NASA Contractor Report 178112

(NASA-CE-178112) CRITERICN FCfi A I X E D E40DE ERAC'IUBE I N CCIIPOZZ'IE ECNDED J C I N T S Report [nissouri U n i v . )

F i n a l 27 p EC A03/HP 801

N86-263 80

CSCL 11D Unclas G3/24 43587

CRITERION FOR MIXED MODE FRACTURE I N COMPOSITE BONDED JOINTS

S, Mal l and N , K, Kochhar

UNIVERSITY OF MISSOURI-ROLLA ROLLA, M I S S O U R I

GRANT NAG1-425 May 1986

National Aeronautics and Space Ad ministration

Langley Research Center Hampton, Virginia 23665

https://ntrs.nasa.gov/search.jsp?R=19860016908 2018-05-31T05:30:53+00:00Z

ABSTRACT

A study was undertaken t o character ize the debond growth mechanism

o f adhesively bonded composite j o i n t s under mode I , mixed mode 1-11,

and mode I1 s t a t i c loadings.

epoxy (T300/5208) composite adherends bonded w i t h a toughened epoxy

(EC 3445) adhesive. The mode I, mode I1 and mixed-mode 1-11 f r a c t u r e

energies o f the tes ted adhesive were found t o be equal t o each other.

Furthermore, the c r i t e r i o n f o r mixed mode f r a c t u r e i n composite bonded

j o i n t s was found t o be:

The bonded system consisted o f graphi te /

(GI/GIC) + (GII/GIIc) = 1.

1

INTRODUCTION

The adhesive bonding of laminated composite materials does n o t

require tha t structural members being jointed be perforated t o

f ac i l i t a t e bo1 ts. Without the bo1 t holes and s t ress concentrations

associated w i t h them, substantial weight savings can be realized

w h i c h i s a major reason for selecting composite materials f o r

structural components.

crack growth and t h u s an appropriate fa i lure criterion must be

based upon the in i t ia t ion and propagation of f l a w inherent i n the

Adhesive jo in ts usually fa i 1 by progressive

jo in t . Consequently, the fracture mechanics approach can be used

to characterize their fa i lure . Such an approach has been used t o

predict the f a i lu re of adhesively bonded jo in t s (1-2).

The majority of this work has been concerned w i t h the opening

or cleavage mode fa i lure (mode ?) . A crack i n an isotropic medium

will propagate i n Mode I fracture regardless of the orientation of

the i n i t i a l flaw w i t h respect t o the applied stress. However, this

i s not necessarily the case i n j o i n t fracture since crack propaga-

tion i s constrained to the adhesive layer regardless of the orien-

tation o f the adhesive layer, except, of course, when the substrate

has a lower toughness than the adhesive.

purposes, attention must be given t o j o i n t fracture under additional

loading modes.

the applicabili ty of the fracture mechanics approach for mode I I

(shear loading only) and mixed mode 1-11 (combination of tens i le and

T h u s , fo r structural design

Several studies were, therefore, undertaken t o extend

shear loading) fractures (1-2).

a l l the above mentioned studies were concerned w i t h adhesive bonds

between metal adherends.

invo lv ing the fracture behavior o f a composite-adhesive-composite

system under mode I condition only (3) .

As f a r as the au thors are aware,

Recently, a study has been reported

The objective o f the present study was, therefore, t o characterize

the debond growth mechanism o f adhesively bonded composite jo in ts

under mode I , mixed mode 1-11, and mode I1 s t a t i c loading.

purpose, graphi te/epoxy double-canti lever beam (DCB) specimens,

For this

c;acked-lap-shear (CLSj specimens acd end-notch flexur e (ENF

were tested u s i n g EC 3445 adhesive. * T h i s study focussed on the

measuring o f the c r i t i ca l strain-energy-release rates G J C 9

and Gl ic t o determine the fracture mode dependence o f debond failure.

sixcjme,is

G(I - i j I C

TEST MATERIAL AND SPECIMEN CONFIGURATION -

The debond system consisted of g raph i te/epoxy (T300/5208)

i-.:'herenc's bondcd w i t h EC 3445 :dhesivc. Thc 3f45 adhxive i s 2.

thermosetting paste w i t h a cure temperature o f 121°C, Specimens

were fabricated by the conventional secondary bonding procedure.

