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ELSEVIER

Composifes Science and Technology 58 (1998) 721-733

I ; 1998 Published

by Elsevier Science Ltd. All rights r eserved

Printed in Great Britain

PII: SO266-3538(97)00153-X

0266-3538/98 19.00

EXPERIMENT L ND NUMERIC L STUDY OF

DEL MIN TION C USED BY LOC L BUCKLING OF

THERMOPL STIC ND THERMOSET COMPOSITES

F. Lachaud, B. Lorrain, L. Michel & R. Barrio1

Ecole

Nat ional e SupPri eure ’l ngknieurs de Constr uctions Pronauti ques, ipar tement

de GEnie MCcanique.

1

Pl ace Emi l e Bloui n. 31056

Toulouse. France

(Received 29 October 1996; accepted

24 July 1997)

Abstract

2 EXPERIMENTAL

Experi mental and numeri cal studi es of delam inat ion

caused by local buckling have been carried out on ther-

moset and t hermopl asti c carbon-j ibr e composi t es. The

propagati on of delam inat ion appears only aft er the

appearance of macrocracks in t he buckli ng pl i es. I n the

fir st part of this w ork, acousti c emission (Feli cit y rati o)

is used t o quali fy damage accumulat ion before propaga-

t ion of delami nati on. The second part deals w it h the

determinati on of the init iat ion of delami nation by tw o

numerical methods, the j rst of w hich all ow s us to calcu-

lat e t he global resti tut ion energy rat e (vi rt ual crack-

extension method) and the second i t s part it ion int o modes

I , II and II I (mod ed crack-closure int egral). A

mechanical fai lur e crit eri on is then appli ed t o a stacking

sequence and tw o mat eri al s. Thi s crit eri on i s compared

w it h an int erfacial stresses crit eri on determined by the

j i ni t e-element method. 0 1998 Publ ished by Elsevi er

Science Lt d. Al l ri ghts reserv ed

2.1 Materials

The compression test samples were cut out from T300/

914 carbon/epoxy and AS4/PEEK carbon/poly(ether

ether ketone) plates. During the fabrication process,

circular (20mm diameter) Teflon films (aluminium for

the thermoplastic) of 20 pm thickness (12 pm for alumi-

nium) were introduced between plies of different orien-

tation in order to create a macrodefect. The stacking

sequences

studied

Were: [~~,~~,~~~,-~~~,~~,~~~,~~~]s,

[~~2,~~,~2,-~~2,~~2,~2,~~2]~ and [452~~~,~2,-452,9~2,~2,9~21s,

designated here as 1, 2 and 3. The sign (II) gives the

position of the macrodefect in the thickness of the

laminate.

Keywords: C. delamination, D. acoustic emission,

damage, local buckling, numerical simulation

The mechanical properties of the materials studied

were determined by tests on specific samples for plane

elastic moduli and failure properties, and by double-

cantilever beam (DCB) and end-notched flexure (ENF)

tests for the critical-energy release rate in mode I and II

(Tables 1 and 2). G23 and

1.~23

values were taken from the

literature.‘*

2.2 Sample and test configurations

1

INTRODUCTION

The failure of composite materials includes several

damage mechanisms. Delamination is one of these

mechanisms which must be taken into account for

structural design. Indeed, delaminations can be created

by impacts on composite structures. This damage, when

it appears, reduces the resistance of a structure to com-

pressive loading, causing great difficulties for structural

design (damage tolerance).

The samples were submitted to uniaxial compressive

strength measurements. During loading, the plies loca-

ted under the macrodefect buckle. The compressive

loading is stopped when the delamination propagates.

The measurement of Ad,,, (Fig. 1) takes into account

local and global buckling.

2.3 Acoustic emission

Many studies have been carried out on the delamina-

tion of thermoset carbon-fibre composite materials.‘23

Nevertheless, since the use of thermoplastic carbon

composites is increasingly important, we have attemp-

ted, in this study, to compare delamination propagation

by local buckling in T300/914 (thermoset) and AS4/

PEEK (thermoplastic) carbon-fibre composite materials.

