABL-4 90 0.020 0.051 56.5 43.5

ABL-5 45 0.024 0.061 45.0 55.0

ABL-6 45 0.023 0.058 45.8 54.2

ABS-3 0.022 0.056 43.3 56.7

ABS-4 0.023 0.058 40.8 59.2

ABS-2 90 0.020 0.051 61.9 38.1

ABS-7 90 0.015 0.038 58.5 41.5

ABS-5 45 0.022 0.056 43.4 56.6

ABS-6 45 0.023 0.058 42.5 57.5

BL-2 90 0.018 0.046 56.3 43.7

BS-2 90 0.018 0.046 50.6 49.4

BS-4 90 0.022 0.056 35.1 64.9

28
O

•HP

rH 03 n) a) pi ^-N a d CO •H cO CO v—

U H- 0~) rH LO C a, a on CN CM

•H

O • • •

5-<

d co o

P-l -rH

W • •rH u o QJ Ph

enO

5-i

4-1 CJ

cfl M-ld

rH

d

N cO e X B s r~- cu

CO

O t-^ cys 4J

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4->

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a

g

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O

a)

d Cu

S-i •H

X QJ •H ^^ 5-J T3 n-t CN m <r

x> > m • CO

QJ rH o CN rH •H ,d rH

4-1 4-1 d a X

•H

B

CO <Tl cO 3 o 5-1 rH rH oo 2 N o

T3 e X 5-1 O CX S co s o <J\ <r

•H r-~ rH ro CO

co 3

CN •H

_ ^

60 4-1 CO a 5-1 CD 3 o d

•H o •r-] •H

4-1 >H cfl in

5-1 S O T3)

CD

N rH QJ a. Pi 5-( o •H X 3 n \ co

PL|

m CN o cO x • • QJ rH rH o rH u~l B

cO rH ro

•H 4-1 H O

0)

d

-U

od CO £ CO

0)M ^

cfl 4-1

5-1 >^ 5-i QJ o QJ > rH a, < rH rH >> > o

tt) crj

X

X 5-i 1 •H o o a.

5-1 6 a

a

<- QJ

4-1

dd

QJ QJ CO •H

QJ cO •H

a co ,C| rH £ B o co H

XI 3 5-1 cO ^—

v

CO rH o rH cO H < P3 O ^^

29
Table 5 - Results of Elastic Behavior Measurements

Experimental

Coupling

Ply

angle

Laminate analy sis coefficient

6 x

+ *y

2y

Shear i

Coupling coefficient

Tube Shear modulus

ex/ Y

e y/v

x + v aodulus

No. U eff

G eff °eff

B.ff ' degrees lbf/ in2 N/m2 lbf/ in2 N/m2

AL-1 _ 0.000 0.000 0.000 3.9 x 10s 27 x 10s 0.016 3.7 x 10s 26 x 109 AL-2 - 0.000 0.000 0.000 3.9 27 -0.005 3.9 27

AL-3 - 0.000 0.000 0.000 3.9 27 -0.002 4.0 28

AS-1 _ 0.000 0.000 0.000 3.9 27 0.003 3.5 24

AS-2 - 0.000 0.000 0.000 3.9 27 0.000 3.8 26

AS-3 - 0.000 0.000 0.000 3.9 27 -0.008 4.0 28

ABL-1 0.000 0.000 0.000 2.1 15 0.013 2.0 14 ABL-3

9 J(b)

0.000 0.000 0.000 2.1 14 0.003 2.1 14 ABL-2 0.002 -0.005 -0.002 2.2 15 -0.003 1.9 13 ABL-4 0.002 -0.006 -0.002 2.3 16 -0.004 2.4 16 ABL-5 45 -0.209 -0.209 -0.209 4.1 28 -0.211 4.2 29