The bonding process followed the manufacturer's recommended proce-

dure. The nominal adhesive thickness was 0.10 mm.

Three specimen types were fabricated: DCB, CLS and ENF specimens,

as shown i n Figures 1, 2 and 3. The DCB specimens were used t o

characterize debond growth under opening mode 1 l oad ing ( F i g 1.)

and also under mixed-mode loading ( F i g 4) . The CLS and ENF specimens

were employed to study debond fa i lure under mixed-mode 1-11 and sl iding

mode I1 loading, respectively.

The DCB specimen ( F i g 1) consisted of two bonded adherends, each

hav ing 14 unidirectional plies with an i n i t i a l debond length of 38 mm.

T h i s debond was introduced by a Teflon film of thickness equal t o the

adhesive bondline. Two aluminum end t abs were bonded t o the DCB

specimen t o apply the load. The adherends of CLS specimens (Fig 2)

consisted of quasi-isotropic lay-ups, [O/45/-45/90Js and [0/45/-45/90]2s.

Two configurations o f CLS specimens were tested:

t o 16-ply l a p and 16-ply strap bonded t o 8-ply lap.

did n o t have an i n i t i a l debond l ike the DCB specimen.

8-ply strap bonded

The CLS specimen

The ENF specimens were ubtained by bonding LWO cJmpos'lte adherends w i t h an

i n i t i a l debond introduced by a Teflon film. These adherends were

15-ply unidirectional laminates.

TESTING PROCEDURE

The objective of the t e s t program was to measure the c r i t i ca l

strain-energy-release rates , GIG, GIIc and G(I-II)c for opening,

:hear and mixec'-mode lozdinas, resFecti*?ely

separately in the following.

Mode I t e s t

These are described

All s t a t i c t e s t s of DCB specimens were performed in a displacement

controlled t e s t machine.

fatigued t o create a debond o f a t least 6 mm beyond the end of the

Teflon film.

a t a s low crosshead speed (5.0 mm/min).

Prior t o testing, these specimens were

The t e s t involved the application of displacement

When the load reached the

c r i t i ca l value, the debond grew in a stable manner. The onset of

I

growth resulted i n a deviation from linearity i n the load versus

4

crosshead displacement record.

decreased until a zero load reading was observed. After each

s t a t i c t e s t , the specimen was fatigued until the debond grew a t

The applitd displacement was then

least 6 mm further, thus forming a sharp crack for the next s t a t i c

tes t . A series of s t a t i c t e s t s was performed on each specimen,

which provided compliance and c r i t i ca l load measurements for

several debond lengths. These measurements provided the c r i t i ca l

strain-energy-release rate as explained i n the section ent i t led

I ANALYSIS . Mode I1 t e s t --

Prior t o testing, the ENF specimen was fatigued t o create a

debond of a t least 6 mm beyond the end of Teflon film. T h i s specimen

was, then, loaded i n three-point bending in a displacement controlled

mode.

were recorded.

from l inear i ty i n the load versus displacement record.

G,*o;lth was stab:e in a l l t cs t s . A ~ l i p - j a ~ e iiedr t h z crack ?ant

was also used t o measure accurately the c r i t i ca l load corresponding

t o the onset of debond growth.

growth occurred a t the mcment when there was a deviation from

l inear i ty in the load versus displacement ( a t the center) record.

Two or more s t a t i c t e s t s were performed on each specimen. After each

s t a t i c t e s t , the specimen was fatigued until the debond grew a t

least 6 mm further, thus forming a sharp crack for the next s t a t i c

tes t .

