Bonded joints increasing fatigue strength by bevelling

I "r."".

'VLlt;"" .. _{., ." ,jDS} Ó.~l;J:'i~~:

BONDED JOINTS - INCREASING FATIGUE STRENGTH BY BEVELLING

ltCHNISCHE HOGESCHOO

L ElFT

l: CHlVAART- EN RUIMTEVAARTTECHNIEK

BIBLIOTHEEK

Kluyverweg 1 - DELFT

September, 1970.

by

D. R. Hamel

~ONDED

JOINTS

~ INC~ASING

FATIGUE

STRENGTH BY BEVELLING

by

D. R. Hamel

Man~script received June, 1970.

ACKNOWLEDGEMENT

The author wishes to thank the Director of the lnstitute for Aerospace Studies5 University of Toronto5 for providing the opportunity to work on this project.

The nature and scope of this project were established by Dr. G. K. Korbacher after discussions with various aircraft manufacturing companies in the Toronto area. Dr. Korbacher also provided the supervision and encouragement during the course of the study.

Funds for this project were provided through a cost sharing contract (M-37) between Fleet Manufacturing Ltd. of Fort Erie, Ontario and Canadian Defence Industrial Research. This was the first venture by the U.T.l.A.S. into a cQ-operative research study with an aircraft manufacturing companYJ a venture ~hichp+oved very stimulati~g and satisfactory for both parties involved.

I.

II.

lIL IV.

V.

VI.

VII.

TABLE OF CONTENT SUMMARY

NOTATION and DEFINITIONS INTRODUCTION

EQUIPMENT AND TEST PROCEDURE TEST SPECIMENS

3.1 General

3.2 Solid Metal Specimens 3.3 Bonded Specimens

3.4

Specimen Tolerances TEST RESULTS

4.1 Solid Metal Specimens 4.2 Bonded Specimens STATISTICAL ANALYSIS DISCUSSION

6.1 Experimental Scatter 6.2 Fatigue Strength Increase

6.3

Tensile Strengths

6.4

Strength-to-Weight Ratio CONCLUSIONS

REFERENCES

APPENDIX A: Effect of Strap Misalignment APPENDIX B: Effect of Glue Line Thickness TABLES 1-10 FIGURES 1-10 1 2 2 2 2

3

3 3

3

3

4

5 5

5

6 7

7

8

SUMMARY

The fatigue strength of double strap joint bonded specimens using 2024-T3 Clad Aluminum alloy and FM-123-2 adhesive was investigated. Two joint configurations were stu_{died 3 a} joint with the conventional square edge on the strap and a joint with a sharp3 100 bevelled edge on the strap. The fatigue str~ngth wgs not appreciably increased by the 100 bevel; the endurance limit (10 to 10 cycle range) for both glue and metal failure was increased at most by 5 per cent_{3 a} gain which does not justify bevelled edges.

NOTATION AND DEFINITIONS

N fatigue life, number of cycles to failure

n sample size

KSI thousand pounds per square inch

log logarithm to base 10

Y.

l S p G max G . mln R S e G U b a 5 K log N _n mean of log N,

L

! ./n l i=l n

from shortest to longest life

sample standard deviation,

~

order number, ranking of failures n-l

probability of failure,q!Vn + 1)

stress level for fatigue testing, maximum tensile stress in the metal minimum tensile stress in the metal

stress ratio, G . /G

mln max

endurance limit, G that will produce failure at a specified N

max

average tensile stress in the metal when specimen failed under statie load

length of joint overlap glue line thickness

significanee level, probability that two samples, which are taken from the same population, will be found to be significantly different

strap misalignment

I. INTRODUCTION

Joining of met al parts by bonding is an attractive fabrication technique

both from the aerodynamic and structural point of view. The bonded joints are

aerodynamically smooth and the metal structure is not weakened by removing metal or introducing residual stresses, as is the case for rivetted or welded joints. Another factor which should be considered is the fatigue strength of the bonded joint. Bonding normally produces a joint which does not have a constant thickness

and therefore stress concentrations are introduced. These stress concentrations

are important and under conditions of fatigue loading, may be critical. The present study of bonded joints was defined by Project M-37,

Canadian Defence Industrial Research. The objectives stated in Project M-37 were,

to reduce the stress concentration factor of bonded joints by at least 33 per cent and increase the fatigue strength by 25 per cent. For a given metal-adhesive system, the only way to increase the fatigue strength is by reducing the stress concentration. Since only one metal-adhesive system will be used in this pro-ject, the experiment al results will be analyzed only in terms of an increased fatigue strength.

There have been a number of photoelastic experimental studies which have produced considerably lower stress concentrations by altering the conven-tional square edge of the material (adherend) at the end of the joint overlap. From an approximate mathematical analysis of a double strap joint, Lerchenthal

(Ref.7) found that the shear stress distribution in the adhesive is most uniform

for a rectangular hyperbola-shaped adherend. His photoelastic results showed

that the shear stress concentration factor (compared to a square strap edge) decreased by a factor of 3.05 for an approximate rectangular hyperbola and by a

factor of 2.3 for a 26.60 straight bevel. Feher (Ref.10) also investigated the

change in shear stress concentration factor by altering the edge geometry of

the strap. Instead of models made from photoelastic material, he used

bire-fringent coatings on 2024-T3 aluminum alloy bonded by two different adhesive

systems - Epon 828jversamid 123 (high shear modulus) and Narmco 7343 (low shear

modulus). The effect of a higher shear modulus is to increase the shear s~ness

con-centration factor: for a square edge strap, the EponjVersamid gave a shear stress

concentration factor of 4.5, the Narmco 3.25. From a square edge to a bevelled

strap edge the shear stress concentration factor decreased by a factor of 1.15

for the EponjVersamid adhesive and 1.63 for the Narmco adhesive. Niranjan's

(Ref.14) photoelastic models were shaped to simulate the bonded joints shown in Figures 2 and 3, except that he used bevel angles of 15, 30, 45 and 90 degrees. He concluded that bevelling the edge of the strap reduced the stress

concen-tration factor in both the adherend and the adhesive. For example, the peak

shear stress in the adhesive was decreased by 50 per cent in going from a

900 to a 38° bevel. The photoelastic results of Durelli, Parks, and

co-workers (Ref's. 8, 9, 11) are also of interest. Instead of bonded joints, their photoelastic models were intended to simulate two different materials bonded

together, that is, a composite material. Their specimens consisted of a

photoelastic material bonded to a rigid met al. By various edge shapes in the photoelastic material, they obtained changes in both normal and shear stress concentration factors of the order of 2.

