Interlaminar fracture studies in Portugal
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Fatigue & Fracture of Engineering Materials & Archimer http://www.ifremer.fr/docelec/
Structures Archive Institutionnelle de l’Ifremer
September 2004; 27(9) : 767-773
© Blackwell Publishing, Inc.
The definitive version is available at www.blackwell-synergy.com
Interlaminar fracture studies in Portugal: past, present and future
A.B. de Morais1*, C.C. Rebelo2, P.M.S.T. de Castro3, A.T. Marques3 and P. Davies4
Department of Mechanical Engineering, University of Aveiro, Campus Santiago, 3810-193 Aveiro, Portugal
Department of Mechanical Engineering, Politechnic Institute of Coimbra, Institute of Engineering, Rua Pedro
Nunes – Quinta da Nora, 3030-199 Coimbra, Portugal
Faculty of Engineering, Department of Mechanical Engineering and Industrial Management, University of Porto,
Rua Dr. Roberto Frias, 4200-465 Porto, Portugal
Materials and Structures group, IFREMER, Centre de Brest BP70, 29280 Plouzané, France
*: Corresponding author : : A. B. de Morais. E-mail: [email protected]
Abstract: This paper reviews the state-of-the-art in interlaminar fracture testing of composite
materials, with particular emphasis on the work performed in Portugal over the last 15 years. Early
work, carried out within the ESIS Polymer and Composite Technical Committee, was concerned with
improving test methods on unidirectional [0°]n specimens. The focus was on the mode I double
cantilever beam (DCB) test and on mode II end-notched flexure (ENF) and end loaded split (ELS)
tests. In spite of some remaining controversy on mode II testing, the main issue nowadays is fracture
toughness measurement on multidirectional specimens. Remaining difficulties are discussed in the
light of the most recent work. Guidelines for ongoing and future research are also presented.
Keywords: double-cantilever-beam-DCB; end-notched-flexure-ENF; interlaminar-fracture;
INTERLAMINAR FRACTURE STUDIES IN PORTUGAL: PAST, PRESENT AND
A. B. de Morais1,*, C. C. Rebelo2, P. T. de Castro3, A. T. Marques3, P. Davies4
University of Aveiro, Department of Mechanical Engineering, Campus Santiago, 3810-193 Aveiro, Portugal.
Politechnic Institute of Coimbra, Institute of Engineering, Department of Mechanical Engineering,
Rua Pedro Nunes - Quinta da Nora, 3030-199 Coimbra, Portugal.
University of Porto, Faculty of Engineering, Department of Mechanical Engineering and Industrial
Management, Rua Dr. Roberto Frias, 4200-465 Porto, Portugal.
Materials and Structures group, IFREMER, Centre de Brest BP70, 29280 Plouzané, France.
Corresponding author, Tel. 234 370830; Fax. 234 370953; E-mail: [email protected]
This paper reviews the state-of-the-art in interlaminar fracture testing of composite materials,
with particular emphasis on the work performed in Portugal over the last 15 years. Early
work, carried out within the ESIS Polymer and Composite Technical Committee, was
concerned with improving test methods on unidirectional [0º]n specimens. The focus was on
the mode I Double Cantilever Beam (DCB) test and on mode II End Notched Flexure (ENF)
and End Loaded Split (ELS) tests. In spite of some remaining controversy on mode II testing,
the main issue is nowadays fracture toughness measurement on multidirectional specimens.
Remaining difficulties are discussed in the light of the most recent work. Guidelines for
ongoing and future research are also presented.
Keywords: Interlaminar fracture; Double Cantilever Beam (DCB); End Notched Flexure
(ENF); unidirectional laminates; multidirectional laminates.
Polymer matrix composites have become highly relevant structural materials, owing to their
high stiffness and strength combined with low weight. However, the usual laminated nature
and the relatively low matrix strength make them particularly susceptible to delamination. For
example, low velocity impact can generate relatively large delaminations, which are highly
detrimental to compressive strength because of localised buckling phenomena. The
characterisation of delamination resistance is thus highly relevant for design of composite
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 2
parts. The main delamination resistance parameters of composites are the critical strain energy
release rates, Gc, measured in interlaminar fracture tests.
