Bonded joints; a photoelastic study

BONDED JOINTS

',J

A

PHOTOELAS~IC

STUDY

by

v.

Niranjan

•

IJ

..

BONDED JOINTS A PHOTOELASTIC STUDY by V. Niranjan

Manuscript received JUly,1969.

•

ACKNOWLEDGEMENT

The author wishes to thank Dr. G. N. Patterson, Director of the Institute for Aerospace Studies for providing the opportunity towork on this project.

The author is also grateful to Dr. G. K. Korbacher for his advice and supervision and to Dr. R. C. Tennyson for his help and guidance in the photoelastic work and for lending some of his equipment.

Last, but not. least, the author wants to thank Mr. Jim Bradbury whose help in many technical problems was very much app-reciated .

This project was financially supported by NRC and Fleet Mfg . Ltd., Fort Erie.

l . 11. l I l . • IV.

V.

TABLE OF CONTENTS~ SUMMARY NOTATION INTRODUCTION

REVIEW OF LITERATURE ON BONDED JOINTS TEST EQUIPMENT AND SPECIMENS

3.1 Test Equipment 3.2 Specimens

ANALYSIS AND DISCUSSION OF EXPERIMENTAL RESULTS CONCLUSIONS REFERENCES APPENDICES TABLES FIGURES 1 2 3 3 3 3 7 9

•

NOTATION

(Re,fer t o. Fi g, 3 for a clear unders tanding of the Nota ti on) G G l ' 2 1 n ,n o 1 n t2 P t x ,x ,x 1 2 3 8 T cr UN cr 2 cr 3 SUBSCRIPTS

AV

Max', UN Theory shear Modulii length of overlap

shear stress concentration factors defined in Appendices A and B,

Tensile stress concentration factor along boundary OB =( cr / cr )

2 UN Max',

Tensile stress concentration factor along boundary OC = ( cr / cr )

3 UN Max, Axial load

width of specimen,

thicknesses of adherents

distances along OA, OB, OC from 0

angle of Chamfer

shear stress along "adhesive layer." OA

stress at point

D

which is in the uniform stress region stress along boundary OB

stress along boundary OC

Average

Maximum measured value Uniform

•

SUMMARY

The existing literature on bonded metal-to-metal joints deals primarily with the stress distributions in the adhesive

layers. This particular, stress distribution is of significance for

bonded joints designed to fail in the adhesive, either under static

or under f-atigue loads.

However, the conventional thicknesses of metals currently

used in bonded joints in combination with present day adhesives make i t possible to take full advantage of the a-dhesive joint

strength and shift failure from the adhesive to the metal. When a

joint is designed for metal f.ilure, the interest in stress distri-butions shifts from the adhesives to the metal at and in the vicinity

of the surface discontinuities of the joint. Stra~gely the case

of metal failure in bonded joints has, perhaps because of

pre-conceived ideas, received l i t t l e attention and hardly an~ discussion

in the literature.

A joint, designed to fail in the metal under static loads,

achieves the full static strength of the metal. However, under

fatigue loading, the role and magnitude of stress concentrations ,

in the metal becomes very significant.

This note deals primarily with the stress distributions

in the metal due to stress concentrations around the bonded joint'.

rt shows, how these high stresses can be reduced in both the

I. INTRODUCTION

The majority of pap~rs published to-date on the stress

distributions in bonded metal-to-metal joints deal with the aimple or unsupported lap joint shown in Fig. la·. This type of lap joint is used primarily for testing adhesives and for specimens employed in the quality control of production-bopding. Simple lap joints are, in general, not used in weIl designed load carrying structures.

A metal-to-metal joint that is expected to carry loads is always

given some form of support to minimize tearing stress es in the adhesive. Such supported lap joints are shown in Fig. lb and Ic. Very of ten, these joints are des~gned so that the failure occurs in the metal, thus realizing the full load c.arrying capacity of

the joint. When a joint is designed to fail in the adhesive, either under statie loads or fatigue loads, the stress distribution in the adhesive becomes significant. But when a joint is designed to fail in the metal, the interest shifts to the stresses in the metal at the discontinuities of the joint. If a joint fails in the metal under statie loads it normally achieves, because of its ductility, the full statie strepgth of-the metal, not withstanding the stress concentrations in the metal. However, when a joint is to fail in the metal under fatigue loads, the stress concentration in the

metal become significant. Fatigue cracks normally initiate cn the specimen surface, where maximum stresses usually occur. This no e deals primarily with these surface stresses in the metal of metal -to-metal lap joints.

Chamfering the metal as a means of reducing the stress concentrations both in the adhesive and in the metal of lap joints was investigated.

Three type~ of photoelastic models were considered for this study. They are shown in. Fig.2. The first one is an in.e-grally machined specimen. The second one is made by joining the adherends with an adhesive. The third one is made by joining

the outer adherend with an adhesive to a sheet of lower shear modu-lus than the adherend (in simulation of the adhesive layer) and

joining this in turn to the central adherend.

For making a photoelastic model that truly represents a metal-to-metal joint, the principles of similarity have to be observed. The similarity pa·rameters for the measurement of maximum shear stress in the adhesive are given in Ref. 1. These similarity parameters, however, do not apply when the boundary s~resses are sought. For perfect similarity, the elastic moduli of the joint materials and the dimensi~ns o~ the joint have to be properly scaled. Near perfect similarity can be achieved by making up the typ~ of specimen which is shown in Fig. 2c . But such a specimen usually turns cut to be unusually large, if one desires to make accurate measurements, in.particular, along the ~dhesive layer, In· general, it is easier to achieve pruper similarity with

speci-mens of Fig. 2c, than. with those of Fig. 2b, but with both types of specimens it is very difficult to avoid air bubbles in the

joints as Ref.2 reports. Furthermore, when a scaled model as shown in Fig. 2c i s made, i t represents just one adhesive-adherend

combination and the results are not valid for a different adhesive or for a different adherend.

When one wants to make a general study and not a study of one particular adhesive-adherend combination, the model of Fig. 2a turns out to be the simplest, cheapest and easiest to work with due to the absence of size limitations. For this reason, specimens of the type shown in Fig.2a we re chosen for this study. This choice is further supported by inherent limitations in attempts to repre-sent actual joints by two-dimensional models as discussed in Ref.l.