Four acoustic emission (AE) piezo-electric sensors were

bonded to the sample (Fig. 1). AE indicates the occur-

rence of irreversible phenomena (cracking, fibre break-

age,

etc) and permits the analysis of damage

development.4 The main parameter used in this study is

the Felicity ratio, which is the ratio of the load where

AE reappears on second loading to the previous max-

imum load (Fig. 2). The Felicity ratio is one or less than

one:

721



728

AS4/PEEK

T300/9 14

I?:, GPa)

142

138

F. Luchaud et al.

Table 1. Mechanical properties of the two materials

~~~ ~__._~~ ~~ ~~~

Ej, (GPa)

G’,z (GPa)

Gz~ (GPa)

“IZ u2i lply (mm) tiamlnate mm)

9.5

5.8 3.6 0.29 0.42 0.132 3.24

9 4.8

3.2

0.32 0.4 0.12 2.88

__ ~

Table 2. Materials properties at failure and critical strain-energy release rate

OTIR MPa) FllR (%) ‘I;& (MPa) Fl2R (%) (TlzR (MPa) cl2R (%)

G&. (N mm- )

CL, PJmm )

AS4/PEEK

T300/914

1605 I .05 95

I.5

180

15 I.950

2.850

1520

I.14

60

I.2 95

6.0

0.190 0.485

F=

I

-+ undamaged material

OtF<l + damaged material

F=O -+ broken material

By analogy with the measurement of stiffness loss which

characterizes the laminate damage (d= I -&/.I&), the

AE parameter will be written as:

f-1-F

(1)

In theory, J’must be equal to 1 at failure. But failure,

which is an unstable phenomenon, may nevertheless

occur forf< I.

2.4 Material behaviour: local buckling

The local buckling behaviour is characterized by a non-

linear curve of the load/displacement Ad,,,. Figures 3

40

f

60

Load

Measure of transverse

dtsplacement by laser

SC”SCX

,,i..

._._i_: -. .+

I.. _,

k i

90”

Fig. 1. Sample and experimentation configuration.

Fig. 2. Example of the Felicity ratio computation.

and 4 show the load/displacement Ad,,,,, curves for

T300/914 and AS4/PEEK materials subjected to load-

unload cycles.

The first inflection of the load/displacement Ad,,,,,

curve indicates the initiation of local buckling (5000N

for the T300/914 and specimen no. 2; Fig. 3). The load

at which local buckling appears increases with the dif-

ference in angle between the buckled plies and the

loading axis as well as with the thickness of the buckled

plies. For example, local buckling of the laminates no. 1

and no. 3 begins, respectively, at loads of about 3 kN

and 8 kN. For the AS4/PEEK, local buckling starts at

lower loads than for the T300/914 although the plies are

thicker. This characteristic is attributed to the presence

of high internal stresses in the material, created by the

manufacturing process. These internal stresses are not

so great in the T300/914 material. The behaviour of

AS4/PEEK also differs from that of T300/914 by the

marked residual displacement of the buckled plies after

loading. The transverse tensile and shearing strains to

failure of the AS4/PEEK material are, in fact, very high

and show the plastic behaviour of this material

(Table 2).

Experimentally, propagation of the delamination

occurs when two macrocracks appear. These cracks are

located on both sides of the defect and develop along

the fibres in the buckled plies (Fig. 3). For the T300/914

these macrocracks are a consequence of the transverse

-

50

5

B 40

3

70

20

IO

0.C

0.0 02

0.4 0.6 0.8 I o I2

Transverse displacement, Admax (mm)

Fig. 3.

Transverse displacement versus load for T300i914

[302,]],02,-302,902,02,90& laminate.



Experi mental and numeri cal study of delam inat ion

729

0.4 0.6 0.8 1.0 1.2

Transverse

displacement, Ad, (mm)

Fig. 4. Transverse displacement versus load for AS4/PEEK

[30~,~~,02r-30~,90~r0~r90~]saminate.

tensile failure of the buckled plieq2 whereas for the

AS4/PEEK, there is fibre breakage before transverse

tensile failure (Fig. 4). The delay and the difference in

the damage development between the two materials are

essentially due to the greater failure stress in transverse

tension, ~~2, and in shearing, o12, of the AS4/PEEK

(Table 2).

2.5

Development and quantification of the damage by

acoustic emission

Acoustic emission, and especially the use of thefpara-

