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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
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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.
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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),
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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).
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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.
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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.
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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-
tures in linear material analysis.
The delamination propagation caused by local
buckling is delayed by the use of a thermoplastic
carbon-composite material.
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I.
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