All the theoretical and experimental studies of bonded joints undertaken so far have assumed a two-dimensional state of stress in the joint. The bonded joints in this study have also been r~presented by two-dimensional modeIs. The specimens that were studied and the specimen nomenclature used are shown in Fig.3. These specimens represent double lap joints with various angles of chamfer for the adherends, various adherend thicknesses and various lengths of overlap. This study shows chamfering to be very effec-tive in reducing the stress concentrations both in the adhesive and the adherend. In addition a wider specimen as shown in Fig.27a was made and studied to give some idea of how the stress systems in three-dimensional specimens deviate from two-dimensionality. 11. REVIEW OF LITERATURE ON BONDED JOINTS

A review of work done on bonded joints up to 1951 may be found in Ref.l and a thorough review of key-papers up to 1961 on the distribution of stress in adhesive joints is presented in Ref.ll. In particular, the section on experimental investi-,gations of the stresses in joints in Ref.ll is fairly extensive.

The stresses in the adhesive layers of several types of metal-to-metal joints have been theoretically analyzed by Volkersen (Ref.3),

Goland and Reissner (Ref.4), De Bruyne (Ref.5), Plantema (Ref.6),

Niles and Newell (Ref.7), Cornell (Ref.2), Cohen and De Silva

(Ref.8), Ferenc Szepe (Ref.9) and Lunsford (Ref.lO). Volkersen (Ref.3), De Bruyne (Ref.5) and Lunsford (Ref.lO) arrive at identi-cal results for the shear stress distribution in supported lap joints under tensile shear loading. The approach in Ref. 7 is

pretty much the same, except that here the shear deformation in the adherends is considered. Lunsford (Ref.lO) analyzes two more

types of joints in addition to the one mentioned above. Ferenc Szepe (Ref.9) derives an approximate, but very simple relation for the maximum shear stress in a supported lap joint.

The photoelastic work of Refs. 12 and 13 has also to be mentioned here. The author of Ref.13, under crude assumptions,

finds a rectangular hyperbola to be the desirabIe thickness con-tour of the adherend in order to obtain a uniform distribution of shear stress along the adhesive layer. Several attempts have been reported to improve the stress distribution in adhesive

joints. Most of the suggested modifications are geometrical ones. Improvement of the stress distribution by varying the

elastic properties of the adhesive along the length of overlap was first suggested by StegIer (Ref.14) and an analytical approach to

•

this probl em is presented in Ref. 15.

For an up-to-date and more comprehensive and detailed

review, the reader is referred to Ref.

16.

111. TEST EQUIPMEN.T AND-· SPECIMENS

3.1 Test Equipment

A pneumatic universal testing machine made by the Allied

Research Associates was used for load application to the photo

-elastic specimens .

A reflection polariscope from the Tatnall Measuring

Systems Co. was employed f0r measuring the photoelast ic signaIs.

All measurements were made using a white light souree and the Tardy

method of compensation.

The test equipment is shown in Fig.

4.

3.2 Specimens

The shape of the photoelastic specimens that were studied

is schemati cally shown in Fig. 3. The nomenclature and dimensions

used are tabulated at the bottom of Fig. 3. T.he specimens were

machined out of PSM-l, a highly sensitive polyester sheet supplied

by Photolastic Inc. The thickness of the sheet used was 0.3'75".

The properties of PSM-l are givèn below:

Stress - optical coefficient

=

40 psi/fringe/inch

Young's Modulus

=

340,000 psi

Poisson's Ratio

=

0.38

IV. ANALYSIS AND DISCUSSIONS OF EXPERIMENTAL RESULTS

The experimental results are presented in tabular form

in Tabl es 1 to 14 and in graphical form in Figs o 5 to 27,

The shear stress along the adhesive l ayer was calculated ,

knowing the isochromatic fringe order and isocl inic par ameter of

points along the adhesive layer, from the relationship :

T

=

where () --() 1 2

F

=

sin 28 _p T

=

shear stress sin 28 p

()

ï

IT₂

=

_{Principal stress difference}

\

I

8

=

Isoclinic Parameter

p

K

=

a constant

A nomogram is presented in Ref. 17 that is very handy for calculating the shear stress from the principal stress difference

and the isoclinic parameter. The boundary stresses are especially

easy to calculate, since only one principal stress exists on the boundary, which is directly proportional to the isochromatic fringe order on the boundary.

The shear stress distribution along the adhesive layer for adherends with various angles of chamfer is shown in Fig. 5.

For

e

=

900 _{i t is seen that the shear stress reaches its maximum}

value very close to the end of overlap and sharply falls off

again. Thus, the total load is carried by a very small region near

the end of overlap. Chamfering of the adherends was attempted to

distribute the load more uniformly along the whole length of the

overlap. As is seen from Fig.5, the load is distributed more

uni-formly as the chamfer is increased (as

e

is decreased), thereby

reducing the peak shear stress. Note also that the location of

the peak shear stress appears to be shifting away from the end of

overlap with decreasing

e.

The variation of measured maximum shear stress with the

angle of chamfer is shown in Fig.6. An angle of chamfer of 380

has reduced the maximum shear stress by 50% from the unchamfered

value. Thus, chamfering is seen to be very effective in reducing

the peak shear stress in the adhesive layer.

Two shear stress concentration factors are defined in

Appendices A and B. The stress concentrtion factor (SCF) no is

defined for a joint under shear loading. The SCF n

1, is defined

for a joint that is under a combination of shear ancr normal load-ing (see Appendices).

Variation of SeF n

l , with the angle of chamfer is shown

in Fig.7. It follows already from Fig.6 that n_l should decrease

with deoreasing 8. Thus, the strength of a bonaed joint can be

increased by chamfering the adherends. The calculations for

ob-taining n_l are shown in Table 12.

The stress distributions along boundary OB (see Fig.3.)

for various angles of chamfer are shown in Fig.8. For all the

specimens, there is a stress-peak at point ~ from where the boundary

stress gradually falls off to zero at B. For the specimen that is

not chamfered ( 8= 900 ) , the boundary stress falls off rapidly

to zero and takes on small negative values before coming back to

zero at B. It is interesting to note that the boundary stress

distribution shown in Fig.28 (obtained from Ref.18) is similar

to the stress distribution shown in Fig.8 for 8

=

900 • This is

to be expected from the similarity of the two specimens and the type of loading on them.