There are two reasons why actual fatigue tests of bonded joints are necessary to confirm the improvements èlaimed in the photoelastic studies:

(1) photoelastic models are only approximations of the actual bonded joint,

(2) fatigue strength does not necessarily increase in direct proportion to stress

concentration reduction.

In addition to testing the bonded joint specimens~ static and fatigue

tests of solid metal specimens were necessary to establish the basic strength of

the metal. When a joint is designed with sufficient length of bonded overlap to ensure that metal failure takes place~ the basic strength of the metal beco~es

the l'tl}'\...ximuro. strength that the joint can possibly achieve.

11. EQUIPMENT M"D TEST PROCEDURE

All fatigue tests were carried out on a model SF-I-U Sonntag Fatigue l~.chine with static loed maintainer. The static load maintainer automatically Baintained the correct static laad throughout the period of the fatigue test.

Tensile axial loading was used for all tests with a ratio of minimum to maximum load in the fatigue cycle of R

=

0.1. The basic SF-I-U machine capacity of 1~000 pounds statie and 1~000 pounds dynamic laad was adequate for the solid metal

specimens (Fig.l). For the bonded specimens (Fig. 2 and 3) higher loads were

re-quired g,nd these higher loads were obtained by using a multiplying fixture

attached to the SF-I-U machine. The multiplying fixture increased both static

and dynamic load by a factor of five. Figures 4 and 5 show the SF-I-U Fatigue

Machine and 5:1 multiplying fixture w:th a bonded specimen ready for testing.

Static tensile tests were carried out at Fleet Manufacturing Ltd. on

a. model N3T~l Detroit Testing Machine.

For both fatigue and static tests the temperature of the environment

was always in the range from 710 to 760 _F.

A Hilger T.500 Universal Measuring Projector was used to measure the glue line thickness and strap misalignment of the bonded s~ecime~s.

111. TEST SPECIMENS 3.1 General:

Both the solid metal specimens and Qonded specimens were made by Fleet

~~lufactQ~ing Ltde of Fort Erie~ Ontario to the specifications shown in Fig. l~

2~ e.nd 3. The 2024-T3 clad aluminum alloy was taken from material purchased for

aircraft use~ the rolling direction, since not specified was not necessarily

the same irom specimen to speci:nen. The clad surface was left in the "as received"

co_dition except for necesGary cle~~ing. The FM-123-2 adhesive used for the

bonding was taken from rolls of supported film that Fleet uses for their bonded

aircraft assemblies. (Supported film means that the adhesive is in the form of

a film hich has been formed by irepregnating a carrier mat with the liquid

ad-hesive which hardens ~~d a flexible sheet or film is the result). FM-123-2 is a low-curing temperature (2250 - 250Op) adhesive which is manufacturèd by

the American Cyá.W'1mid Compan.y ~ Bloomingdale Department • Producti on bonding procedures were used for the bonded specimens, that is, the procedures were the

same as those used by Fleet for bonding aircraft assemblies.

3 .2 Solid. Metal Specimens:

The solid metal specimens were roughly shaped by metal saw and then

~illed to the specified shape. The final milling cuts were made in the U.T.I.A.S.

workshop and there were no milling bw::rs to remove since the final cuts were

microinches was left on the edges of the specimens by the final milling cut.

3.3

Bonded Specimens:

For bonding, the joint was left in a sheet approximately

48

inches wide. The edge shape of the strap, square or 100 bevel, was formed before the

bond-ing pperation. Af ter bonding, a metal saw was used to give the rough specimen shape and the edges were machined to give the specified shape. (The final

machining operation left shallow router bits along the edges of all the 100 bevel-led specimens). To remove the machining burrs the edges of the specimens were either scraped with a hand tool or lightly ground on an abrasive wheel. Both methods of deburring, especially the hand tool method, left irregular edges on

the bonded specimens. The finished specimens did not have a uniform glue line thickness and the strap misalignment varied from one specimen to another.

Appendices A and B cover these two topics in detail.

3.4

Specimen Tolerances:

The retention of the original mill finish of the metal surface, the choice of aircraft materials and the use of standard production procedures were all deliberate actions. By such actions it is hoped that the test results will be typical of aircraft assemblies bonded under normal production procedures.

IV. TEST RESULTS

4.1 Solid Metal Specimens:

Statie tensile and fatigue test results are recorded in Tables 1 and 2. A sample size of

5

was used for the statie tests and 10 for the fatigue tests. 4.2 Bonded Specimens:

For the bonded specimens a sample si ze of 10 was used for both the statie and fatigue tests, Tables

3

to

6.

The one exception was the fatigue test

of the 100 bevelled specimens at the 52 KSI stress level, where the sample si ze was 11. All glue failures were cOhesive, that is, the fracture line was within the glue rather than between the glue and the metal surface, which would have been an adhesive failure. By mounting the specimens upside down and backwards,

it was proven that the grips did not influence where the glue failures mriginated. Nine out of ten of the statie test square edge specimens failed in

the metal approximately one-half inch from the edge of the strap. There was considerable necking of the metal before fracture. The bonded straps restricted necking in the metal near the strap. Glue fatigue failures for the square

edge specimens consistently originated in the glue line which was thinner near

the end of the overlap (see Appendix B for more details). The location of metal fatigue failures varied from the edge of the strap to

3/4

inch beyond the strap,

that is, 1/4 inch outside the parallel test section. Olit of the 14 metal fail-ures,

7

were at the edge of the strap,

3

were 1/8 of an inch, and

4

were

3/4

of

an inch from the strap.

glue, although there was noticeable metal necking which was most severe

approxi-mately 1/2 inch from the strap. The origin of the glue fatigue failures could

not be related to the glue line thickness in the bevelled specimens. The

location of metal fatigue failures varied from the edge of the strap to one inch

beyond the strap. Out of the 22 metal failures,

5

were at the edge of the strap,

and the remainder were scattered over the one inch length with four failures

beginning at one of the shallow ll'o.utè:n·:.btl!,tS .. :tC:ll.S.

v

.