meter, allows us to follow the damage development in

the two materials. The plot of applied compressive load

versus

f

(Fig. 5) shows the local damage accumulation

for the three T300/914 laminates considered in this

study.

The damage (f parameter) is greater when the angle

between the fibre direction and loading axis increases.

For example, for laminate no. 3, the ‘critical’ Felicity

ratio takes a value three times greater than that of

laminate no. 1. The local damage in laminate no. 1 is

essentially due to the transverse tensile stresses, u22,

whereas the local damage in laminates no. 2 and no.

3

is

caused by the transverse and the shearing stresses. The

introduction of local shearing stresses creates a char-

acteristic increase in f (Fig. 5).

Appearance of

* 45//0testn”2

macrocracks

- - -

45110

identified curve

. .... .... .... . . .. .... .... ....

0

0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4

f=l-F

Fig. 5. f parameter development for T300/914 and the no. 1,

no. 2 and no. 3 laminates.

loo00

0

. AS4/PJZK test n”2

T3W914 test n”l

1 T3W9 14 test no2

0 0.05

0.1 0.15 0.2 0.25 0.3 0.35 0.4

f= 1-F

Fig. 6. f parameter development for the two materials and the

[302,(1,02,-302,902,02,9021, laminate.

The f parameter indicates a greater damage level in

the AS4/PEEK material than in the T300/914 material

(Fig. 6). Experimentally, this high local damage in the

thermoplastic is correlated with a high residual dis-

placement when the load is zero (Fig. 4).

2.6

Observation of the delamination surface

The propagation of the delamination appears much

later in AS4/PEEK than in T300/914. In addition to its

better transverse tensile (u22) and shear (o12) stress

resistance, it appears that the fibre/matrix interface

behaviour is stronger in AS4/PEEK than in T300/914.

Figure 7 shows, for the thermoset, that more fibres

are made visible by the propagation of delamination.

For the thermoplastic composite (Fig. S), delamination

propagates in the resin.

3

NUMERICAL STUDY

3.1 Mesh boundary conditions and computation

hypotheses

The numerical modelling has been carried out with the

help of a non-linear finite-element code, SAMCEF@.

Figure 9 shows the volume mesh used for the non-

linear geometric analysis. The numerical circular defect

is created by the node duplication of the mesh in the

thickness, in order to separate the plies around delami-

nation.

The element used in the numerical model is an iso-

parametric element (two degrees, 60d.o.f: u,v,w dis-

placements) especially designed for the study of

composite materials. The sample tabs are not modelled.

A contact condition has been introduced in order to

prohibit the interpenetration (experimentally impos-

sible) of the buckled plies on the lower laminate.5

Two numerical methods have been used to compute

the strain-energy release rate. The first is the virtual

crack-extension method (VCE), which permits the

determination of the total strain-energy release rate on

each node of the delamination front.16 The second

method is the modified crack-closure integral (MCC),



730

F. Luchaud et al.

which permits the calculation of the partition of the

total strain-energy release rate in modes I, 11 and 111.

The details of the methods are given elsewhere.‘h The

computations of all strain-energy release rates were

carried out by a linear analysis.

3.2

Numerical modelling for the two materials

The numerical load/displacement model represents the

behaviour of T300/914 well. Experimentally, the local

buckling (first inflection, Fig. 10) is more pronounced

and begins earlier than that achieved numerically. The

introduction of Teflon films to model the macrodefect in

the experimental study, creates a geometric imperfection

and then initiates the local buckling. The behaviour

does not change significantly before a high load. The

damage accumulation in the buckled plies introduces an

increase in AL&,,,.~ It is quite understood that the dif-