This paper addresses the state-of-the-art in mode I and mode II testing, which is
illustrated with results obtained by the authors. Finally, current and future research guidelines
2. UNIDIRECTIONAL LAMINATES
2.1. Mode I
The mode I Double Cantilever Beam (DCB) test (figure 1) is nowadays standardised for GIc
measurements on unidirectional (UD) [0º]n specimens1,2. In these tests, the load P and the
displacement δ recorded for specified crack positions a are usually processed with the
Corrected Beam Theory (CBT)
GIc = , (1)
2b(a + ∆ ) N
where b is the specimen width, typically 20 mm, ∆ is a correction for crack tip rotation and
deflection, determined from a linear regression analysis of (δ/PN)1/3 versus crack length (a)
data, F is a correction factor for large displacements and N is a correction factor for the
stiffening caused by the metal blocks1,2.
Most composites present an R-curve, which can be quite pronounced for thermoplastic
matrix composites3-5. Figure 2 depicts results obtained from C/PEEK5 and C/epoxy
specimens6. R-curves are generally associated with fibre bridging between the arms of the
specimen, a phenomenon that is specific to the DCB specimen. Therefore, it is quite
important to obtain accurate initiation values, GIc,i, and this is an issue that has not yet been
The first question is whether GIc,i should be measured from the film generated starter
crack or from a mode I precrack. It was shown that GIc,i becomes independent of film
thickness below 15 µm1. Moreover, GIc,i values from the insert are usually lower than those
from precracks. On the other hand, it can be argued that crack initiation from the film does
not occur under self-similar conditions. In fact, the distribution of GI along the width of a
DCB specimen with a straight crack is not uniform, due to anticlastic curvature of the
specimen arms6,7. Figure 3 shows a width-wise distribution of GI in C/epoxy specimens
obtained from a 3D FE analysis6. Naturally, under steady-state propagation, a curved
delamination front develops, so that GI = GIc. This would favour the use of mode I precracks.
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 3
Currently, however, the standards recommend that GIc,i are measured from both film and
mode I precrack, to be generated in a first precracking test1,2.
Another question concerning initiation is the definition of the exact instant when it
occurs. Three criteria are proposed in ISO 150242 (figure 4): the non-linearity (NL); the 5%
offset or maximum load point (5/M) and the visually (VIS) determined. The NL criterion
defines crack initiation at the point where the load-displacement curve deviates from linearity.
Besides giving the most conservative values, the NL criterion seems to correlate with
Acoustic Emission detections1. It has been shown, however, that locating the NL point is
somewhat dependent on the plot scale. The 5/M criterion stipulates that a line corresponding
to a compliance 5 % larger than the initial one is intersected with the actual load-displacement
curve (figure 4). This intersection point is taken as initiation, unless it occurs at a larger
displacement than the maximum load point. In the latter case, initiation is precisely the point
of maximum load. Although less ambiguous, the 5/M criterion tends to give higher GIc,i
values than the other criteria, even for materials with relatively mild R-curves (figure 5).
Moreover, the 5% value is obviously arbitrary. Finally, the VIS criterion is operator
dependent, but this limitation could be compensated by the increasing use of video recording
of the tests. Nevertheless, it is highly unlikely that VIS detection from the film will be
accurate, as crack growth at the edges tends to occur later than in the middle of the specimen.
2.2. Mode II
In contrast with mode I, there is much more controversy about the measurement and
meaningfulness of the mode II fracture toughness8-10. It has been argued that the microcracks
observed in the tests are actually oriented at approximately 45º from the fibre direction, thus
showing that crack propagation is locally mode I dominated11. Nevertheless, most of the
present design approaches are based on Macromechanics and many structures are subjected to
bending loads, which naturally give rise to significant mode II. Moreover, it was found that
the compression after impact strength of composite plates was proportional to the mode II
critical strain energy release rate, GIIc, of unidirectional specimens12.
Various test configurations have been proposed to measure GIIc1,9(figure 6): end-
notched flexure (ENF); end-loaded split (ELS) and 4-point end-notched flexure (4ENF).
Owing to its simplicity, the ENF specimen has been the most used, in spite of the
inherently unstable crack propagation. Stabilisation is possible in servo-controlled testing
machines, which, however, are not always available and increase the complexity of the test
setup1,9. The main advantage of the ELS specimen is precisely the stability of crack
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 4
propagation if a/L > 0.55 (figure 6), but the specimen is more prone to large displacements
and to variable clamping conditions8. There is still little experience with the 4ENF test, which
seems to combine the simplicity of ENF with the stability of ELS. Comparisons between the
various test methods have not yet been able to indicate “the best method”9,10.