The center point displacement and the corresponding load

The onset of debond growth resulted i n a deviation

The debond

This confirmed further t h a t debond

5

Mixed-mode t e s t

The mixed-mode fracture tests were conducted with DCB and CLS

specimens. T h i s was accomplished w i t h the DCB specimen by restraining

the vertical motion of the uncracked end while loading only one end

of the cracked end, a s shown i n F ig 4.

t o measure interlaminar toughness by Jordon and Bradley (4 ) .

this purpose, a f ix ture was devised fo r the Instron testing machine.

The test involved the application of displacement a t a slow crosshead

speed (5 mm/min) .

T h i s procedure has been used

For

The debond grew i n a stable manner and a corre-

near s ronding c r i t i c a l load WPS recorded accuwately w i t h a clip-gage

the, crack front.

Fracture t e s t s w i t h CLS specimens were conducted i n a d i s p

Prior t o s t a t i c tes t ing, this specimen was f a controlled mode.

acemen t - igued ,

and thus i t had an i n i t i a l sharp debond. During the t e s t , the axial

ioad and displacement were recorded. The displacement was measured

w i t h two displacement transducers attached on the opposite sides of

the specimen.

propagated.

was measured and verified by the deviation from l inear i ty i n the

recorded load-displacement curve.

The applied load was increased slowly u n t i l the deboiid

The c r i t i c a l load corresponding to unstable debond growth

ANALYSIS

The measured data from the above mentioned four t e s t s were

analyzed different ly t o compute the c r i t i ca l strain-energy-release

ra tes i n each case. These are described separately i n the following.

Mode I

a

.

The measured data provided the c r i t i c a l load, P , and the cr

compliance, C , f o r each debonded length, a , which were used t o

compute the fracture toughness. The de ta i l s of this procedure

are given i n Reference 5. A compliance relationship o f

3 C = Ala

was f i t ted through the experimental data points by the method of

l eas t squares.

f i t t e d very well w i t h the experimental dcta. The constant Al i n

Eq 1, from l inear beam theory, i s 2/3EI where E i s the extensional

s t i f fness and I i s the second moment of area of each side of the

DCB specimen. The experimental value of A1 was i n agreement w i t h

i t s counterpart obtained from the l inear beam theory. Further, a

f i n i t e elecient analysis of the CCB specimen was carried out (5).

Th2 FEM resul ts were also i n agreement w i t h the measured compliance,

as expressed by Eq 1, t h u s verifying the linear beam theory repre-

sents the appropriate behavior of the current DCB specimen. Based

on the l inear beam theory, a relationship of the form

T h i s relationship, based on l inear beam theory,

was f i t t e d t o the experimental data by the method

Then, the averaged value of G I c f o r each specimen

the re1 ationshi p

,2 - r cr - 3A1A;/(2w) GIC - 2w aa -

o f l ea s t squares.

was computed from

where w i s the specimen w i d t h .

7

Mode I1

The end-notched flexure test.s have been developed t o measure

the interlaminar shear fracture toughness, GIIc, of composite

laminates (6) . A closed-form equation t o compute GII was derived

for t h i s t e s t us ing the l inear beam theory. This analysis yielded

the following expression of compliance, C and strain-energy-release

rate G I I ,

2~~ t 3a3 C = 8E b h3

where P i s the applied load, E is modulus, and a , b and h are as

shown i n Fig 2.

was analyzed w i t h a two-dimensional f i n i t e element program called

GAMNAS ( 7 ) t o evaluate i t s performance.

However, i n the present study, th i s t e s t specimen

A f i n i t e clement model, shown i n F i g 5, cunsisted o f 1000

isoparametric four-node elements and had about 2400 degrees of

freedom.

with the debond front a t the middle of the adhesive layer.

element size in the vicinity of the crack f r o n t was 0.02 x 0.02 mm

The adhesive was modeled with four layers o f elements

The

in order t o evaluate accurately the strain-energy-release rate GII.

This size was selected by previous experience (5) as well as by

conducting a convergence t e s t on the GII calculation w i t h mesh

refinement. The error in GII obtained i n the present study i s

8

estimated to be less than 22 percent.

ra te , GII, i n the analysis was computed us ing a virtual crack

closure technique (7 ) .

the f i n i t e element analysis.