The stress distributions along boundary OC (see Fig.3.)

are shown in Fig.9 for various angles of chamfer. The boundary

stresses have a peak at the origin and gradually level off at some

•

distance from the origin.

The measured maximum stress along boundary OB decreases

with decreasing 8, as shown in Fig.lO. Similarly, the measured

maximum stress along boundary oe decreases with a decrease in 8, as

shown in Fig.ll. Thus, in addition, to reducing the peak shear

stresses in the adhesive layer, chamfering also reduces the peak

boundary stresses in the adherends. If a joint is designed for

metal failure, the statie strength is not likely to be improved (due to the ductility of the metal) by the reduction in peak boun-dary stress achieved by chamfering the adherends, but the fatigue strength is expected to be improved.

The shear stress distribution for various thickness

ratios t _{l /t 2 and}

e

=

900 _{is shown in Fig. 12. The load is again}

carried by a small region near the end of the overlap whereas the rest of the adhesive layer carries practioally no load, for all

the thickness ratios considered. It is seen that the measured

maximum shear stress in Fig. 12 decreases with increasing t _l /t₂,

as shown in Fig.13. This is to be expected, since a larger

value of t

l /t2 for a fixed tI means a smaller discontinuity at

the joint and thus a smaller maximum shear stress. The largest

value of t /t 2 that may be chosen for a double strap joint is

2.0 and vatues greater than this would make the straps weaker than

the central adherend. Thus, in addition to chamfering, a thickness

ratio of 2.0 would minimize the shear stresses in a double strap

joint. The SCF n_l (see Appendix B) remains almost a constant wi th

increasing t

l /t2 , as shown in Fig. 18. This is so, because the

maximum shear stress decreases with an increase in t l /t 2 as shown in Fig. 13, and so does the average shear stress as may be seen

from Appendix B. The SeF no (see Appendix A) on the other hand

decreases when tl/t2 increases as shown in Fig. 19, since the maxi-mum shear stress decreases with an increase in t l /t2' while the

average shear stress remains constant as may be seen from Appendi x

A. The maximum shear stresses used in the calculations of both

no and nl are the same, since according to St. Venant's principle, the stress distribution far away from the loading region is

identi-cal for two statiidenti-cally equivalent loadings. The calculations for

obtaining n and n a r e presented in Tables 11 and 14.

o 1

The stress distributions along boundary OB (see Fig.3)

for various thickness ratios are given in Fig. 14. All the stress

distributions have a peak at point

e

and take on small negative

values (compressive stresses) before becoming zero at B. The

measured maximum stress along boundary OB does not seem to vary with varying thickness ratio as shown in Fig. 16, for the range of thickness ratios considered.

The stress distribution along boundary oe (see Fig.3)

for various thickness ratios is given in Fig. 15. The stress

distribution seems to be more or less the same for all the

thick-ness ratios considered. The boundary stress has a peak at point

o and gradually levels off to the stress value in the uniform

remains constant with varying thickness ratio as demonstrated in Fig. 17 for the range of thickness ratios considered.

The significanee of the above results, seems to be that, once a -joint is designed for metal failure, the thiokness ratio t_{l /t 2 , if in the range of one to two, does not have a noteworth} influence on the strength of the joint₁

The shear stress distribution for various lengths of overlap is shown in Fig. 20. _{For l / t l}

=

1.0, the shear stress distribution has two maxima, one at each end of the overlap with

a small region of uniform shear stress at the middle. For l / t_l

=

2.0, the same type of distribution is found except for the smaller

maxima. Two points are noteworthy, first the small decrease in maximum shear stress with increase of overlap (see Fig.21) and second, the large decrease in average shear stress with increase in the length of overlap. As aresult, the BeF no (see Appendix A) increases strongly with an increase in the length of overlap as demonstrated in Fig. 26. The calculations for obtaining no are given in Table 13.

The distribution of stresses along boundaries OB and oe (see Fig.3) for various lengths of overlap are shown in Figs. 22 and 23. The stresses along OB follow the already discussed trend with a peak at point 0 and falling off again to small negative values before becoming zero at B. The stresses along oe are also similar in their distribution to that previously encountered with a peak at 0 and then levelling off to the value of stress in the uniform region. The measured maximum boundary stresses along both OB and oe at first ·decrease and then remain constant with increase in the length of overlap as shown in Figs. 24 and 25. Except

for unusually small lengths of overlap, the maximum boundary stress does not vary with length of overlap. Thus, a joint designed for metal failure has a fixed statie and fatigue strength, irrespec-tive of the length of overlap.

The wider specimen shown in Fig. 27a was built to obtain some indication of the deviation of the stress distributions in practical joints from the stress distributions of the above dis-cussed two-dimensional models.· The curve shown in Fig. 27b was obtained using the specimen of Fig.27a. The true maximum boundary stress along oe (see Fig.3) can then be obtained by multiplying the maximum boundary stress obtained from the two-dimensional models with a factor of approximately 1.2. This factor of 1.2 merely indicates the order of magnitude of the deviation from a

two~dimensional distribution of stress and not the actual deviation

for any general case.

The average values of shear stresses obtained from the experimental results by integrating the areas under the .shear stress curves in Fig.20 are compared with values calculated using the equations of Appendix A. The table in Fig.20 shows the experi-mental values to be 4% lower than the theoretically calculated values. The measurements were accurate within + 3% of a fringe and the overall accuracy is expected to be about + 5%.

Attempts to measure the peak boundary stresses with bri ttIe

coatings on bonded double strap joints made of 2024-T3 Alclad and

bonded with FM-lOOO were unsuccessful due to the fact that (a) the peak stresses occur at the discontinuity of the

joint and

(b) the brittIe lacquer forms a fillet right in the region of interest.