ABL-6 45 -0.209 -0.209 -0.209 4.2 29 -0.214 4.2 29

ABS-1 0.000 0.000 0,000 2.3 16 -0.002 1.9 13 ABS-3 0.000 0.000 0.000 2.2 15 0.002 2.3 16 ABS-4 % 90<b> 0.000 0.000 0.000 2.2 15 -0.012 2.1 15 ABS-2 0.002 -0.006 -0.C02 2.3 16 0.002 2.4 17 ABS-7 9000 6.002 -0.006 -0.002 2.6 18 -0.034 2.8 19 ABS-5 45 -0.204 -0.205 -0.204 4.3 30 -0.220 4.1 28

ABS-6 45 -0.209 -0.209 -0.209 4.2 29 -0.224 4.5 31

BL-1

9 S<b> 0.000 0.000 0.000 0.59 4.1 -0.021 0.60 4.1BL-2 0.004 -0.008 -0.002 0.65 4.4 -0.059 0.80 5.5 BL-3 45 -0.410 -0.410 -0.410 2.0 14 -0.380 2.0 14

BS-1 0.000 0.000 0.000 0.58 4.0 -0.008 0.56 3.9 BS-1A 0.000 0.000 0.000 0.58 4.0 0.000 0.66 4.5

BS-1B 0.000 0.000 0.000 0.58 4.0 0.027 0.62 4.3

BS-2 90<b> 0.004 0.008 0.002 0.64 4.4 -0.023 0.66 4.5 BS-4 90 0.000 0.000 0.000 0.58 4.0 0.009 0.54 3.7

BS-3 45 -0.410 -0.410 -0.410 2.0 14 -0.400 2.1 14

GL-1 0.000 0.000 0.000 0.44 3.0 0.013 0.56 3.9 GL-2 90 0.000 0.000 0.000 0.44 3.0 -0.028 0.50 3.5

AGL-1 C.000 0.000 0.000 2.1 15 0.001 2.3 16

BL~2A<a) 90TM 0.000 0.000 0.000 0.65 4.1 0.015 0.84 5.8

(a)

(b)

See specimen BL-2. Specimen BL-2A has a length of 15 in.

Nominal 90 degree ply orientation. These specimens are tape wound. Actual ply orientation angle,

89.5 degrees. These specimens do not have a 0.001-in (0.003-cm) scrim cloth per ply.

30
O O <H

o o o o o 1*"- ON U1 no o>

r-* r-. i-< OJ <fr <U aj CO M-. H-i '

o o o o o o o

o C") o o O O O cu o o o o CO en

nO p* ON o

OJ

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o o o o o o o o o

<T m rvi o no o ON

CO OJ

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A.

en OJ

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o o o o o O o o o

o o o O o o o o o

<-" <t o m o o CO CC <r

r-. r-. ON o

oj m

OJ no

no

OJ r-J en

o o o o o o

no no r-- r-1 i-t o

•-< CM OJ OJ en en en

o o o o o o o o o o o o

m co m o o o

o o o o

o o o o o o

. <t no o -j- \d oj N CO r^ (M H S

<t >t ^ -J vO iO

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s s s s s s s s s s m in oj o <t en 888 888 OJ OJ en O m oj en .-i r-t 88S8SSS 88 8

co en co no no vo

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CO vO NO sO vO CO nO o o o o o o o

en r-t m oj oj oj 888888

en rsj OJ OJ OJ en oj 8888888

33 <>> J, J. ,i i J, Jj

•** < -t: p; pa po pa

en oj

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I

I I I I L kJ ^J t-1 M M r-; i/j vj VJ VJ vj vj vj | i i^S«« 9933SS 9SS99S9 3 ti

•H 5

£ 5

31
Table 7 - Results of Buckle Angle and Buckle Length Measurements

m 1- t»i /-. Buckle count „ , . _ . - Tube Ply Gage t^t Buckle Buckle

No. angle length Predicted v Measured angle length

degrees in cm degrees in cm

5 (c)

5 5< a> 5 5

12 12

12 12

9 (c)

5 5< a)

5 5

4 (c)

4 (c)

4 5< a> 4 4

10 (c)

10 9

10 9^ aJ

9 11

10 9

7 13

7 13

7 6

4 (c)

14 12 < a) 7 23< a)

6 7

5 5(a)

fa") v 'Estimated from incomplete buckle pattern.