STATISTICAL ANALYSIS

Two statistical tools were used to help in evaluating the fatigue results, the median log fatigue life and significance tests. A log-normal frequency dis-tribution was assumed, that is, a normal distribution of log N. If this assump-tion is valid a plot of log N on normal probability paper will form a straight line. By assuming a log-normal distribution the mean of log N

(1)

can be used as the median of log N. (The median is the middle value in a frequency distri-bution). The other statistical parameter required was the standard deviation

(S).

Y

and S could not be accurately calculated for stress levels where both

metal and glue failures taok place because, considering glue failures, all the

metal failures were tests which were stopped before the glue failed, and con-sidering metal failures, all the glue failures were tests which were stopped be-fore the metal failed. Values of

Y

and S, calculated by the equations given in the Notation, are recorded in Tables 7, 8 and 9. The antilog

Y

values in brackets in Tables 8 and 9 were obtained in a different way.

Log-normal probability plots were made of the fatigue test results for the solid.metal and bonded specimens (Fig.6,

7

and 8). For stress levels, where

both metal and glue failure took place, dotted lines were drawn through the

ex-perimental points. The antilog

Y

values in brackets in Tables 8 and

9

were taken

as the value of N where the dotted lines intersected the 50 P line in Figures

7

and 8. Since the mixture of metal and glue failures in effect meant that some tests were discontinued, that is, stopped before failure occurred, a modified order number (q) had to be used for calculating P. A method of weighting the q's to take the discontinued tests into account was used (Ref.6).

The solid lines in Figures 6,7 and 8 represent the log-normal

distri-butions which have the same

1

and S as the experimental data. These lines were

drawn by including 68 per cent of the population (16p to 84p) in ~ S. The

ex-perimental points follow the lines fairly closely. Therefore, the assumption of

a log-normal frequency distribution appears to be jus~ified. Plotting the

ex-perimental points on extreme-value probability paper did not give any more linear

a plot than the plot on log-normal probability paper.

The significance tests were used to determine if the standard devia-ti ons and fadevia-tigue lives of two samples were significantly different. For

com-paring standard deviations, a significance level

(a)

of

5

per cent was used.

A significance level of

5

per cent means that five times out of one hundred the test will indicate a significant difference between two samples when both samples are from the same population. Only at stress levels where the failures were

completely metal (25 KSI) or completely glue (52 KSI) was it possible to apply

the significanee tests, since· bbth

1

and S are required for the tests. The

pro-cedure in Ref. 5 was followed for the "F" and "t" significance tests. Standard

deviations are compared by the "F" test and means by the "t" test.

specimens were found to be significantly different from the square specimens. At the 25 KSI stress level, only the Y's

(a

=

0.5%

)

were significantly different. The Y's will be used to draw S-N curves for the two bonded specimens and these

curves will then be used to campare endurance limits (Se). Therefore, it is

important that the fatigue lives of the two specimens be shown to be significantly different. At least at the 25 and 52 KSI stress levels, the fatigue lives of the 100 bevel+ed specimens were shown to be significantly different from the fatigue lives of the square specimens.

The antilog

Y

values from Tables

7, 8

and 9 were used to draw S-N

curves for the solid metal, 100 _{bevelled, and square specimens (Fig. 9).Endurance}

limits for both metal and glue failure were read from the S-N curves and strength

ratios were calculated to compare the tnree different specimens (Table 10).

VI. DISCUSSION

6.1 Experimental Scatter:

o From Tables

8

and 9 it can be seen that the standard deviations of the

10 bevelled specimens are generally higher than those of the square specimens. This increase is not considered to be caused by the 100 bevel. There were two factors in the manufacture of the 100 bevelled specimens that could account for the high scatter in the experimental results compared to the square specimens:

(1) an accurate length of overlap was more difficult to maintain, because the bevelled strap ended in a sharp edge; thus even slight machining af ter the sharp

edge had been reached would significantly decrease the length of overlap, and

(2) uniform pressure on the glue line during adhesive cure was not maintained since the bevelled surface was not supported,due to the t001ing technique used. The second factor is likely responsilile for the more variable and unsymmetric glue line thickness of the bevelled specimens (see Appendix "B" for more de-tails). A re-run of bevelled specimens with uniform pressure over the bevelled

surface is believed to result in reduced scatter.

From Tables

7, 8

and 9 it appears that the scatter in fatigue life for

metal failure is least for the square specimens. Reasons for the high scatter of the bevelled specimens were given in the preceding paragraph. But the solid metal specimens also have a higher scatter than the square specimens. One

pos-sible explanation is that the scatter in fatigue life of the solid metal speci-mens is the result of crack initiation at random flaws in the metal, whereas, the square specimens have a more consistent factor responsible for crack

initiation, that is, stress concentration at the edge of the strap. The higher percentage of fractures at the strap edge for the square specimens, 50 per cent compared to 23 per cent for the bevelled specimens, supports the theory that the stress concentration in the metal for the square specimens is high enough to influence fatigue crack initiation.

6.2 Fatigue Strength Increase:

The object of this study was stated in the Introduction: increase the

fatigue strength of bonded joints by 25 per cent. Since fatigue test results are obtained as fatigue lives, it became necessary to convert the results into endurance limits (Se) by means of S-N curves • . Before making the conversion, the difference between the fatigue lives of the 100 bevelled and the square specimens was proven as far as it was possible by means of the "F" and "t"

significance tests. The S-N curves were drawn for the median log fatigue lives, which are the same as the antilog

Y

since a log-normal frequency distribution was assumed. S ratios of the solid metal, 100 _{bevelled, and square specimens}

e

were recorded in Table 10. At a life of 10 5 cycles the maximum possible endurance limit increase for metal failure of the square edge double strap joint is 8.5

per cent (see S ratio metal!square). The literature survey in Ref. 13 quotes a

10 per cent pos§ible increase for Redux adhesive and not any for Metlbond 4021

adhesive (Hartman and DeRijk). By using a 100 bevel on the strap edge, 3.5 per

cent of the possible 8.5 per cent increase in S was achieved. For glue

fail-ures, approximately the same S increase (3.5 t6 5 per cent) was achieved by the

100 bevel on the strap edge. Even if the joint fatigue strength could be made

the same as the solid metal, the approximately 10 per cent strength increase would

not likely justify the additional production costs required to modify the square

edge of the strap.