The isochromatic fringe pattern for specimen No.2 .3 is

shown in Fig.29. This fringe pattern is representative for the

series of specimens 2.1 to 2.4, 1.1 and 3.1. The stress c

oncen-trations around corners A and Bare obvious. The isochromatics

for specimen No.l.4 are shown in Fig.30. This pattern is

rep-resentative for specimens 1.2 to 1~4. The weIl spaced horizontal

fringes are indicative of a gradual variation in stress caused by

the taper. The stress concentrations at points A and Bare seen

to be less pronounced. The isochromatic fringes for specimen

No.3.3 are shown in Fig.3l. This pattern is representative for

specimens 3.2 and 3.3. The stress concentration at corners C

and D are less severe than at A and B. This is due to the

dis-continuity at the plane CD being smaller than that at the plane

AB. The stress analysis was not done by whole field measurements

from the photographs but by point-to-point measurements with the

telescopic arrangement on the polariscope. The point-to-point

analysis, though time consuming, is more accurate than a photo-graphic analysis.

CONCLUSIONS

1) Reducing the chamfering angle (00 s e S900 ) of the adherends

(see Fig.3),

(a) reduces the peak (maximum) shear stress in the adhesive

layer e.g. by 50% fore

=

380 _{(see Fig.6), thereby}

reducing the stress concentration factor also to half its unchamfered value (see Fig.7),

(b) moves the location of maximum shear stress away from the end of overlap (see Fig.5) and

(c) reduces the peak boundary stresses in the adherends, a fact which should improve the fatigue strength of joints designed for metal failure.

2) Varying the thickness ratio (IS t l /t 2 S2) of the adherends does not seem to affect appreciably the maximum boundary stresses.

3) Increasing the length of overlap (IS I / t l S4.5)

(a) reduces the maximum shear stress by a very small amount, but

(b) causes a large decrease in the average shear stress value

(c) does not affect the maximum boundary stress except for very smalloverlaps, where a small reduction was observed.

4)

If a joint is designed to fail in the metal under fatigue

loading, the failure should occur in the region of maximum boundary stresses, in the absence of flaws in the metal. As the boundary stress concentrations are fairly low for

conventional joint dimensions, i t is not impossible to encounter a flaw, which causes the highest stress in a region away from the region of maximum boundary stress. In this case, failure would start at the flaw.

1. 2 . 3.

4.

5. De Bruyne, N. A. Houwink, R. Corne11, R. W. Volkersen, O. Go1and, M. Reissner, E. De Bruyne, N. A. 6. Plantema, ·F. J. 7. Ni1es, A. S. Newe11, J. S. 8. Cohen, H. De Si1va, C. N. 9. Szepe, F. 10. Lunsford, L. R. 11. E1ey, D. D. 12. Tuzi, I. Shimada, H. 13. Lerchentha1, C. H. 14. Steg1er, R. E. REFERENCES

Adhesion and Adhesives. E1sevier

Pub-lishing Co., 1951.

Determination of Stresses in Cemented

Lap Joints. J. App. Mech. September 1953.

Die Nietkraftsvertei1ung in Zugbeans-pruchten Nietverbindungen mit konstanten

Laschenquerschnitten. Luftfahrtforschung,

15, (1938)41.

The Stresses in Cemented Joints . J. App.

Mech., March 1944.

The Strength of G1ued Joints. Aircraft

Engineering, April. 1944.

De Schuifspanning in een lijmnaad.

Nationaal lucht-en ruimtevaartlaboratorium,

The Netherlands, 1947.

Airp1ane Structures, Vo1.I. John Wi1ey

&

Sons Inc., 1954.

Adhesive Stresses in Bonded Meta1 P1ates Rev. Roum. Sci. Techn.-Mec. App1., Tome

g, No.4. p.883-893, Bucarest 1964.

Strength of Adhesive-Bonded Lap Joints With Respect to Change of Temperature

and Fatigue. Expt. Mech., May 1966.

Stress Ana1ysis of Bonded Joints - in

Structura1 Adhesives Bonding, edited

by Bodnar, M. J. Interscience Publishers, 1966.

Adhesion, Oxford University . Press, 1961.

Photoe1astic Investigation of the Stresses

in Cemented Joints. Bulletin of Japan

Society of Mech. Engrs. Vo1.7, no.26, 1964.

Design of Bonded Lap Joint~ for Optimum

Stress Transfer - Part I. The

Symme-trical (or double) Lap Joint. Israe1

Journalof Techno10gy, Vo1.2, No.1, 1964.

Composite-Adhesive Bonds Cases for

Solid-Fue1 Rocket Motors. Iron Age,

15. Raphael, C.

16. Niranjan, V.

17. Campbell, D. M.

18. Zandman,

F.

Variable-Adhesive Bonded Joints - In Structural Adhesive Bonding, edited by Bodnar, M. J., Interscience Publishers, 1966.

Bonded Joints - A Review for Engineers. UTIAS Review No.28, 1969.

A Nomogram for Photoelasticians, Expt. Mech., December 1964.

Photoelastic Coating Analysis in Thermal Fields. Expt. Mech., September 1963.

APPENDIX A _ - - - , r - - - -... - - - - -----'

x.

_ _ _ _ _ '---"""1 ~--t

---11--tr,

/O"üN

)t1~l(

t.r

/1üt.J

)"V

o

₁

FIG A.I. JOINT UNDER SHEAR LOADING

Derivation of au Expression for 'n ':

0

-If 'tl is the

n

o

dim7sion of .the specimen

T.t. diX = P/2 o P t.t 1 O"UN P

=

O"UN.t.tl .i

J

T.t.cL~

= o 1

J

o

.

1

(

~UN

)av

(~

)Max

(;UN

)av

1 2"

normal to' the plane of the paper,

I

APPENDIX B

r---...,---.,.- ______

t--.--p

.

tz.

/

(t:

,

+

2

't:

1) X

-P

,

t.

,j(

\:

,+2.t1.

)

... - - f - - - -....

1

- - -

--

-o

₁

p

.

tl./(

t,

+'LtJ

('T/~N

)MAll

(T/Oü

~ )

AV

FIG. A. 2. JOINT UNDER A COMBINATION OF SHEAR AND NORMAL LOADING

Derivation of.an Expression for 'lli~

If, 't' is the dimension of the specimen normal to the plane of the paper,

t

J

T.t.dX

=

o P cr

=

UN o 1

J

o

(

~;)av

=

1

( ç

)Max.

--=--(;UN

)--==Max_

SPECIMEN NO: 1.1,

_,

~ .. ;lA or :6.::)..