'According to Chao program.

(c)'Testing discontinued when first buckle appeared.

No buckle visible for measurement after test completed.

AL-1 - AL-2 - AL-3 - AS-1 - AS2

- AS-3 - ABL-1

ABL-3

ABL-2 90

ABL-4 90

ABL-5 45

ABL-6 45

ABS-1

ABS-3

ABS-4

ABS-2 90

ABS-7 90

ABS-5 45

ABS-6 45

BL-1

BL-3 45

BS-1B

BS-3 45

GL-1

AGL-1

20 51

20 51

20 51

2 5

2 5 2 5 20 51

20 51

20 51

20 51

20 51

20 51

2 5

2 5

2 5

2 5

2 5 2 5 2 5 20 51

20 51

2 5

2 5 20 51

20 51

24 8 20

24 13.5 34

21 10.5 27

52 2 5

53 2 5

(d) (d) (d)

15 12.5 32

13 12.5 25

35 10 32

35 11 28

45 8 20

45 18 46

(d) (d) (d)

58 2 5

57 2 5

48 2 5

50 2 5 45 2 5

45 2 5 20 (d) (d)

45 (d) (d)

27 2 5

45 2 5

(d) (d) (d)

20 10.5 27

32
022..000

.gure 1. Aluminum—alloy tube specimens. All dimensions are given in

inches (1 _!n = 2.54 cm).

33
Figure 2. Wood mandrel covered with heat shrinkable tubing.

Figure 3. Tape winding glass /epoxy tube,

34
Figure 4. Tape winding boron/epoxy tube

Figure 5. Lay-up of 0-degree reinforced aluminum specimen,

35
Figure 6. Lay-up of 45-degree specimen.

Figure 7. Placement of release glass cloth over lay-up,

36
Figure 8. Placement of glass bleeder cloth over lay-up,

Figure 9. Installation of heat shrinkable tubing over the part prior

to cure cycle.

37
Figure 10a. Specimen ABS-5 (lOOx)

.

Figure 10b. Specimen ABL-3 (lOOx)

38
Figure 10c. Specimen ABS-7 (lOOx)

Figure 11. Set up for profile measurements,

39
z

LU

LUu

<

<

Of

SPECIMEN AL-3

0.005

• 0.005

0.005

e ® ® © © ®

is e

© © © <*©©©©©

) © o _a 2_

0.005|-

0.005(10 © ©

0.005 .

-fi fi a 2 2_ © © © e

0.005 ©® a e9° e e

© Q © © ©

0.005

005|-

(

0.005

1 19 B ©

• _1 _l L _1_ l_ 1 S s _l_

©

J ©_l © ©

©

_l ©

_1_ © ©

—1 ©

-J

10 15 TUBE LENGTH, in

20

SPECIMEN ABL-5

0.005

- 0.005

t

° e « © 5

1

<s ©©a 9ee ®® 8 °e ® s

U

<

<

Q

<

a:

0.005 —©2

0.005

© © © © e

© 9 © © © © 9 e © © 6

0.005

0005

0.005

(i—9 1* 9

9 © © © e

© © e ® °

e eoe©©

0.005 o©©e°<» 0seo ® es ©©° o ©©

0.005

0.005

<i

»- 9 9 ©

w

9 © ©

_l I I I I I l_l ' ' 10 15 TUBE LENGTH, in

9 a s » * a X-

•^ First buckle as indicated by strain gage reversal

Figure 12a. Surface imperfection profile measurements.

40
0.005 - SPECIMEN ABL-6

0.005

o o

© GOO ©000 o © ® a

0.005

~ © ©

0.005 - © © o © © © © ©

o © o < 0.005

• 0.005

Q 0.005 <

1 1—o—©- © © © g e © s ©see

0.005 - oooooooeoo

0.005

1 T

8 © © o a u o © © o

0.005 • » , l_ 1_ , L - , , 1 i ! | 1 1 1 10 15 TUBE LENGTH , in

20

SPECIMEN AS -2 SPECIMEN ABS-3

0.002

•0.002 -

0.002 - z

UJ - 0.002 f- LUU

<-J 0.002 Q -0.002

0.002

•0.002

0.002

- 0.002

1 2 TUBE LENGTH , in

0.002

- 0.002

c

0.002 z

' UJ - 0.002

3.UJU

<

Q.