The effect of friction has also been raised as a possible problem in mode II tests.
However, numerical analyses have showed small friction effects in ENF and 4ENF
On the other hand, the problems concerning crack initiation mentioned above are even
more relevant in mode II testing. Figure 7 shows the results obtained from ENF tests on
glass/epoxy specimens8 using Corrected Beam Theory13
9a 2 P 2 ⎡ E ⎛ h ⎞ ⎤ F2
GIIc = ⎢1 + 0.2 ⎜ ⎟ ⎥ , (2)
16b 2 Eh 3 ⎢
⎣ G ⎝ a ⎠ ⎥ N2
where E and G are the specimen flexural and shear moduli, respectively, and F2 and N2 are
correction factors for large displacements13. Precracking seems to be of great relevance, since
initiation GIIc from mode I and mode II precracks were significantly lower than those from the
film (figure 7). As to defining crack initiation, in this case, the NL criterion lead to
unacceptably low GIIc values because it was associated with the onset of large displacements.
The 5/M criterion did not seem to be significantly affected, but it still gave somewhat higher
values than visual detection. However, the contact between the cracked arms of the specimens
makes visual detection more difficult than in mode I, especially in carbon fibre composites.
When performing ENF tests from a mode II precrack, the exact precrack length a must
be determined. Glass fibre composites are usually translucent, thereby enabling visual
determination of the precrack position. This is generally not the case of carbon fibre
composites. Therefore, ESIS recommends the compliance calibration13
C = Co + ma 3 (3)
3ma 2 P 2
GIIc = , (4)
although its accuracy may be affected by a low m coefficient.
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 5
3. MULTIDIRECTIONAL LAMINATES
3.1. Mode I
In spite of the remaining questions discussed above, it is clear that mode I and mode II testing
of UDs have reached a reasonable degree of maturity. In practice, however, the vast majority
of applications involves multidirectional specimens (MDs), and delaminations always occur
between layers of different orientations. It is thus essential to obtain toughness values of MDs
for the applicability of Fracture Mechanics based design approaches.
Several studies have already been presented on DCB testing of MDs6,14-22. The first
difficulty with MDs is the selection of appropriate stacking sequences. In fact, significant
errors in GIc measurements may be caused by the elastic membrane-bending and bending-
bending couplings of MDs7,23. Particular attention should be given to avoiding excessive
anticlastic curvature of the specimen arms, which results in highly curved thumbnail shaped
delamination fronts. The magnitude of anticlastic effects is proportional to the parameter Dc =
D122/(D11D22), where Dij represent the Classical Lamination Theory (CLT) bending stiffness
coefficients of each specimen arm7,23. It has been suggested that DCB specimens should have
Dc < 0.257,23. Bending-twisting and membrane-bending elastic couplings should also be
minimised. The former can be characterised by the Bt = ⏐D16/D11⏐ parameter and could cause
markedly unsymmetrical delamination fronts. The latter may introduce relevant contributions
of thermal residual stresses to the measured GIc23,24. Membrane-bending couplings are absent
when both cracked and uncracked parts of the specimens are symmetric about their own mid-
planes. However, this is not possible when the delamination is placed between interfaces of
different orientations, which is precisely the case of greater practical interest.
There is also a theoretical problem with cracking between layers of different
orientations, because the stress field is oscillatory in the vicinity of such cracks25-28.
Consequently, although the total strain energy release rate G is well defined, its individual
components GI, GII and GIII cannot be determined using their classical definition, since the
crack extension integrals do not tend to a limit as the crack extension increment ∆a tends to
025-28. This mode partitioning ambiguity can be solved by considering “finite extension strain
energy release rates”, where ∆a should be set equal to a characteristic damage zone length,
lc27,28. Based on stress field analysis and on interlaminar strength properties, it has been shown
that lc is of the order of the layer thickness27,28.