TABLE NO: la TABLE NO: lb . TABLE NO: lc

xl/tl T x 2/t1

<J!<J

UN x3/t1

<J!<J

UN

-<JUN 0.0625 0.73 0.03 1.51 0.125 0.375 0.03 1. 49 0.0625 1.42 0.25 0.271 0.125 0.43 0.125 1.232 0.375 0.229 0.25 1.075 0.5 0.212 0.25 0 0.375 1.0 1.0 0.139 0.5 1.0 1.5 0.067 SPECIMEN NO: 1.2

TABLE NO: 2a TABLE NO: 2b TABLE NO: 2c

xl/tl

-

_(JUN T x it l

<J!<J

_UN x₃/t1 (J3/<JUN 0.0625 0.42 0.03 1.385 0.03 1.39 0.25 0.263 0.125 0.952 0.125 1.09 0.375 0.179 0.25 0.79 0.25 1.02 0.5 0.129 0.375 0.605 0.375 1.0 1.0 0.105 0.5 0.563 0.5 1.0 SPECIMEN NO:l.3

TABLE -NO: 3a TABLE NO:3b TABLE NO:3c

xl/tl T/(JUN x₂/t₁

<J!<J

UN x3,ft1

<J!<J

UN 0.25 0.257 0.03 1.19 0.03 1.27 0.375 0.338 0.125 1.04 0.0625 1.15 0.5 0.333 0.25 0.828 0.125 1.06 1.0 0.214 0.375 0.622 0.25 1.0 1.5 0.128 0.5 0.518 0.375 1.0 0.5 1.0

TABLE NO: 4a .

X~/t1

T/erlJN

0.046 0.114 0.103 0.099 'r~LE NO: 5a PART OF SPECIMEN · DAMAGED TABLE NO: 6a x/tl

T/er

0.0625 0.58 0.125 0.407 0.25 0.22 0.375 0.198 0.5 0.167 1.0 0.098 1.5 0.044 SPECIMEN NO: 1.4 TABLE NO: 4b x₂

/t

₁

~

/erUN

0.03 1.18 0.125 1.11 0.25 0.996 0.375 0.86 0.5 0.805 1.0 0.647 SPECIMEN NO: 2.2 TABLE NO: 5b

x

₂

/t

₁ ~

/er

_UN

0.03

'

1.46 0.125 0.438 SPECIMEN NO: g.3 TABLE NO: 6b x 2/t1

er/er

UN 0.03 1.48 0.125 0.13 TABLE NO:

4c

x/tl

er/er

_UN 0.03 1.16 0.125 1.06 0.25 1.0 0.5 1.0 TABLE NO: 5c x/tl

er/er

_UN 0.03 1.47 0.125 1.19 0.25 1.06 0.375 1.01 0.5 1.0 TABLE NO: 6c x/tl

er/er

_UN 0.03 1.49 0.125 1.15 0.375 1.0 0.50 1.0

TABLE NO: 7a x/tl T/o-_UN 0.0625 0.55 0.125 0.222 0.25 0.167 0.375 0.121 0.5 0.1 1.0 0.053 TABLE NO: 8a PART OF SPECIMEN DAMAGED TABLE NO: 9a X/tl T/o-_UN 0.0625 0.782 0.125 0.362 0.25 0.256 0.375 0.254 0.5 0.253 1.0 0.24 105 0.177-1.625 0.17~ 1. 75 0.146 1.875 0.145 1. 9375 O~~184 2.00 0.0 SPECIMEN NO: 2,4 TABLE NO: Th x₂/t_l O-!O-UN 0.03 1.5 0.125 0.247 0.25 -Ve 0.375 -Ve 0.5 0 SPECIMEN NO: 3.2 TABLE NO: 8b x₂/t l o-!O-UN 0.03 1.51 0.125 0.4 0.25 0 SPECIMEN NO: 3.3 TABLE NO: 9b. x₂

/t

_{1 o-!o-UN} 0.03 · 1.54 0.125 0.398 0.25 0 TABLE, NO: 7 e x

3

/tl o-!o-UN 0.03 1.46 0.125 1.19 0.25 1.1 0.375 1.0 0.5 1.0 TABLE NO: 8e x

3

/tl O-!O-UN 0.03 1.53 0.125 1.34 · 0025 1.11 0.375 1.06 0.5 L O TABLE NO: 9c x

3

/t

1 cr!O-UN 0.03 1.53 0.125 1.33 0025 1.11 0.375 1.0 0.5 1.0

SPECIMEN NO: 3.4

.

TABLE NO: 10a

TABLE NO: lOb

TABLE NO: lOc

I i

Xl/tl

T/O"UN

x

₂

/t

_l

O"!O"UN x

3

/t

l

O"~O"UN

'

0.0625

0.805

0.03

·

2.61

·

0.03

.

2.53

0.125

0.64

0.125

0.813

0.0625

1.9

0.25

0.545

0.25

0.327

0.25

1.1

0.375

0.495

0.375

0

0.375

1.0

0.5

0.49

0.5

1.0

0.625

0.48

0.75

0.396

0.875

.0.322

0.9375

0.354

1.0

0

TABLE NO: 11

t

2

t)./t 2

t

2

/(t

1

+2t

2

)

(T/O"

k

~=

t 2

1 see UN

X t +2t

. 4.5

n_l

(App.B)

1

2

1"

1

0.333

0.73

·

0.074

9.86

0.625"

1.6

0.278

0.58

0.062

9.35

0.5"

2

0.25

0.55

0.056

9.82

TABLE NO: 12

.

8 _{( T/O"UN)Max (T/O"UN)aV =}

t 2

1 (see

App. B)

t

l

+2t2

. 4.5

n

1

90°

0.73

0.074

9.86

45°

0.42

0.074

5.68

30°

0.338

0.074

4.57

15°

0.1l4

0.074

1.54

TABLE NO: 13

( T/O"UN)Max (T/O"UN) aV

=

_2" 1 1

_(,g/t

(see App.A)

1) n 0 0" 1.0 1" 0.805 0.5 1.61 2" 0.782 0.25 3.128 4.5" 0.73 0.111 6.58 TABLE NO: 14 t 2 t/t2 ( T/O"UN)Max (T/O"UN)aV

=

~

1 _{n (see App.A)} O/t_l ) 0 1" 1 0.73 0.111 6.58 0.625" 1.6 0.58 0.111 5.23 0.5" 2 0.55 0.111 4.95

• · .. lo ,.

p .