Q

<

ae.

0.002 -

- 0002|-

0.002

i -0.002

0.002

-0.002 €> _e a_

1 2 TUBE LENGTH , in

-^* First buckle as indicated by strain gage reversal Figure 12b. Surface imperfection profile measurements (continued)

41
SPECIMEN ABS-4

0.002

- 0.002

0.002 z^ - 0.002 •

<—ia. 0.002

0.002

9 0.002

0.002

0.002 -

il- -0.002 -

1 2 TUBE LENGTH, in

SPECIMEN ABS -6

0.002

-0.002

0.002 - z

111 ^ -0.002h

114 U

<

i 0.002 - " -0.002 <

Q

< 0.002

06 -0.002

002

( - 0.002 - X

-e 1

-»2

-• 3

Figure 12c

1 2 TUBE LENGTH, in Surface imperfection profile measurments (continued)

42
Figure 13. Typical strain gage installation on exterior surface

of a tube.

Figure 14. Typical strain gage installation on interior surface

of a tube.

43
Figure 15. Typical strain gage installation on specimen AL-1.

Figure 16. Troptometer set-up showing auto-collimators and

mirrors.

44
7

A

I 0.81

V H

'

A. Nominal 6 in. - Machined to fit individual specimen

Figure 17. End fixtures. All dimensions are given in inches (1 in =

2.54 cm)

45
Figure 18. Radiant heat lamps used to bond end caps to specimen.

Figure 19. Heated collars used to bond end caps to specimen,

46
o u

CO

00d

d

•od

ind o

gnoaoi

47
22x10"

2/

uua e

a- I o z

xl(f

2.2

2.0

1.8

1.6

1.4

1.2

1.0

0.8

0.6

0.4

0.2

L

STANCE STRAIN GAGE

TOMETER

SHEAR STRAIN Figure 20b. Torque-shear strain curves for specimens AL-2, AS-1 and AS-2

48
i.OxlC?

7.0

g E

6.0 o z

5.0

4.0

3.0

2.0

W

70x10 -

RESISTANCE STRAIN GAGE - TROPTOMETER

SHEAR STRAIN

Figure 20c, Torque-shear strain curve for specimen AS-3.

49
"o

u !-i9l

iuN

anoaoi

50
X

"!-W l to<cI co<

CII to

pa<

CNII CO

PQ<

D.O

U-l

C/) >Uouu

<y .c

U)I <U3

cruoHop

00

X o "7CO ui-n

anoaoi

51
7.0x10"

6.5

6.0

5.5 -

5.0

4.5 -

P Z

3.5

3.0-

2.5

2.0

1.5

1.0 -

0.5

L

64x10 -

48 -

32 -

24 -

16 _ fABS-5

RESISTANCE STRAIN GAGE

TROPTOMETER

I ABS-6

0.004

SHEAR STRAIN

Figure 20f. Torque-shear strain curves for specimens ABS-5 A ABS-6

52
z<x

to

-£-o d

d

"!-jqi

UiN

gnoaoi

(U3

53
o

"! -jqi

uj-n

anoaoi

54
i.ixio

3

1.0

0.9

0.8

0.7

§ i 0.6

0.5

0.4-

0.3

0.2

0.1

10x10

I 2

RESISTANCE STRAIN GAGE

SHEAR STRAIN

Figure 20i. Torque-shear strain curve for specimen AGL-1.

55
Figure 21a. Typical failure of AL series specimen.

Figure 21b. Typical failure of AS series specimen.

56
Figure 21c. Buckle failure of ABL series specimen reinforced

at 0^ degree ply angle.

Figure 21d. Buckle failure of ABL series specimen reinforced

at 90 degree ply, angle.