From the practical viewpoint, the major problem with MDs is clearly the high tendency
for intraply cracking and crack jumping between neighbouring interfaces. The complex
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 6
damage morphology leads to pronounced R-curves, with final apparent GIc values 3 to 4 times
higher than those of [0º]n specimens. Figure 8 shows R-curves obtained from DCB tests on
carbon/epoxy [0º]24 and cross-ply [(0º/90º)6//(0º/90º)6] specimens, where // denotes the starter
crack position6. Crack propagation in the latter involved periodical cracking of the 90º mid-
layer and interlaminar crack growth in the neighbour 0º/90º interfaces, as schematically
depicted in figure 9. However, recorded data points always corresponded to local interlaminar
propagation. In those conditions, an FE analysis indicated that the measured GIc were valid6.
Although no significant fibre bridging was observed, some non-linearity in the load-
displacement curve might have contributed to the much higher GIc.
In order to avoid crack jumping problems, Robinson and Song18 proposed the edge pre-
delaminated (EPD) DCB specimen (figure 10). While crack jumping was avoided, the
monitoring of crack position became difficult, due to the contact between the pre-delaminated
edges29. Moreover, recent numerical analyses showed that the EDP-DCB specimen is
inadequate to measure initiation GIc30. Another important drawback is that intralaminar
damage is not always avoided19.
Using thick (over 6 mm, 48 layers) and narrow (between 4 and 10 mm) specimens, Chai
observed pure interlaminar propagation in MD CFRP specimens15. Measured toughnesses
were practically identical for specimens with delaminations on 0º/0º, 45/-45, 0º/45º and 0º/90º
interfaces. It is important to mention that the delamination was not placed at the specimen
mid-thickness, a feature that could generate significant mode-mixity effects. Nevertheless,
numerical analyses30 showed that accurate GIc can be obtained with those specimens, which
thus require more experimental studies.
3.2. Mode II
As in mode I, intralaminar damage affected many of the mode II toughness results for MDs
presented thus far31-37. Again, with thick and narrow ENF specimens, Chai was able to obtain
pure interlaminar propagation in C/epoxy and C/PEEK specimens with 30º/-30º delaminating
interfaces31. The specimens with 30º/-30º interfaces presented significantly higher GIIc,
especially for a brittle matrix C/epoxy composite. Studies involving GRPs and specimens
with θ/-θ delaminating interfaces indicate a θ-increasing GIIc31,33,35,37. This trend is easily
interpreted in terms of larger plasticity zones ahead of the crack tip. However, observed non-
linearity for GRPs specimens with θ ≥ 30º casts doubts about the validity of the measured GIIc
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 7
On the other hand, results from ENF tests on flat filament wound glass/polyester
specimens revealed an intermediate GIIc decrease from θ ≈ 0.8º (hoop winding) to θ = 5º
(figure 11). This somewhat unexpected variation could be due to the particular nature of
filament wound specimens, combined with a strong effect of the thickness of the resin rich
interlaminar layer, as hoop wound specimens have a higher degree of compactation. In fact,
Chai31 showed that GIIc of adhesive joints was highly sensitive to the adhesive layer thickness.
It is very likely that this effect is present in laminated composites, because of fibre nesting in
UDs. Therefore, it seems essential to study the mode II interlaminar fracture of specimens
with θ/-θ interfaces at low θ.
Tao and Sun have investigated several types of MD carbon/epoxy ENF specimens34.
They observed that, as a result of intralaminar cracking, the delamination always jumped to a
0º/θ Interface. They subsequently tested specimens with starter delaminations on such
interfaces, and succeeded in avoiding intralaminar cracking by positioning the specimens so
that the θ-oriented layer would be under compression. In those circumstances, GIIc decreased
for θ = 0º to 90º, thus reinforcing the interest in studying mode II fracture of composites.
4. CONCLUSIONS, ONGOING AND FUTURE RESEARCH
The present review of the state-of-the-art in mode I and mode II interlaminar fracture testing
of composites shows the need to pursue research on three major topics:
- crack initiation criteria;
- mode II specimen configuration;
- testing of multidirectional specimens (MDs).
The latter is highly relevant, as structural applications usually involve MD laminates,
with delaminations developing between layers of different orientations. Furthermore, some
results indicate that the common tests on unidirectional [0º]n specimens (UDs) may not give
the lowest GIIc values. MD stacking sequences must be carefully chosen to minimise the
effects of curved delamination fronts, mode-mixity and residual stresses on Gc measurements.
Current efforts30 have been devoted to “design” MDs using 3D FE analyses. The intralaminar
damage and crack jumping phenomena common to MDs are now the main obstacle. A current
experimental programme is being carried out with thick MDs, since it was reported that they
were free from those difficulties15,31.