.,p

FIG. 1 A. SIMPLE OR UNSUPPORTED LAP JOINT

FIG. 1 B. DOUBLE OR SUPPORTED LAP JOINT

2P -

~ _ _ _ _ _ _ _ _ _ _ _ _ ~ _ _ _ _ ~ _ _ - L _ _ _ _ ~ _ _ _ _ _ _ _ _ _ _ _ _ ~ ~-!.--

2P

p

.

p

p

p

-p

p

Fictitious Adhesive - - Loyer

-- -- -- --

-(~) First Specimen - Integrally Machined

J

I

-L -L ~ LL.L

J

I

(b) Second Specimen - Adherends Bonded with au Adhesive.

Sheor Modulus G₁

2P

Adhesive

-

2P

Fictitious Adhesive Loyer (G₂<G₁₎

1--~2P Adhesive

(thickness exn.goeroted)

(c) Third Specimen - A plastic sheet of proper modulus is used to represent the adhesive layer.

B

c

o

~

___

_--.A

Xs

O·

P ---t-~ XI T

I

Cl

~

I

I

:

5"

-I

10" POINT D I I I ONG CTun = STRESS AT CTs = STRESS AL CTz = STRESS AL T =SHEAR STR XII xz,x, = DISTA BOUNDARY

o

l

c

8

= ANGLE OF I = LENGTH OF SPECIMEN N!! 1.1 1.2 1.3 1.4 2.1 2.2 2.3 2.4 3.1 3.2 3.3 ONG BOUNDARY OB ESS ALONG OA

NCES ALONG OA,OB,OC FROM 0

CHAMPHER OVERLAP

8

ti 90° I 45° I" 30° I" 15° I" 90° I" 90° 0.75" 90° 0.625" 90° 0.5" 90° I" 90° I" 90° I"

FIG. 3. SPECIMEN NOMENCLATURE

i

J

,.... _p tz

t

-,

!

:-i:

I

::*=

OA = GLUE LlNE 7?

-[--2L]

t2 CTun max 7? -~

f

eh ] t, - CTun max. tz I I" 5" I" 5" I" 5" I" 5" I" 5" I" 5"

I"

5" I" 5" I" 4.5" I" 2" I" I"

...I-~

O"un 1\

I \

0.8

+ \

,

\

,

.

0

.

7

ti

I/ "

0

.

6T'

, e

=900

'I

0.51/

:1,

"

0.4T',

Ijl

11,

0

.

3TII

lil

11/

0

'

1, /

.

o

SPECIMEN N!! 1.1

8

SPECIMEN N!! 1.2 X SPECI M EN Ng 1.3

o

SPECIMEN N!! 1.4

~

/ . >.5' 0

Olt~

___

8

~I ~

________ . ____ _

r

./

[

.1:..1

O"unJavg.

=0

.

074

,..../

I

I

o

0.5 1.0

I.~

T (~)mox un 0.8 0.7 0.6 0.5 0.4 0.3 0.2 0.1

o

SPECIMEN N!! 1.1 A SPECIMEN N!! 1.2 X SPECIMEN N!! 1.3 [J SPECIMEN N!! 1.4

..

_....--8

FIG.

6.

VARIATION OF MEASURED MAXIMUM SHEAR STRESS WITH ANGLE

OF CHAMFER.

n,

8 6 4 2 0

0

SPECIMEN N!! 1.1 A SPECIMEN N!! 1.2 X SPECIMEN N!! 1.3 [J _{SPECIMEN N21.4} ~

8

900 600 ₃₀0 ₀0

02

O'"un

0

e=

90° I SPECIMEN N~ 1.1

2. ê

e

= 45° I SPECIMEN N2 1.2

)(

e

=

_{30°, SPECIMEN N! 1.3}

8

e

= 15° I SPECIMEN N! 1.4

FIG.

8.

STRESS DISTRIBUTION ALONG BOUNDARY OB OF FIG. 3.

0

e

=90° I SPECIMEN N! 1.1 0'"3 ê

e

=45°, SPECIMEN N2 1.2 X

e

_{=30° I SPECIMEN N2 1.3}

8

e

=

15° , SPECIMEN N21.4 2. 0.5

o

0.2 0.4 0.6 0.8 1.0

0

SPECIMEN N2 1.1

Uz

é

ntl

ntl

=

(ë7Url)max.

SPECIMEN N2 1.2 X _{SPECIMEN N2 1.3} 1.6

0

SPECIMEN N2 1.4 1.4 1.2 1.0 900 _60°

..

8

3 ° 0°

nts

1.6 .1.4 1.2

FIG. 10. VARIATION OF MEASURED MAXIMUM STRESS ALONG BOUNDARY OB WITH ANGLE OF CHAMFER.

0;

₀

_{SPECIMEN Ng 1.1}

nts

=

(CT

un

)max.

ä SPECIMEN N2 1.2 X SPECIMEN N2 1.3

0

SPECIMEN N21.4 1.0 9pO _{60° 30° 0°}

..

8

FIG. 11. VJ\RIATION OF MEASURED MAXIMUM STRESS ALONG BOUNDARY OC WITH ANGLE OF CHAMFER.

r (Tun 0.8 0.7 1

Il\

0.6i1~'

i~

0.5 0.4 0.3 0.2 0.1 o 0 SPECIMEN N!! 2.1, ti /12 = 1.0 X SPECIMEN N!! 2.3, ti /tz = 1.6 0 SPECIMEN Na 2.4, ti /t₂ =2.0 ti /t_{z -1.0}

( SEE APPENDI CES FOR THEORY)

ti /t_z =2.0 [ r

J

-0.074 OUn avo Theory

~~

_ _ _ _ _ _

«lciu~a

The =0.062

::~~__

_ _ _ / "" V. ory

-... --..;..--- --

_-

~..::: ~~~----=---

_-

_-

_{- - - = - - - ,}

--

__

-

--=--=--:::... _ _

-

__ _

_

~-=---====~_

_ - - I

--...:....- -

~[_l

-I - r I 0ü;J avo Theory =0.056 2 3 4 4.5

FIG. 12. SHEAR STRESS DISTRIBUTION FOR VARIOUS ADHEREND'THICKNESS RATlOS (9 = 90°).