In theory the bevelled strap edge shape shown in Fig. 3 is very

desir-abIe, since it produces a gradual change in cross-section at the strap edge. A

shallower (less than 100 ) bevel would have given an even more gradual change in

cross-section, but was not considered feasible, since accurate control of the

overlap becomes very difficult at low bevel angles. Besides, bevelling to a sharp

edge is not practical for a production joint, some finite strap thickness would have to be left at the strap edge. This finite strap thickness would then

re-sult in a higher stress concentration than bevelling the strap to a sharp edge. As mentioned earlier, the 100 bevelled specimens appear to have a higher scatter

in their fatigue results compared to the square specimens. The Statistical

Analysis confirmed a higher scatter (standard deviations significantly different)

at the 52 KSI stress level (glue failure) but not at the 25 KSI stress level

(metal failure). Since the method of manufacture appears to have affected the

scatter of fatigue test results for glue failure, the glue fatigue strength of

the bevelled specimens may be higher than the experimental results indicate. The

metal fatigue failures do not appear to be affected (standard deviations for the bevelled and square specimens were not significantly different). Therefore, for

metal failure a production bevelled joint (some fini te strap thickness at the

strap edge) could not be expected to have even a 3.5 per cent higher fatigue

strength than a square joint.

The curves in Fig.

9

show that at the short fatigue lives the one-half

inch overlap length was less than the optimum overlap length. By definition,

the overlap length that is just sufficient to cause the joint to fail in the

metal is the optimum overlap length. The optimum overlap length for any fatigue

life can be determined from a series of fatigue tests on specimens with varying

lengths of overlap. Such a series of tests have already been made, and the

re-sults will be published as Ref.16.

6.3 Tensile Strengths:

The lower ultimate tensile strength (~ ) of the 100 bevelled specimens,

compared to the square specimens (Tables 3 and 4~, may als 0' be caused by the

manufacturing method used for the 100 bevelled specimens. Since all of the

be-velled specimens failed in the glue under static test, it was a reduced glue

strength that was responsible for the lower ~. There is no reason why the

pre-sence of a bevel should lower the glue streng%h. But the manufacturing method

used for the bevelled specimens could account for a lower glue strength: the

sharp edge on the strap could appreciably vary the length of overlap and the un-supported bevel during cure could cause appreciable variations in the glue line pressure. (see comments at end of first paragraph of Secte 6.1).

that of the solid metal specimen, 69.3 compared to 70.8 KSI. This close

agree-ment was expected since the extensive necking of the specimens prior to static

failure was evidence of large plastic deformations which would eliminate the

effects of any stress concentrations at the strap edge.

When the tensile tests of the square specimens were found to be

pre-dominantly metal failure, i t was anticipated that even at the high fatigue stress

levels metal failures would predominate. Table

8

and Fig.

9

show that in fact

glue failures dominated until the fatigue stress level was reduced to

approxi-mately half the tensile strength of the metal. The primary difference between

the tensile and fatigue tests was the rapidly fluctuating load (1,800 cycles

per minute) for the fatigue tests. Possibly the glue is more sensitive to the

type of loading than the metal, and therefore suffers a relatively higher strength

loss than the metal under vibrating loads. There is another more plausible

explanation that involves the relative shape of the glue and metal failure curves

for the square speci~en. Although the glue curve is below the metal curve at

a fatigue life of 10 cycles, it could still intersect the metal curve at a

10wer life, thus at N

=

1/4

(tensile test) metal failure would occur. This

sec-ond explanation must now be resolved with respect to the 100 bevelled glue

curve, which also intersects the N

=

1/4

axis below the metal curve (TabIe

4,

tensile tests gave all glue failures). However, at higher va"lues of N the

bevelled glue curve was found to be above the square glue curve, see Fig. lO~

The lower glue tensile strength has already been explained by the manufacturing

method used for the bevelled specimens. Therefore, under static load, where

stress concentrations have little effect, the bevelled specimens had a lower

glue strength than the square specimens. But, under fatigue load, where stress

concentrations become important, the bevelled shape reduced the stress

concen-trations which led to higher glue strength than the square shape. Figure 10

was drawn to include the static and fatigue experimental results plus the

preceding explanations.

6.4

Stength-to-Weight Ratio:

It is possible to make a rough estimate of the increased fatigue

strength-to-weight ratio which results from a 100 bevel on the strap edge of

a double strap joint. This estimate is based on a metal fatigue failure, a

metal thickness of 0.065 inches, a joint width of one inch either side of the

overlap, and a one-half inch overlap. Two factors contribute to a higher

fatigue strength-to-weight ratio, the

3.5

per cent higher fatigue strength found

from the experimental results and the reduced area of the joint cross-section

because of the bevel. Bevelling the strap edge reduces the cross-section by

approximately 1.5 per cent. Therefore, the total increase in fatigue

strength-to-weight ratio is

5

per cent. To be able to estimate the increase in fatigue

strength-to-weight ratio for a bonded structure, one would have to know what

percentage of the structure is made up of joints.

VII. CONCLUSIONS

(1) In a double strap bonded joint the metal fatigue

endurance limit is lowered by approximately 10 per

cent because of stress concentrations.

(2) When the strap ed§e of a double strap bonded joint

is bevelled to 10 , the metal endurance limit is

increased by approximately

5

per cent. The increase

(3) The fatigue strength of bevelled specimens may be possibly improved if bonding is done under uniform pressure over

the bevelled surface.

----1. McClintock, F. A. 2 . Wei bull , W. 3. Dieter, G. E. Jr., 4. Forrest, P. G. 5. ASTM,Committee E-9 6. Johnson, L. G. 7. Lerchenthal, C. H. 8. Durel1i, A. J. Parks, V. J. 9. Durelli, A. J. Parks, V. J. DelRio, C. J. 10. Feher, S. 11. Parks, A. J. 12. Fu-Pen, Chiang. Durelli, A. J. 13. Kutsha, D. Hofer, K. E. Jr., 14. Nirartjan, V. RE FE REN CES

The Statistical Planning and Interpretation of

Fatigue Tests. Metal Fatigue, Ed. G. Sines and

J. L. Waisman, McGraw-Hill Book Co., New York;1959. Fatigue Testing and Analysis of Results. Pergamon Press, London, 1961.

Statistics Applied to Materials Testing.

Mechani-cal Metallurgy, McGraw-Hil1 Book Co., New York,1961.

Fatigue Testing. Fatigue of Metals, Addison-Wesley

Pub. Co., Reading, Mass. 1962.