57
Figure 21e. Buckle failure of ABL series specimen reinforced

at 45 degree ply angle.

Figure 21f. BufcMe failure of ABS series specimen reinforced

at a degree ply angle.
'

Figure 21g. Buckle failure of an ABS series specimen reinforced

at a 90 degree ply angle.

Figure 21h. Buckle failure of an ABS series specimen reinforced

at a 45 degree ply angle.

59
Figure 21i. Buckle failure of BL series specimen with all plies

oriented at degree.

Figure 21j . Material failure of BL series with all plies

oriented at 90 degrees.

60
Figure 21k. Material failure which occurred after buckling in

a BL series specimen with all plies oriented at

+45 degrees.

Figure 211. Material failure in a BS series specimen with all

plies oriented at 90 degrees.

61
Figure 21m. Buckle failure in AGL series specimen reinforced

at a ply angle of degrees.

Figure 21n. Buckle failure in GL series specimen with ply

angle of 90 degrees.

62
5.0x10

4.5

46x10

44

4.0

3.5-

a.o

3.0-

2.5

2.0-

1.5 -

1.0-

0.5

42

40

38

36

34

32 -

30

Calculated

28

c 26

j5 24

SHEAR STRAIN

Figure 22a. Experimental and calculated torque-shear strain behavior

for ABS specimens with 0-degree reinf orcment

.

63
8.0x10 - 70x10"

7.5 r

7.0 -

6.5 -

6.0-

5.5 -

65-

60

55-

50-

5.0 - 45

4.5 40

=3 i a z

o

4.0

3.5

3.0

2.5

2.0

1.5

1.0

0.5

35

30

25

Experimental

20

15

10

- ABS-6

Calculated

0.001 kSHEAR STRAIN

Figure 22b. Experimental and calculated torque-shear strain behavior

for ABS specimens with 45-degree reinforcement.

64
<

a.

on<

cu

cuu

00

cuI o

•H

COc

cu£

•HU

0)a

en CO

cq<o

4-1uO

•H>

<0 ,c

<D 43U

CO

CU J=

coIcu3

cro

cu3aH

coo

-ac

CO • 4-1 -H C

CO CUe

"! - *qi c

cuE

•H

J-i CUa,xw

CJ CN

CN

O

CO oCO CN o

CN 6 o

ui-N

anoaoi

cuu3

00

65
APPENDIX A

MATERIAL PROPERTY TESTS

Al. SPECIMENS

Material property tests for determination of longitudinal

modulus, transverse modulus, and Poisson's ratio were made on all

materials used in this program.

a. Aluminum-Alloy Specimens

Tensile specimens as shown in figure A-l were machined from 6061-

T6 rolled aluminum-aHoy sheet in two thicknesses. These sheets were

0.020 in (0.05 cm) and 0.032 in (0.08 cm) thick. Twelve specimens

were removed from each sheet, three each in the 0, +45, -45 and 90-

degree directions with respect to the direction of rolling. In

addition, two specimens also shown in figure A-l were removed from the

wall of an untested long-tube specimen in the axial direction of the

tube.

b. Boron/Epoxy Specimens

Boron/epoxy tensile coupons as shown in figure A-2 were

fabricated from four plies of unidirectional boron/epoxy broadgoods

material. The laminates for both and 90-degree material properties

were fabricated simultaneously. A dam was machined from a single

bakelite sheet 0.032 in (0.08 cm) thick. A shim was placed in the dam

to achieve a final laminate thickness of approximately 0.02 in (0.05

cm) . The parts were cured in a heated platen press using the

manufacturer's recommended time- temperature cure cycle. The laminates

were allowed to cool in the press under a minimal pressure after cure. The cured laminates were 3 in (7.6 cm) wide and 12 in (30.5 cm) long.

Each laminate was then sliced lengthwise, using a diamond grit saw,

into specimens of the dimensions shown in figure A-2. Only the four

coupons in the center of the laminate were used for determination of

the material properties.