XI

~tl-0.5 0.4 1.5 1.0

o

~ ~ Uur; 1.5 1.0 0.5

o

0

SPECIMEN N!! 2.1 X _{SPECIMEN Ni 2.3}

0

SPECIMEN Ni 2.4

t,

=

I"

e

=900 1.0 1.2 1.4 1.6 1.8 2.0

t,

/t₂

FIG. 13. VARIATION OF MEASURED MAXIMUM SHEAR STRESS WI'I'H THICKNESS RATIO.

o

SPECIMEN N22.1 t₂

=

I" 6 SPECIMEN N!! 2.2 t₂ = 0.75"

X SPECIMEN Ni 2.3 t₂=0.625"

8

SPECIMEN Ni 2.4

t

₂

=

0.5"

FIG. 14. STRESS DISTRIBUTION ALONG BOUNDARY OB.

0

SPECIMEN Ni 2.1

_t2

=

I" A SPECIMEN Ni 2.2

_t2

=

0.7'5" X SPECIMEN N!! 2.3

t2

=0.625"

0

Ni 2.4 11 \ SPEOMEN

t2

=

0.5

'-.

t,

= 1"

..

e

=900 0.2 .4 0.6 0.8 1.0

n _

r..QLl

t2 -

LO"unJmax

.

o

SPECIMEN N!:! 2.1 6 SPECIM EN N2 2.2 X SPECIMEN N!:! 2.3

o

SPEQMEN N~ 2.4 1.54----~~---_y_---l:J 1.3 nt ₃ FIG. 16. I. 3 1.6 _2.0

VARIATION OF MEASURED MAXIMUM BOUNDARY STRESS ALONG OB

WITH THICKNESS RATIO.

0 SPECIMEN

6 SPECIMEN

"t3

- O"'un max.

-[~

X SPECIMEN

0 SPECIMEN N!:! 2.1 N!:!2.2 N!:!2.3 N~2A 1.3 I _{I. 33 1.6}

FIG. 17. VARIATION OF MEASURED MAXIMUM BOUNDARY STRESS ALONG OC WITH

'l'HICKNESS RATIO. IO~

________________

~---~--O

o

SPECIMEN N!:! 2.1 X SPECIMEN N!:! 2.3

o

SPECIMEN N!:! 2.4 5~---~~~---~---~---~ _I 1.6

FIG. 18. VARIATION OF SIfEAR STRESS CONCENTRATION FACTOR WITH THICKNESS

RATIO FOR THE CASE OF COMBINED SHEAR AND NORMAL LOADING.

o

SPECIMEN N!:! 2.1

X SPECIMEN N2 2.3

o

SPECIMEN N!:! 2.4

O~I---+---;----~t~I~/~

...L

(Tun 0.8 0.7 0.6 O.IS 0.4 Q.3 0.2 0.1

'\

\ (T/CTun)av.= 0.5 l.:.-~F.::::::": - ~ - - , I/tl=I.O

I

I

A

11

0 SPECIMEN N~ 3.1 X SPECIMEN Ng 3.3 Q SPECIMEN Ng 3.4

SPECIMEN Ng

[~OV

.

theory fciu~ov

.

experiment ~

3.4 0.5 0.48 4

3.3 0.25 0.24 4

SEE APPENDICES FOR THEORY

, I

\1

~~_

... _____

#I:..._::::.:

___

(T/a:_un)_OV.=_0.2_5 - - l I/tl

=

2.0

'I

.

.

I

_..-- _ .J...T{$dOV.

=O.O~

_ _

,

': _ _ I

I

'I

\ I

\1

1 r

-o

~---~---~~---+---+---O.IS 1.0 I. 2.0

2L

ti

[ciun]m

0

SPECIMEN N~ 3.1 0.9

X

SPECIMEN N5! 3.3 0.8 0- _~ [;) SPEOMEN N5! 3.4

-0

0.7 0 2 3 4 5 I/t,

FIG. 21. MEASURED MAXIMUM SHEAR STRESS VS LENGTH OF OVERLAP.

2.5 2.0 SPECIMEN N5! 3.4, I /t, =1.0 1.5 SPECIMEN N2s 3.1, 3.2,3.3, I/t, = 4.5, 3.0, 2.0 1.0 0.5

o

0.2

FIG. 22. STRESS DISTRIBUTION ALONG BOUNDARY OB.

a;

I

(Tun \ SPECIMEN N2 3.4 , I/t

=

1.0 N2

_s

_{3.1,3.2,3.3. I/t, =4.5,3.0, 2.0}

o.

o

_{0.2 0.4 0.6 0.8 1.0}

2.0 3.0 2.0

0

SPECIMEN N2 3.1 n

=

[CT.~

~ t2

Oü

max. à SPECIMEN N! 3.2 X SPECIMEN N2 _3.3

"-

[;] SPECIMEN N!3.4 )f ₆

₀

2 3 4 5 I/tl

FIG. 24. MEASURED MAXIMUM BOUNDARY STRESS ALONG OB VS. LENGTH

OJ"