A Guide for Fatigue Testing and the Statistical

Analysis of Fatigue Data. ASTM Special Technical

Publication No. 91-A, 1963.

The Statistical Treatment of Fatigue Experiments. Elsevier Publishing Co., New York, 1964.

Design of Bonded-Lap Joints for Optimum Stress

Transfers. Part 1. The Symmetric (or double) Lap

Joint. Israel J. of Techno1ogy, Vo1.2, (1),1964.

Photoelastic Stress Analysis on the Bonded Inter-face of a Strip with Different End Configurations. American Ceramic Society Bulletin, Vol.46 (6),1967.

Stress es in SquareSlabs, with Different Edge

Geometries, when Bonded on One Face to a Rigid Plate

and Shrunk. Experimenta1 Mechanics, Nov, 1967.

Research Study of Common Bulkhead and Manufacturing

Technology I~provement Program for Saturn Stages.

Final Report NAS 8-20376, June 1966 to June 1967,

~fuittaker Corp., Narmco R & D Division.

Maximum Stress at the Angular Corners of Long Strips

Bonded on One Side and Shrunk. Experimental Mechanies,

June, 1968.

Handbook for Adhesives (Bloomingdale Department).

Ameri can Cyanamid Co., Havre De Grace, Mary1and, 1969.

Feasibility of Joining Advanced Composite Flight Vehicle Structures. Air Force Materials Laboratory,

TR-68-391. Wright-Patterson Air Force Base, Ohio,

J anuary, 1969.

Bonded Jomnts - A Photoe1astic Study. UTIAS Tech.

15.

Niraniian, V. 16. Niranjan, V. Hamel, D. R. Yang, C. A.

Bonded Joints - A Review for Engineers. UTIAS Review NO.28, Toronto, Canada, 1969.

Statie and Fatigue Strength of FM-123-2 Adhesive in Double Strap Joints of Various Lengths of

Overlap, UTIAS Teeh. Note No. 160, Toronto, Canada, 1970.

APPENDIX A: EFFECT OF STRAP MISALIGNMENT

The Measuring Projector at UTIAS was used to measure the strap misalign-ment

(5).

Strap misalignment is defined as the amount that the two straps are

offset from one another, that is, the edges of the straps are not exactly opposite (see Fig. A-.l). Of the four possible corners for measûring 5, only two diagonal ones could be used since the edge machining left a "feather" on the remaining two corners. The results from the two corners that were measured were averaged to give 5. Strap misalignment was investigated since it makes the joint un-symmetrie, and thus results in higher loads at right angles to the glue line surface than are found in anormal symmetric double strap joint. Adhesives can withstand shear loads much better than normal loads. In addition, strap

mis-alignment reduces the glue shear area. Both effects will lower the glue strength of the joint, and possibly even the metal strength by introducing 'bending loads. The question is, over what, 5 range are the changes in strengths negligible?

All the square edge specimens were measured for 5. Misalignment o! the static and fatigue test specimens, Tables 3 and 5, varied from 0.0005 to 0.0065 inches with a spread of approximately 0.005 inches within any one stress level. Neither the static or fatigue test results appeared to be affected by a strap misalignment of this magnitude. In addition, comparison statie tensile tests were conducted on a Tinius Olsen testing machine at UTIAS (loading rate much slower than the Detroit Testing Machine at Fleet). Two groups of ten speci-mens each were statically tested; misalignment of group A varied from 0.001 to 0.006 inches, àf group B from 0.014 to 0.018 (Table A.l). The resultsweiI"è com-pared to determine if the ~ 's were significantly different. Anormal distri-bution was assumed for ~ ~d all ten specimens in each group were assumed to be from the same populat~on, although the mode of failure was mixed, with four metal failures in group A and two in group B. The standard deviations were significantly different for an

a

of 5 per cent and the tensile strengths were significantly different down to an a of approximately 3.5 per cent. The ratio of the mean tensile strenghts (A!B) was 1.01. A one per cent difference can be ignored.

There were not enough 100 bevelled specimens to determine the effect of strap mis~lignment on static tensile strength. A short comparison test was conducted for the effect of 5 on fatigue life. The 5 of the specimens in Tables 4 and 6 varied from zero to 0.007 inches. Five additional specimens with a 5 of 0.034 uo 0.039 inches were fatigue tested at the 45 KSI stress level (Table A.2); all failures were glue failures. Since the main test at the 45 KSI stress level produced both glue and metal failures (Table 6), it is not possible to get an accurate sample median or standard deviation for the main test. Therefore, the significance tests cannot be used to compare the effe cts of 5 on the fatigue life. Just comparing the approximate sample means

(Y),

the specimens with the smaller 5 had a 4.6 per cent higher

Y.

4.6 per cent is a conservative estimate since the approximate

Y

for the main test was calculated by taking the lives of the three metal failures to be glue failures. (There is not sufficient data to express this effect in terms of an increase in the endurance limit). The changes in

Y

between the bevelled and square edge specimens were 4.2 per cent at the 52 KSI stress level (glue failure) and 3.3 per cent at the 25 KSI stress level (metal failure). These changes are of the same order as the effect of strap misalignment at the 45 KSI stress level.

Although the evidence is not complete, it appears that the strap mis-alignment can vary at least as much as 0.010 inches without having any appreciable

effect on either statie or fatigue strength. In terms of per cent of overlap

length, the allowable variation in 5 would be 2 per cent. Since the maximum 5

for the main tests (Tables 3 to 6) was 0·.007 inches, strap misalignment did not

APPENDIX B: EFFECT OF GLUE LINE THICKNESS

In both specimens, square strap edge and 100 bevelled strap edge,

there was a noticeable variation in glue line thickness (b) along the length

of the overlap. The UTIAS Measuring Projector was used to measure the glue line

thickness, accuracy estimated at

!.

0.0003 inches. The words "upper" and "lower"

will be used to indicate the specimen orientation during bonding.

Variation of b was very consistent for the square edge specimens. The

upper glue line was thicker at the edge of the strap and the lower glue line

was thinner at the edge of the strap. Measurements were made at twelve locations

for two typical specimens and the results were plotted in Fig. B.l. (The

devia-tion of the points from a smooth curve is caused by the + 0.0003 inches measuring

accuracy). In the Test Results it was pointed out that the glue failures of

square edge specimens consistently originated in the lower glue line, where the

minimum b is found. Although b is also small in the centre of the upper glue

line, the edge of the strap is logically a location more sensitive to glue line

variation since the peak shear stresses occur near the ends of the joint

over-lap. The theory for shear failure in the glue line supports the preceding

findings: fr om the theoretical analysis, the shear strength of the adhesive

in-creases as the glue line thickness increases (Ref.15).