The s t ra in energy release

The plane s t ra in condition was assumed i n

The analysis indicated t h a t mode I1 deformation i s achieved

a t the crack t i p and tha t the accompanying mode I deformation causes

closure and overlapping of the opposite faces o f the crack. T h i s

i s not possible physically.

faces, the nodal coupling technique, available w i t h the GAMNAS

program (7), war ured.

was applied a t corresponding nodes to have the same displacements

normal to the crack faces.

condition, i .e . GI = 0.

To prevent the overlapping of crack

For this purpose, the m u l t i p o i n t conztraint

This resulted i n the pure mode 11

Figure 6 shows the comparison of the measured compliance w i t h

FEM and t h e theoretical compliance (Eq 5). T h i s c lear ly shows that

the FEM resu l t s are i n good agreement w i t h the experimental values.

figure 7 shows the comparison of GII obtained from FEM analqsis

and from a linear beam theory, i.e. Eq 5.

GIIc was computed from the FEM analysis, since the theoretical

expressions (Eqs 4 & 5) were n o t developed for the bonded ENF specimen.

Mixed mode 1-11

In the present study,

The tested CLS specimens were analyzed with the f i n i t e element

program GAMNAS ( 7 ) t o compute GI and GII for a given geometry, debond

length and applied load. This two-dimensional analysis accounted

for the geometric nonlinearity associated w i t h large rotation i n

these sp:?cimens.

been reported i n

The de ta i l s of the FEM analsis o f CLS specimens have

Reference 8.

9.-

Jordon and Bradley (4) have developed the following relationships

based on the l inear beam theory t o compute GI and GII associated with

interlaminar crack growth of composite laminate from an asymietrically

loaded DCB specimen as shown in Fig 4.

- P2,* -4wEI

2 2

16wE I - 3P a

GII - - (7)

1.1 the present study, gecmetrically non1;near FFM analysis o f this

specimen was, however, conducted t o evaluate i t s performance fo r

bonded systems, and t o account for i t s nonlinear behavior due t o

large deflections.

DEBOND MECHANISM

In a17 the fracture t e s t s , the debond growth occurred i n a

This growth cohesive manner, i .e . i t grew within the adhesive.

remained i n the bondline d u r i n g the mode I and mode I1 t e s t s w i t h

DCB and ENF specimens, respectively. However, dur ing the mixed mode

test with b o t h DCB and CLS, the debond propagated into the composite

adherend a f t e r i t s cohesive ini t ia t ion in the adhesive.

RESULTS AND DISCUSSIONS

The cr i t ica l strain-energy-release rates, GIG, GIIc, G(I-II)c and GI/GII obtained from a l l thespecimenstested are summarized i n

Tables 1-4. The observed variation in GIG, G I I c and G(I-II)c i s

- 10

reasonable as compared t o other mechanical properties of adhesives

as well as with previous studies (1-2):

The difference i n G I I c obtained from FEM analysis and Eq 5 ,

as given i n Table 2, shows t h a t the closed-form expression derived

for delamination studies (6) does: not' represent the appropr ia te

behavior of the bonded system. The same observation should also be

noted f o r G(I-II)c obtained from the DCB as given i n Table 4.

values of GIIC and G(I-lI)c from FEM analysis i n Tables 2 and 4 will

be, therefore, considered i n the following.

The

To show the interaction between fmcture modes J and TI,

experimental da t a from a l l the speci'mens are plotted in Fig 8. The

I 1 da ta i n F i g 13 define the functiotwl veaat7finship I E ~ . \ J C ~ I - I 6 i~ntl C; j

fo r the debond growth i n the presence of tensile and in-pSi.tie shear

stresses. T h i s mixed-mode interaction is usually expressed i n the

fracture nechanics l i t e ra ture as

Therefore, the present da t a have h e n replot t ' - ,d j1-1 Fig 9 tls*irig

the average values o f G I C and GIIc.

relationship f o r mixed mode debond growth i n EC 3445 adhesive.