End tabs were prepared for the tensile specimens by curing four

plies of fiberglass prepreg into laminates 0.5 in (1.3 cm) wide and

12.0 in (30.5 cm) long. These laminates were cut into tabs 3.0 in

(7.7 cm) long and chamfered in a belt sander. Pairs of end tabs were

bonded simultaneously to each end of each specimen using epoxy resin.

This epoxy was cured using the recommended time-temperature cure cycle.

The cured epoxy was allowed to cool to room temperature before the

pressure was removed.

The dimensions of these specimens are given in Table A-l.

66
c. Fiberglass/Epoxy Specimens

fabricated from six plies of unidirectional 3-in (7.7-cm) wide tape

material. The material was sliced into 0.5-in (1.3-cm) wide, 12-in

(30.5-cm) long strips and laid up using techniques similar to those

used for boron/epoxy specimens. Only O-degree-ply-orientation

material properties were measured. The coupons were cured in a heated

platen press using the recommended time-temperature cure cycle. The

laminates were allowed to cool in the press after cure. End tabs,

prepared in the same way as those for the boron/epoxy specimens, were

bonded to the coupons using the technique described above.

The dimensions of these specimens are also given in table A-l.

A2. TENSILE TEST PROCEDURE AND RESULTS

a. Aluminum-Alloy Specimens

aluminum-alloy sheet material are shown in table A-2. Axial

extensions were measured using a linear variable differential

transformer (LVDT) . The results do not show any significant

anisotropic behavior due to sheet rolling.

The specimens machined from a spare tube were instrumented with

electrical resistance foil strain gages to measure both the

longitudinal and the transverse strains in the specimens. The

material properties computed from these results' are also shown in

table A-2.

b. Boron/Epoxy Tensile Specimens

These specimens were instrumented with electrical resistance foil

strain gages to measure longitudinal and transverse strains. The

results from these tests are shown in Table A-3. These specimens

failed in the gaged section of the coupon.

c. Glass/Epoxy Tensile Specimens

These specimens were instrumented with an LVDT to measure axial

strains. The results from these tests are shown in table A-3. These

specimens always failed in the tab section of the coupon, not in the

gaged section.

67
Table Al - Dimensions of Boron/Epoxy and Glass/Epoxy Tensile Specimens

type

Specimen Average Crossectional

in cm

1 0.060 0.152

2 .059 .150

3 .059 .150

4 .059 .150

5 .060 .152

thickness Average width area Orientation

deg

TBL-1 0.026 0.066 0.507 1.288 0.013 0.084

TBL-2 .025 .064 .510 1.295 .013 .084

TBL-3 .023 .058 .507 1.288 .012 .077

TBL-4 .023 .058 .507 1.288 .012 .077

TBT-1 .026 .066 .509 1.293 .013 .084 90

TBT-2 .027 .069 .514 1.306 .014 .090 90

TBT-3 .024 .061 .512 1.300 .012 .077 90

TBT-4 .024 .061 .516 1.311 .012 .077 90

Glass/epoxy

0.756 1.910

.732 1.859

.732 1.859

.736 1.869

.734 1.864

0.045 0.290

.043 .278

.043 .278

.043 .278

.044 .284

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71
-J 0.5 j-*-

fiber

direction

12.00

6.00

T1.0

2.0

1.0 chamfer to! feather edge

Notes

Tab ply orientation is 0, 0,0,0,

Specimen thickness does not vary by more than 0.002

over its length or width

Figure A-2. Boron/epoxy and glass/epoxy material property specimen.

All dimensions are given in inches (1 in = 2.54 cm).

72
orm NBS-114A d-71)

U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO.

NBS TN-728

2. Gov't Accession

No.