The 100 oevelled specimens did not have the same consistency in the

variation of b as the square edged specimens. There were always points along

the overlap where the b's were visibly different, but there was no. symmetry

to the variation in b. A few typical specimens were measured in the same way

as the Fig. B.l specimens, and glue lines as thick as 0.0065 inches and as thin

as 0.003 inches were found. In these extreme cases the b changed sharply along

the overlap. Where there was little variation in b along the overlap, the b

varied from 0.003 to 0.004 inches. It was not possible to relate the origin

of the glue failures with glue line thickness.

Spec M5 M8 MlO MIl MB M'14 M21 M50 M36 M53 M30 M31 M32 M34 M38 M40 M44 M45 M48 M51 TABLE 1

STATIC TENSILE TEST RESULTS FOR SOLID METAL SPECIMENS

Spec Tensile Strength, cr (KSI) u M19 11. 0 M33 10.4 M35 10.5 M39 11.6 M52 10.6 ave rage 10.8 TABLE 2

FATIGUE TEST RESULTS FOR SOLID METAL SPECIMENS Stress Level 1000 Cycles ppec Stress Level

cr to Failure cr max max (KSI) N (KSI) 60 19.94 M3 35 60 19.58 M6 35 60 19.58 M1 35 60 18.00 M12 , 35 60 19.03 M16 35 60 22.12 M20 35 60 22.21 M29 35 60 11.97 M43 35 60 25.61 M41 35 60 19.94 M49 35 45 89.88 M4 26 45 81.64 M9 26 45 111. 45 M15 ·26 45 94.12 M18 26 45 89.45 M23 26 45 104.03 M25 26 45 93.19 M26 26 45 100.94 M41 26 45 100.61 M42 26 45 98.10 M46 26 1000 Cycles to Failure N 218.3 204.8 181.2 213.2 225.1 213.1 191.4 230.1 186.6 215.2 1162.5 128.0 452.0 611.0 865.8 152.5 614.6 526.8 551.2 161.1

TABLE 3

STATIC TENSILE TEST RESULTS FOR SQUARE EDGE BONDED SPECIMENS

Spec ~ensile Strength, cr (KSI) Failure

u SU-21 69.5 metal 8U-22 68.8 metal SU-23 69.5 metal SU-24 69.5 metal

.

SU-25 69.5 metal SU-26 68.8 metal 8U-27 68.8 glue , sU-28 69.5 metal sU-29 69.5 metal

8U-30 69.5 met al·

ave rage 69.3

TABLE 4

STATIC TENSILE TEST RESULTS FOR 10° BEVELLED

EDGE BONDED SPECIMENS

Spec Tensile Strength, cr (KSI) Failure

u TU~l .·63.9 glue TU-2 66.2 glue TU-3 64.7 glue Tu-4 65.4 glue TU-5 63.1 glue Tu-6 63-.9 glue TU-7 63.1 glue Tu-8 65.4 glue TU-9 64.7 glue TU-IO 63.9 glue average I 64.4

8pec; 8tress Level cr (K8I) max 81-8 52 81-3 52 81-6 52 81-4 52 81-2 52 81-1 52 81-7 52 81 .. 9 52 81-10 52 81-5 52 82-1 45 82-7 45 82-2 45 82-3 45 82-5 45 82-10 45 82-8 45 82-9 45 82-4 45 82-6 45 I TABLE 5

FATIGUE TE8T RE8ULT8 FOR 8QUAR~ EDGE BONDED 8PECIMEN8

10 3 Cycles Failure 8pec 8tress

to Failure Level cr _max (K8I) N 7.61 glue 83-.3 38 7.73 glue 83-6 38 8.09 glue 83-5 38 8.24 glue 83-1 38 8.42 glue 83-2 38 8.49 glue 83-8 38 8.61 glue 83-4 38 8.61 glue 83-10 38 9.06 glue 83-7 38 11.18 glue 83-9 38 15.9 glue 84-1 25 22.2 . glue 84-4 25 26.7 glue 84-3 25 28.4 glue 84-7 25 29.9 glue 84-2 25 30.2 glue 84-9 25 30.3 glue 84-8 25 32.5 glue 84-10 25 35.1 glue 84-6 25 35.4 glue 84-5 25 103 Cycles Failure to Failure N 58.5 glue 95.2 glue 99.1 glue 105 glue 113 metal 117 metal 124 glue 129 glue 145 metal 151 metal 490 metal 545 metal 549 metal 558 metal 638 metal 665 metal 671 metal 690 metal 793 metal 888 metal

Spec cr T3-6 T3-1 T3-8 T3-3 T3-2 T3-5 T3-4 T3-7 T3-10 T3-9 T3-11 Tl-5 Tl-9 Tl-l Tl-6 Tl-10 Tl-3 Tl-2 Tl-4 Tl-7 Tl-8 TABLE 6

FATIGUE TEST RESULTS FOR 100 BEVELLED EDGE

BONDED SPECIMENS

Stress 10 3 Cycles Failure Spec Stress

Level to Failure Level

(KSI) N

max cr max (KSI)

52 5.36 glue T2-6 38 52 10.0 glue T2-1 38 52 10.2 glue T2-3 38 52 10.8 glue T2-9 38 52 12.3 . glue T2-4 38 52 12.6 glue T2-2 38 52 14.4 glue T2-7 38 52 14.6 glue T2-10 38 52 \ 15.9 glue T2-5 38 52 16.7 glue T2-8 38 52 26.7 glue T4-2 25 45 20.9 glue _{T4-4 25} 45 23.5 glue T4-6 25 45 24.0 glue _{T4-5 25} 45 31. 9 glue T4-10 25 45 32.6 glue T4-1 25 45 38.6 glue T4-8 25 45 45.0 metal T4-9 25 45 50.2 glue T4-3 25 45 90.2 metal T4-7 25 45 96.3 metal 10 3 Cycles Failure to Failure N 103 metal 128 metal 137 glue 148 metal 156 metal 157 metal 161 metal 163 metal 174 metal 201 metal 673 metal 753 metal 867 metal 879 metal 883 metal 891 metal 1072 metal 1440 metal .1609 metal 1790 metal