These show the following l-inear

GII - 1 + - - GI GIc %IC - (91

A previous study [ 9) has shwn t h ? t fracttirc energy -i Ijcrea:,eti 1y

introducing a mode I1 component i n the unmodified epoxy adhesive

11

(DGEBA-TEPA).

an order of magnitude l a r g e r than GIG. toughened epoxy adhesive (DGEBA-CTEN-PIP) exh ib i ted complex behavior.

The mixed mode G~I-II)C values were s i g n i f i c a n t l y lower than the

mode I o r mode I1 values wi.th these l a t t e r two f rac tu re energies

equal i n magnitude.

a t t r i b u t e d t o the i n t e r f a c i a l f a i l u r e .

For t h i s unmodified epoxy adhesive, GIIC was about

On the other hand, the

Th is decrease i n mixed mode values was

The EC 3445 adhesive i s a

s t r u c t u r a l rubber toughened epoxy adhesive. The r e s u l t s o f the

present study w i t h EC 3445 are i n agreement w i t h the previous study

(9) f o r mode I and mode I1 loading, i . e . GI, icnd GIJc are equal

to each o ther f o r a l l p r a c t i c a l purposes.

f r a c t u r e toughness, G(I-II)cy f o r a wide range o f GI and GII r a t i o s ,

was a lso found equal t o GIc and GIIC i n the present adhesive, f o r a l l

p r a c t i c a l purposes.

o f the bondl ine i n the mixed mode loading i n the present study,

u n l i k e the previous study (9 ) where i t occurred adhesively.

Further, the mixed mode

Th is can be a t t r i b u t e d t o the cohesive f a i l u r e

CONCLUSIONS

A combined exper imenta l -analy t ica l i nves t i ga t i on o f composite-to-

composite bonded j o i n t s was undertaken t o character ize the mechanics

o f debond growth. The system studied consisted o f graphite/epoxy

adherends bonded w i t h EC 3445 adhesive. Several types o f specimens

were tes ted which provided the c r i t i c a l strain-energy-release ra tes

under var ious load condi t ions: mode I loading, GIc’ GIIc and G(I-II)C mode I1 loading and mixed mode 1-11 loading. This study l e d t o the

f o l l o w i n g conclusions:

12

.

(a) The mode I , mode I1 and mixed mode 1-11 fracture energies o f

the toughened epoxy adhesive are equal t o each other.

(b) The fracture cri terion f0.r the mixed mode fracture of the ' toughened epoxy adhesive can be expressed as:

GI ' .GII - 1 %it=- ACKNOWLEDGEMENT

The work reported here was supported by NASA Langley Research

Center, Hampton, VA. The authclrs wish td ackr,ow?edge the subpor t

and encouragement of Dr. W. S. Johnson, NASA Langley Research Center

during the course o f t h i s i n v e s t i g a t i o n .

13

- -

REFERENCES

1.

2.

3.

4.

5 .

6.

7.

8.

9.

Kinloch, A.J. mechanics and mechanisms of failure. Journal o f Material Science , 1982 , - 17, 617-651.

Review-the science of adhesion--part 2,

Shaw, S.J. Adhesion 7, Applied Science Publishers, 1982, 173-1 96.

Ripling, E.J., Satner, J.C., and Crosley, P.B. Fracture o f composite-adhesive-composite systems. Adhesive Joints: Their Formation, Characteristics, and Testing, Plenum Press, 1984.

Jordon, W.M. and Bradley, W.L. toughened graphi te-epoxy 1 ami nates. Toughened Composi tes , ASTM STP 937, American Society for Testing and Materials, 1987 ( i n press).

Mall, S. and Johnson, W.S. mixed-mode failure o f adhesive bonds between composite adherends. NASA Technical Memorandum 86355 , 1985.

Micromechanics of fracture in

Characterization o f mode I and

Russell, A.J. and Street, K.N. laminar fracture energy of graphite/epoxy laminates. Progress in Science and Engineering o f Composites, Proc. ICCM-IV, Japan Society for Composite Materials , 1982.