3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Torsional Instabilities in Composite and Composite-Reinforced

Aluminum-Alloy Thin-Walled Cylinders

5. Publication Date June 1972

6. Performing Organization Code

7. AUTHOR(S)

Donald E. Marlowe

8. Performing Organization

10. Project/Task/Work Unit No. 2130445

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

11. Contract/Grant No.

L-48,826

12. Sponsoring Organization Name and Address NASA Langley Research Center

Hampton, Virginia 23365

13. Type of Report & Period Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summaty of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) The elastic buckling strength has been determinedfor thin-walled aluminumalloy tubes fabricated with and without unidirectional boron/epoxy and glass/epoxy

composite materials applied as reinforcement to their outer surfaces. Three boron/

epoxy ply orientations were investigated. The results of these tests have been

compared with the buckling strengths predicted by two analytical techniques. It was found that reinforcement of the metal tubes with an equal thickness of the

composite material increased the buckling strength about threefold. The effect

on buckling strength of the ply angles investigated is small when compared with

the overall effect of adding the reinforcement. The analyses have approximately

the same degree of accuracy as that generally attributed to Donnell's treatment

of isotropic tubes.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Aircraft structures; boron/epoxy; composite materials; reinforced aluminum; stability;

thin shells; torsion buckling.

18. AVAILABILITY STATEMENT

Fl UNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

77

22. Price

70 cents

USCOMM-DC 66244-P7I
->|o.5 )-*-

12.00

6.00

fiber

direction

T1.0

2.0 r

1.0 chamfer to feather edge

Notes

Tab ply orientation is 0, 0,0,0,

Specimen thickness does not vary by more than 0.002

over its length or width

Figure A-2. Boron/epoxy and glass/epoxy material property specimen,

All dimensions are given in inches (1 in = 2.54 cm).

72
orm NBS-114A (i-7i) U.S. DEPT. OF COMM. BIBLIOGRAPHIC DATA

SHEET

1. PUBLICATION OR REPORT NO. NBS TN-7282, Gov't Accession No.3. Recipient's Accession No.

4. TITLE AND SUBTITLE

Torsional Instabilities in Composite and Composite-Reinforced

Aluminum-Alloy Thin-Walled Cylinders

5. Publication Date June 1972

6. Performing Organization Code

7. AUTHOR(S)

Donald E. Marlowe

8. Performing Organization

10. Project/Task/ Work Unit No. 2130445

9. PERFORMING ORGANIZATION NAME AND ADDRESS

NATIONAL BUREAU OF STANDARDS

DEPARTMENT OF COMMERCE

WASHINGTON, D.C. 20234

11. Contract/Grant No.

L-48,826

12. Sponsoring Organization Name and Address NASA Langley Research Center

Hampton, Virginia 23365

13. Type of Report & Period Covered

Final

14. Sponsoring Agency Code

15. SUPPLEMENTARY NOTES

16. ABSTRACT (A 200-word or less factual summaty of most significant information. If document includes a significant

bibliography or literature survey, mention it here.) The elastic buckling strength has been determinedf or thin-walled aluminumalloy tubes fabricated with and without unidirectional boron/epoxy and glass/epoxy

composite materials applied as reinforcement to their outer surfaces. Three boron/

epoxy ply orientations were investigated. The results of these tests have been

compared with the buckling strengths predicted by two analytical techniques. It was found that reinforcement of the metal tubes with an equal thickness of the

composite material increased the buckling strength about threefold. The effect

on buckling strength of the ply angles investigated is small when compared with

the overall effect of adding the reinforcement. The analyses have approximately

the same degree of accuracy as that generally attributed to Donnell's treatment

of isotropic tubes.

17. KEY WORDS (Alphabetical order, separated by semicolons)

Aircraft structures; boron/epoxy; composite materials; reinforced aluminum; stability;

thin shells; torsion buckling.

18. AVAILABILITY STATEMENT

F1 UNLIMITED.

I I FOR OFFICIAL DISTRIBUTION. DO NOT RELEASE

TO NTIS.

19. SECURITY CLASS

(THIS REPORT)

UNCLASSIFIED

20. SECURITY CLASS

(THIS PAGE)

UNCLASSIFIED

21. NO. OF PAGES

77

22. Price

70 cents

USCOMM-DC 66244-P7I


U.S. DEPARTMENT OF COMMERCE

National Bureau of Standards

Washington. D.C. 20234

OFFICIAL BUSINESS

Penalty for Private Use. $300

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215