ference between the numerical and the experimental

behaviour of the AS4/PEEK is due to the high plasticity

of the PEEK resin.

The global buckling is numerically estimated at 44 kN

for the T300/9 14 and 66 kN for the AS4/PEEK material.

Fi g. 7. Microscopic observation of the delamination surface of the T300/9 14 [301,//.07,~307,902,02,90~]s aminate ~900)

Fi g. 8. Microscopic observation of the delamination surface of the AS4 ‘PEEK [302.](,0r.-302,902.02,902J, laminate (x900).



Experi mental and numeri cal study of delam inat ion

731

aZ o

J

Fig. 9. Volume mesh of the sample used in this study.

Experimentally, global buckling occurs earlier than cal-

culated numerically (respectively, 38 kN and 48 kN) and

especially for the thermoplastic material.

3.3

Global strain-energy release rate development

Figure 11 shows, for the T300/914, the strain-energy

release rate development versus the applied load. For a

similar load, the strain-energy release rate decreases

strongly when the buckled fibre direction increases. We

can note that, for laminate no. 3, the global buckling of

the sample creates a large increase’ (vertical growth) of

the global (total) strain-energy release rate.

3.4

Partition of the strain-energy release rate,

G,

and

delamination propagation criterion

The comparison of G with GtC is a conservative criter-

ion for delamination propagation.7 The partition of the

global strain-energy release rate permits us to determine

a more predictive delamination propagation criterion.’

The usual criterionI combining the contributions of

the different opening modes, is then compared with a

criterion expressed in terms of stresses, 033, 023 and 013,

on the delamination interface.9 These criteria are as

follows:

zc

e

P

3

TXXl/9 14 Numcncal

0. ASUPEEK Expertmenkal

0 3 -0.1 0.1 0.3 0.5 0.7 0.9 1.1 1.3 1.5

Lower di$acement (mm)

Displacement. Ad,,, (mm)

Fig. 10.

Numerical and experimental local behaviour of the

two materials ([30~,11,02,-302,902,02,902]s laminate).

0.3

2

E 0.25

&

2 0.2

:

2 0.15

9

S

& 0.1

5

e 0.05

7

E 0

- - Interface 30//O

-Interface 45//O

0

10000 2oooo 3oooo

4oooo

Load P (N)

Fig. 11. Development of the maximum global strain-energy

release rate versus applied load for the T300/914 laminate.

5+_ ~

1

GlI

Gc GIG

+ GIIC

’

’

no. 1

(2)

The estimation of the criteria is carried out at the load

at which the macrocracks appear for the T300/914

materials (Fig. 10). For the AS4/PEEK, because of the

difference between the numerical and the experimental

behaviour (Fig. lo), we search the load at which these

criteria are unity or greater than unity.

3.4.1 Opening-mode development along t he delami nati on

front

The modes I, II and III strain-energy release rate varia-

tions show the angular position of the maximum values

along the crack front (Figs 12 and 13). Mode I is a

maximum near 65” and gives the position of the max-

imum crack opening (2 perpendicular direction of the

buckled plies fibres). Mode II reaches a maximum value

near 140” (% fibre direction), and mode III is a max-

imum near O”, remaining low.

0

50 100

150 200

Angular position of the nodes along the crack front 8 (“)

- Gtot=CI +GII +GIII - GI - GII + Cl11

Fig. 12.

Mode I, II and III along the delamination front for

T300/914 and the second laminate ([302,//,02,-302,902,0*,

90&): P = 38 kN.



732

F. Lachuud

et al.

For the opening-mode variations for the AS4/PEEK,

we note (Fig. 13) that mode I becomes preponderant in

comparison with the other modes. The angular position

of the maximum values for the different modes does not

change, compared with the T300/9 14 material.

3.4.2 Delamination propagation criteriu

The criteria no.

1

and no. 2 are calculated for each

material and for the second

laminate

([302,11,02,-302,902,02,902],). Figure 14 shows the criteria

variation for T300/914 just before the appearance of

macrocracks. Table 3 indicates the values of the two

criteria for each material.

For the T300/914 material, the criteria no.

I

and no. 2