TABLE 7

STATISTICAL DATA FOR SOLID METAL SPECIMENS 0max \1\.bJ.} 6 oU 4 45 35 n 10 10 10

Y

4.307 4.986 5.318 antilog

Y

20.3 96.8 208 (1000 cycles) 6 26 10 5.841 692 TABLE 8

STATISTICAL DATA FOR SQUARE EDGE BONDED SPECIMENS

cr (KSI)

max 52 45 38 38

n -10 10 6 4

failure glue ,glue glue metal

y _{3.932 4.447} antilog

Y

8.56 27.99 ( i20) (134 ) 25 10 metal -_ 5.805 638.8 S .04728 .03305 .03310 .1162

I

(1000 S cycles) .04664 .1045 -.07956 TABLE 9

STA~ISTICAL DATA FOR 10° BEVELLED EDGE BONDED SPECIMENS

(

a lKSI)

max 52 4 45 4 45 j ö jö

n 11 7 3 1 9

failure glue gl-ue metal glue metal

y _4.103 -antilog Y 12.68 C39 ) (76) (150) (1000 cycles) S .1732 ë) 10 metal 6.013 1030.8 .1446 TABLE 10

ENDURANCE LIMITS (KSI) AND RATIOS

,-~

Iglue 104 failure Ü 5 - . metal -10 ,- 5 -failurel é

-inetal

-

-

44.6 25 -square 51 38.7 41 24 bevelled 53.5 40 42.4 25 -metal/sq.

-

-

1. 085 1. 04 -bey/sq. 1. 05 1. 035 1. 035 1.04 metal/bev.

-

-

: ,- 1.05 1.0 .~ ,,' . .. !-.', .

TABLE A.l

STRAP MISALIGNMENT AND ULTIMATE TENSILE STRENGTH OF SQUARE EDGE SPECIMENS

GROUP A GROUP B

iSpec. 0( inch) cr (KSI) Failure Spec. l5(inch) cr KSI) Failure

u u

~U-ll 0.006 64.9 glue SU-l 0.016 64.2 metal

SU-12 0.004 64.4 glue SU-2. 0.015 64.4 glue

SU-l3 0.004 64.5 glue SU-3 0.018 63.6 glue

SU-14 0.003 64.4 metal su-4 0.017 61. 8 glue

jsU-15 0.003 65.1 metal SU-5 0.014 63.9 glue

SU-16 0.002 65.2 metal su-6 0.016 64.4 glue

SU-17 0.002 64.5 glue SU-7 0.014 64.6 glue

SU-18 0.002 65.0 metal .su-8 0.014 64.6 glue

SU-19 0.001 . 64.4 glue SU-9 0.014 64.3 metal

SU-20 0.001 64.4 glue SU-I0 0.014 64.6 glue

mean cr = 64.68 KSI mean cr = 64.04 KSI

u u

S = 0.3285 KSI

s

= 0.8506 KSI

/

TABLE A.2

10° BEVELLED EDGE SPECIMENS WITH LARGE STRAP MISALIGNMENT N Spec. (1000 cycles) Tl-Il 27.0 cr = 45 KSI m!1x Tl-12 17.0 y = 4.384 Tl-13 34.0

Tl-14 24.2 main test at 45 KSI,

Y

4.597

FIG.1

1"

I.:l.

ft "

t - - - .;1~

T

f N

--k::

~

'I

_~

11

'---

4%

RADIUS

2024 -

T3

CL-AP A1-U M I NUM

AL..L.oy

O.o<Ó4"

NOM' NA!. THIC.I<.NESS

'DOUBLE

STR.APJOJ~T

80NDE:!>

reST

SPECIMENS

I

I

~.5" "

-

-

- -

-

G,RIP

LJN~S / ' / ' ./'

+

SeR/SE

MAR.J<S

t;:oR..

AL/GNIN~

IN

GR./PS

- - - G,L.UE

LINE >

FM

-/~3

-2

Ap'Hé5/VE

All-

SHeeT

MATER/AL..

0.0(2)4

I1

NOIVIINAL. ïH/CI<.Ne$S

2024 -

, 3

CLAD

'

AL.U/VJINUM

ALLoy

Ft

Gr

.2

SQUAR.E.

STRAP

EDGS

F/G.3

'10 BEVELLSD

o

FIG. 4 SF-1-U SONNTAG FATIGUE MACHINE WITH 5:1 MULTIPLYING FIXTURE

FIG. 5 5:1 MULTIPLYING FLXTURE WITH BONDED SQUARE EDG E SP ECIMEN

1111111111

Ïl

lll

ll

llmIII

I

IIIIÎl

lli

l

llll

~

11J~llj

fu

l

!ll!

l

f

!~

ï

1111

1

11II

ï

llll

l

llll

~

II!

1

1111

~

lll

l

llll

f

llll

i

llll

~

III

~

II

:

~

ll

f

1I1I11I11

ï

llll

l

lllm

lmllll]

lll

l

lll

f

llll

i

llll

]

lll

r.~

~~RKESis

'

.

~;'RKESis

1 .

~;'RKESSIS

~

~~RKESis

I

l

l

illl

l

llll

l

llll

l

ll"

I

I"I

I

IIII

I

I.m~m_tl

m~L

1.II.JIIIIII I U . I· 1IIIIIIIIIilillill!IHU±,IIIIIIIIIIIIIIII!lIl1ll1illllllllllll111111 ,

Ë

LEVEL 111 I 1 , LEVEL

tt

LEVEL. ' LEVEL H+HlIIIIIII IIII IIIIIII.IIIIIIIIIIIIHHIIIIIIIIIIIIIIIIIIIIIIfH+HHllHHH

h:. .. -'~:+ltH j:fJ. t1J±jtF" · iI_ --jO ~-=-~: ~i .~UÜI"~I'J IlI'j)il·;1

H+H-++

+++H+H·H+HHH+H

~

l

IH

!

jJI

~

m+l~i+Jj

~ql*HlI

1

IIHl-H-H+H+

H+t+H

+H+H*H+HHtH

l

l~H

I

+H+

I

·

H·l-H

+I+i

1

-~-=t-+.q-+-·-lH-,_I·--'-i+-J-H_W.tt .... '" '" o w o

...