Dattaguru, B. , Everett, R.A. , Jr., Whitcomb, J.D. , and Johnson, W.S.

Factors affecting the inter-

Geometrically-Nonlinear analysis of adhesively bonded joints: Journal of Engineering Materials and Tec$nology, ASME, - 106, 59-65.

Mall, S., Johnson, W.S., and Everett, R . A . , Jr. of adhesively bonded composites. Adhesive Joints: Their Forma- tion, Characteristics, and Testing, Plenum Press, 1984.

Cyclic debonding

Bascom, W.D. and Oroshnik, J. Effect of bond angle on mixed-mode adhesive fracture. Journal of Material Science, 1978, - 13, 1411-1418.

14

Table 1. G I c from DCB specimens

5 6 Avg .

3 3 3

920 1 952 1 888 1

0.5 0.625 0.75

Avg .

.Table 2. GIIc from ENF specimens

92 9 945 908 952 858 844

1022 900 824

7 07 803 742 722 730 6 90 778 767 673

909 734

15

Specimen

/)I 0.31 0.31 0.31

4 5 6

910 870 7 95

Table 3- G(I-II)C from CLS specimens

0.25 0.25 0.25

Strap P l i e s Lap P l i e s

840 7 90 8d5

1618 1618 1618

Specimen

8/ 16 8/16 8/16

Eqs 6 81 7

0.813 0.925 0.925

858

1.24 963 1053 1.24 998 1165 1.24 93 6 1032

838

I G(I-II)cs J/mL

Avg. I 965 I 1083

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25

~ Standard Bibliographic Page

- May 1986 6. Performing Organization Code

[ 1. Report No. 12. Government Accession No. 13. Recipient's Catalog No.

BONDED JOINTS 7. Author(s)

NASA CR- 178112 4. Title and Subtitle 15. Report Date

- -

N

8. Performing Organization Report No.

I

S . Mal l and N. K. Kochhar

Un ive rs i t y o f Missour i -Rol la 9. Performing Organization Name and Address

Department o f Engineering Mechanics pl\ 5qve 1 1 2 1 \. Rolla, MO 05401

. 12. Sponsoring Agency Name and Address

I CRITERION FOR MIXED MODE FRACTURE IN COMPOSITE

10. Work Unit No.

11. Contract or Grant No.

NAG 1-425 13. Type of Report and Period Covered

Contractor ReDort

19. Security Classif.(of this report) 20. Security Classif.(of this page] 21. No. of Pages

Uncl ass i f i e d 26 Unc 1 ass i f i ed 22. Price

A0 3

National Aeronautics and Space Admini s t r a t i on Washington, DC 20546 14. Sponsoring Agency Code

534-06- 23-03 , 15. Supplementary Notes

Langley Technical Monitor: F ina l Report

D r . W. S. Johnson

16. Abstract

A study was undertaken t o character ize the debond growth mechanism o f adhesively bonded composite j o i n t s under mode I, mixed mode 1-11, and mode I 1 s t a t i c load- ings. The bonded system consisted o f graphi te/epoxy (T300/5208) composite adherends bonded w i t h a toughened epoxy (EC 3445) adhesive. The mode I , mode I 1 and mixed-mode 1-11 f r a c t u r e energies o f t he tested.adhesive were found t o be equal t o each other. -Furthermere, t he c r i t e r i o n f o r mixed mode f r a c t u r e i n com- pos i te bonded j o i n t s was found.to be: (GI/GIc) + ( G I I / G I I C ) = 1.

17. Key Words (Suggested by Authors(s)) Debond growth mechanism Adhesively bonded composite j o i n t s Graphi te/epoxy Mixed mode f r a c t u r e Composite bonded j o i n t s

~

18. Distribution Statement

Unclassi f ied-Unl imited

Subject Category 24

I For sale by the National Technical Information Service, Springfield, Virginia 22161 NASA Langley Form 63 (June 1985)