are much lower than unity. We may deduce from the

maximum values that the theoretical direction of dela-

mination propagation is equal to 67.5” (Fig. 14). We

verify experimentally that delamination propagation

does not occur before macrocracks appear. However,

delamination does not propagate in the expected

0.6

04

0.2

0

0

SO

100 I.50

200

Angular position of the nodes along the crack front 6 (“1

+ Cl lcilc

- GII / Gllc a- Gglobel /GIL

1

Fig. 13. GJclC along the delamination front for AS4/PEEK

and

the second laminate

~[30*,~j,0~.~30~,90~,0*,9021,~:

P=65kN.

277.5 -/IIyJq

270.0

262.5

1 - Criterion no1 - Criterion n”2 1

Fig. 14. Criteria along the delamination front for T300j914

and

the

second laminate ([302J,0z,-302,902,02,9021,):

P=38kN.

Table 3. Maximum values of the two criteria, H= 67.5”

~3~~,~~,~~,3~~,~~~,~2,9~2~~)

T300/9 I4

AS4/PEEK

Criterion no. I 0.58

I .05

Criterion no. 2

067 I.78

numerical direction because of the guidance of propa-

gation by the macrocracks (Fig. 15).

The stress criterion is very close to criterion no.

I

(Fig. 14) and can be used for the pre-designing of com-

posite structures which do not have strong non-linear

material behaviour.

In the case of the AS4/PEEK material, criterion no. I

is only verified (>I) for a load close to 65 kN, even

though experimentally delamination propagation occurs

for a load around 52 kN. The geometric non-linear

numerical study does not include the non-linearities of

materials (plasticity, damage, etc.) and overestimates

the delamination propagation load. We also note that

the numerical global buckling of the thermoplastic is

overestimated, and hence penalizes the computation of

the propagation criteria (cf. numerical study, Fig. IO).

We see from Fig. 16 that delamination spreads before

the appearance of macrocracks along the direction

determined by the numerical study. As for the thermo-

set. we verify that the appearance of macrocracks leads

delamination propagation, and gives the shape pre-

sented in Fig. 15.

Fig. 15. Ultrasonic C-scan for the T300/914 material after

macrocracking ([302,~~,02,~30~.902,0~,90~]~): P=42 kN.

Fig. 16.

Ultrasonic C-scan for the AS4/PEEK material before

macrocracking ([30~,~~,0~,-30~,902r0~,902]s): P= 52 kN.



Experi mental and numeri cal study of delami nati on

The stress criterion (no. 2) is much greater than unity

REFERENCES

133

(1.8) and shows the importance of considering the resin

plasticity in the AS4/PEEK material.

1.

4

CONCLUSIONS

Numerical and experimental studies of delamination

propagation caused by local buckling have been carried

out on thermoset and thermoplastic carbon-fibre com-

posites. This study has permitted us to establish that:

2.

3.

1.

2.

3.

4.

5.

6.

The delamination caused by local buckling of

uncrossed plies in composites plates can only pro-

pagate by damage to the buckled plies (macro-

cracking).

Changes in the acoustic parameter cf= 1-F)

allows us to follow the local damage caused by

local buckling and seems to be sensitive to the type

of damage. It remains to identify the validity of the

critical value of this parameter.

The fibre/matrix interface in the T300/914 material

is weaker than that in the AS4/PEEK material.

By the use of a numerical analysis, the partition of

the opening modes allows us to obtain a delami-

nation propagation criterion with reasonably good

predictive capability for thermoset composite

materials. A non-linear material study is necessary

for thermoplastic composite materials.

The analysis of interfacial stresses at the crack

front permits us to obtain a simple delamination

propagation criterion for the pre-designing of

thermoset composite materials. Nevertheless, this

criterion cannot be applied to thermoplastic struc-

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The delamination propagation caused by local

buckling is delayed by the use of a thermoplastic

carbon-composite material.

4.

5.

6.

I.

8.

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