o g: p (%) '" o " o !Xl o 00 '" <0 o

I I I I I 11 i II!! 111:!II!:::I:::'I"!!I:!I!II!III+t+'+H+4·'-H-It!lt;t I I! 1111 f 1IIIII+tI-Htl+i-H+:·HftHH-H-++f+lfH-H+t++H+HJHIH I I I I I: : 11: 1 f I-H+H-++++++++t:++++lI+l+!I++I+H++tI-H+I+IfjjIHHl~ 11

I , I I I ' I I 1 I ; 11 IIII IIIIIIIII!: :jll!!liljlllll i 111111j Ilillllllllill 1 , I 1 I I I 1 11 1IIIIIIIIIIIIIIIIIIIIIIIIIIIIIlW 111111111111111111111 I I 1 1 I I 1 1 I IIIIIIIIIIII! IIIIIIIIIII!IIIIIIIIIIII i 11111111111:111111 :g

..-4 N W b t n a > -...JOOI.O ... 5 N W b t . n 0 ' l " o J O O C ' O .... 6 N W A t.ncn"'-.lc:oU)o~ 7

10 10 10 10

N .:=. "-J co. CD .... N ~ cn ... e»c'o.... +:0 ","",ooc.o

'

-+-'+H

-H~~~4414

j

~4~

j

+HHHJ~

~II

~

I

'1

1

~1~

11

!!

'

11

I!J!I

I

;!

52 K SI SI . I f-H STRESS SS I H-H-I-H-H-H LEV E L L ! _1_' , , , •. , , • "I 71"tTl ~t111':1, • GLUE FAILURE • META L FA ILURE

lil

1 1 1 1

11~~~

lIlIlIlillllllllll

llll

ll

l

llll

l

:Il

Il

Il

IlHHH-+lm 1111

1

1111

1

1111

1

1111~1~111111111

1

1111

1

111111111

1

11111

11II

I

IIIIII~

1

1

1111

111

11

1

11

1

111111

1

1111

1

111111111

111

11

1

111

.... '" '" o w o "'.$:lo _o g;P(%) ".",,,, _ ... c:::ilO èl co o co '" '" o

'"

01 IIII! 111111111111111111111111111111111111111111111111111111111111,""",",,""" 111111111111111111111111111111111111 f

1111111111111111111111111111111111111111111111111111111IIII~

.. '" a. ... "''''io5 '" "' .. '" "' ... "''''11)6

To':

N

.

.

..

... '" '"

Io

N (CYCLES)

FIG. 7 ~OG-NORMAL PROBABILITY,

C'I ... ClOU)" \oU _ ... , u. __ ...

dllldliill!dUilllitlilllt.lllitl 1111,\'''- 1 I 11 -•

~

'

~

Jli

~

ili

~W

'

1

1111

1

. ij : I II

iI:l

lllt

I ' . d -~. + H~i-HH. 52 KSI -ST RESS LEVEL j .

ml

I '

"

I

'

-=i~

A

!~-u.:'

+w.~

: ::'.

'

=t:=t~l=l

~

~

f

j

~tt.j

~

i~

~j#1

+!+f+l+7l

+++W+!1+.~

j

'1

-~

"

1

1

• GLUE FAILURE ~ • ME TAL F A I L URE

ttti1Jj

jJ.

l

j.~J

j

ttl~ruEI

~-I"""-' ,-IiIr:H

j~

~-

~

T

I

:'--F:1:f:

I

:-'

-"'"'

~.-

'J~

f:

=--1 -:Et

:

~~

..

~~-t~.· fft, ~t

!

~::jj

'

·1

~;::r~:r.f.fllr<

1 -JTI~.lmll!Il.{X·-' 1-' "' .... co "'i0 4 N W I> ' " 0> .... """'10 5 N (CYCLES)

ffiill!

~

a.

., J

-. -. -.0 """'i0 6

FIG. 8 LOG-NO~MAL PROBABILITY,

...

o

...

'" '" o ~w ···0 ,

-...

0 g; P(%) '" 0 .... 0 0> 0 co '" '" 0 '" '" '" co ~

.

~

.

~:

60

~'~

'

~'~;

'

;

'~'

,,~""~

t:r:I l

zZ

~o Oe z~

~~

~~

I-zj!;l:l >~ 8t:r:1 .... t:l

ê>

t:r:Iz '$t""4 • 0

PO

t-AI-zj

->

8

o

e

t:r:I t""4

....

I-zj l'1:!

..

-Um~ (KSI) 50 111111111111111111111111 40 1 111111111111"""'"1 30 1111111111111111111 20 IIII! 1111111111111111111 10 111111111111111111111111

o

I I I I I!! ! ! !!!!!!! 10'" 10 N \CYCLES) ( N U MB ERS NE X T T 0

ARE SAMPLE SIZE)

10

I

70 r!l!!!!ïii:iiiiï--;;;-;-;-~-:-:=~----"-'

__

___

__

....

_.L_. ___ . - -.. - - - i -- . -- - + - - -

-,..--- SOLID MET AL

S Q

u

ARE, ME TAL F A I L URE

60 .. - _._---_ .... --- - - -- - - + ---

-I

BEVELLED, GLUE FAILURE

I I 50

f----

-.~

-

~-

-

---

-

L----___t_

.

I

i I I

i

, . SQUARE,GLUE FAILURE 40

L-

-.-

.

---

----i----.

-

--+_ .-_

.. ---

1--

--

-

----'--I ' !

I

CT max j

~

!

I

(KSI)

I

!

I

!

I

30

l--

-

.

_--

-...

.

I

I

i : I I _. _ _ _ L_ .. __ .' _____ ~._ .. , ... L._ .. ___ ._._ ... __ ... _. __ ~_._. _______ 1 ___ . -.. -_. I ' I ! I I ; 20

f---

- -

-

.--+

.---

.

.

-..

.

.. __

_

.

.L _ _ _ _ ___ ~-

-.---.-

- - - - + - - -

----

.

.

-+---;

I 10 . __ . . . I I __ .

i

i

I _ . • . _ •. _ .. __ _ _ • ___ -J-.. _ _ __ . . . j

o

L -_ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ _ ~ _ _ _ _ _ _ _ _ _ _ ~ _ _ _ _ _ _ _ _ ~ _ _ _ _ ~ --~h---~---100 N (CYCLES)

FIG. 10 S-N CURVES EXTENDED TO COVER FULL RANGE OF FATIGUE LIFE

8

J

FIG., A. 1 STRAP MISALIGNMENT