OVERLAP.

~~~~----~à~---0

1.0 0 2 3 4 5

no

8 6 4 2 0

FIG.

25.

MEASURED MAXIMUM BOUNDARY STRESS ALONG OC VS. LENGTH

OF OVERLAP.

0

SPECIMEN N23.1

X SPEOMEN NR3.3

[;] _{SPECIMEN N!3.4}

2 3 4 5 I/tl

N 1.5 1.0 0.5

C

CR - 39 FIG. 27.A.

1.

1

_.11.

1 _~

I

j

I

~

.

: 11 C E S I V E w = Width= 2" t = Thickness of adherends = 0.2"

d = Glue line thickness = 0.002"

I = lenoth of overlap = 1"

N = Fringe . order

SPECIMEN USED FOB FINDING THE DEVIATION FROM A TWO-DIMENSIONAL STRESS DISTRIBUTION.

Distribution for the 3d

Nmax.= 2.278 - - Nmean =1.917 n

=

N max. =2.278

=

1.19 $::I 1.2 Nmean 1.917

C~ftribution

Nmin:= 1.65 for a 2 d specimen

o

~---r---~r---~ 0.5 1.0 x/w

fr • Tangential stre.s alono

boundary 08

fro • Uniform stress in the plastic far away from

the end of overlap

_.

8

PHOTOELASTIC PLASTIC

BON,DED SURFACE

STEEL STRUCTURE

a=6fLin/in/oF

COMPOSITE STRUCTURE COOLED FROM 75°F TO 19°F

(JrIAS TEX:HNI CAL NOn NO .138

Institute for Aerospace Studies, University of T oronto

Bonded Joints - A Photoelastic Study

Niranjan, V. 10 ptlges 14 tables 31 figures 1. BondÎ.ng 2. Photoelasticity 3. Stress Concentrations 4. Lap Joints

Tbe existing literature on bonded metal-to-metal joints deals primarily witb tbe stress distributions in tbe adhesive layers. This particular stress distribution is of

signi-ficanee tor bonded joints designe'tl to fail in the adhesive, either under statie or under

fatigue loads. However, the conventional thiclalesses of metals currently used in bonded

joints in comblnation with present day adhesives make it possible to take f'ull advantage of the adhesive joint strength and shift failure from the adhesive to the :netal. When a joint is designed tor metal failure, the interest in stress di stributions shifts trom

the adhesive$ to the metaJ. at and in the vicinity of the surface discontinuities of the

joint. Strangely the case of metal failure in bonded joints bas, perbaps because of

preconceived ideas, received little attention and hardly any discussion in tbe literature.

A joint, designed to fail in the metal under statie loads, acbieves tbe full statie strengtb of the metaL However, under fatigue loading, tbe role and magnitude of stress

concentrations in the metal become very significant. This nate deals prilllarily with the stress distributions in the metal due to stress concentratians around. the bonded

jo~nt. It shows, how these high stresses can be reduced in both the adhesive and the

."tal by means of e.g. chamf'ering the metal edge •.

~

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

tJrIAS TEX:HNICAL NarE NO.138

Institute for Aerospace Studies, University of T oronto

Bonded Joints - A Photoelastic Study

Niranjan, V. _{10 ptlges} 14 tables 31 figures 1. Bonding 2. Photoelasticity 3. Stress Concentrations 4. Lap Joints

The existing Uterature on bonded metal-to-metal joints deals primarily with the stress distributions in the adhesive layers. This particular stress distribution is of' SlgD.i

-f'icance f'or bonded joints designe'd to f'ail in the adheslve, either under statie or under fatigue loads. However, the eonventional thieknesses of metals eurrently used in bonded

joints in combination with present day adhesives make it possible to take f'ull advantage of the adhesive joint strength and shift failure from tbe adhesive to tbe metal. When a joint is designed for metal failure, tbe interest in stress di stributions shifts from

tbe adhesives to the metal at and in tbe vicinity of the surface discontinuities of tbe

joint. Strangely tbe case of metal failure in bonded joints bas, perbaps because of

preconceived ideas, reeeived little attention and bardly any discussion in the literature.

A joint, designed to fail in the metal under statie loads, achieves the fuH statie strength of the met al. However, under fatigue loading, the role end magnitude of stres8

caneentrations in the metal. become very significant. This nate deals primarily with

the stress d.1strlbutions in the metal due to stress coneentrations around the bonded

joint. It shows, ho." these high stresses ean be reduced in both the adhesive and the

."tal by means of e.g. chamf'ering the metal edges.

~

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

•

tJrIAS TEX:HNICAL NarE NO.13S

Institute for Aerospace Studies, University of T oronto

Bonded Joints - A Photoelastic Study

Niranjan, y. _{10 ptlges} 14 tables 31 figures 1. Bonding 2. Photoelasticity 3. Stress Concentrations 4. Lap Joints

Tbe existing literature on bonded metal-to-metal joints deals primarily with the stress distributions in the adhesive layers. This particular stress distribution is of signi-, ficance tor bonded joints designe'd to fail in the adhesive, eitber under stD.tie or under

f'atigue loads. However, the conventional thicknesses of metals currently used in bonded

joints in combination with present day adhesives make it possible to take full advantage of the adhesive joint strength and shift f'ailure trom the adhesive to the metal. When a

joint is designed for metal failure, the interest in stress distributions shifts from

the &dhesives to the metal at and in the vicinity of tbe surface discontinuities of tbe joint. Strangely the case of metal failure in bonded joints bas, perhaps because of preconceived ideas, received little attention and hardly any discussion in the literature. A joint, designed to fail in the metal under statie loads, achieves the full statie strength of tbe metal. However, under fatigue loading, the role and magnitude of stress

concentrations in the metal become very significant. This nate deals prima.rily with

the stress distributians in the metal. due to stress coneentratians around the bonded

joint. It shows, how these high stresses ean be reduced in both the adhesi ve and. tbe metal by means of e.g. chamf'ering the metal edges •

~

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

t1rIAS TEX:HNICAL NarE NO.138

Institut~ for Aerospace Studies, University of T oronto

Bonded Joints - A Phptoelastic Study

Niranjan, V. _{10 ptlges} 14 tables 31 figures 1. Bonding 2. Photoelasticity 3. Stress Concentrations 4. Lap Joints

The existing literature on bonded metal-to-met&l joints deals primarily with the stress distributions in the adhesive layers. This particular stress distribution is of signi-ficanee tor bonded joints designetl to fail in the adhesive, either under statie or under fatigue loads. However, the conventional thicknesses of metals currently used in bonded

joints in collilination witb present day &dhesives make it possible to take rull advanttlge of tbe adhesive joint strengtb end shift failure !rom tbe adhesive to tbe metaL When e.

joint is designed for metal failure, tbe interest in stress di stributions shifts from tbe adhesives to tbe metal at and in tbe vicinity of tbe surface discontinuities of the

joint. Strangely the case of metal failure in bonded joints bas, perbaps because of preconceived ideas, received little attention and bardly any discussion in the literature.

A joint, designed to f'ail in the metal under statie loads, achieves the f'ull statie

strength of the metal. However J Wlder fatigue loading, the role and ma.gni tude of stress

concentrations in the metal become very significant. This nate deals primarily with the stress distrlbutlons in the metal due to stress concentratians around the bonded

joint. It shows, how these high stresses can be reduced in both the adhesive and. the metal by means of e.g. chamf'ering the metal edge ••

~