The often observed R-curves make the exact definition of crack initiation particularly
important. In fact, the R-curve is usually associated to fibre bridging and crack jumping
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 8
phenomena that are specimen geometry dependent. Furthermore, such phenomena tend to
occur in the initial stages of crack propagation, and especially in MDs. At this level,
experimental work will be complemented with progressive damage based numerical
simulations. Initiation criteria will be evaluated by comparing predicted Gc values with those
inputted into the damage model30.
As to the choice of the “best” mode II specimen, the 4ENF specimen seems to be quite
promising. The testing rig is simple, and crack propagation is stable. However, the practical
difficulty in following crack propagation and the greater interest in crack initiation may not
provide significant advantages over the ENF specimen. Moreover, the suitability for MDs is
an important factor still to be evaluated. MDs are generally less rigid and, according to some
studies, could also be tougher than UDs. One can expect more difficulties with the ELS
specimen e.g. large displacements and intralaminar damage. Considering the relevance of
MDs and the available results, the present experimental work is being carried out with the
ENF specimen, though studies on the ELS and 4ENF geometries are continuing elsewhere.
Most of the work herein presented was performed in the scope of Round Robins organised by
the Technical Committee 4 (TC4) of the European Structural Integrity Society (ESIS). The
authors wish to thank the other members of TC4 for their cooperation and for providing the
Several projects in Portugal (JNICT and FCT) or in the European Union also
contributed to the understanding of interlaminar fracture. In particular, A. B. de Morais thanks
the Portuguese Foundation for Science and Technology (research project
POCTI/EME/38731/2001, FEDER European Union fund) for supporting the work currently
being performed on the subject.
1. Davies P (1998), Blackman BRK, Brunner AJ. Standard test methods for delamination resistance of
composite materials: current status. Appl. Compos. Mater., 5, 345-364.
2. ISO 15024:2001. Fibre-reinforced plastic composites - Determination of mode I interlaminar fracture
toughness, GIc, for unidirectionally reinforced materials.
3. Friedrich K, Carlsson LA, Gillespie JW, Karger-Kossis J (1991). Fracture of thermoplastic composite
materials. In Thermoplastic composite materials. Edited by L.A. Carlsson. Elsevier Science.
4. Hashemi S, Kinloch AJ, Williams JG (1990). Mechanics and mechanisms of delamination in a Polyether
Sulfone-fibre composite. Compos. Sci. Technol., 37, 429-462.
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 9
5. Davies P et al. (1992). Round-Robin interlaminar fracture testing of carbon-fibre-reinforced epoxy and
PEEK composites. Compos. Sci. Technol., 43, 129-136.
6. Morais AB, Moura MF, Marques AT, Castro PT (2002). Mode I interlaminar fracture of carbon/epoxy
cross-ply composites. Compos. Sci. Technol., 62, 679-686.
7. Davidson BD (1990). An analytical investigation of delamination front curvature in double cantilever beam
specimens. J. Compos. Mater., 24, 1124-1137.
8. Davies P, Ducept F, Brunner AJ, Blackman BRK, Morais AB (1996). Development of a standard mode II
shear fracture test procedure. In Proceedings of ECCM-7, London, 9-15.
9. Davies P et al (1999). Comparison of test configurations for determination of mode II interlaminar fracture
toughness: results from international collaborative test programme. Plastics, Rubber and Composites, 28,
10. Schuecker C, Davidson BD (2000). Evaluation of the accuracy of the four-point bend end-notched flexure
test for mode II delamination toughness determination. Compos. Sci. Technol., 60, 2137-2146.
11. O’Brien TK (1998). Composite interlaminar shear fracture toughness, GIIc: shear measurement or sheer
myth? ASTM STP 1330, 3-18.
12. Evans RE, Masters JE (1987). A new generation of epoxy composites for primary structural applications:
materials and mechanics. ASTM STP 937, 413-421.
13. Fracture Mechanics Testing Methods for Polymers, Adhesives and Composites (2001). ESIS Publication
28. Edited by D. R. Moore, A. Pavan, J. G. Williams. Elsevier Science Ltd.
14. Nicholls DJ, Gallagher PJ (1983). Determination of GIc in angle ply composites using a cantilever beam test
method. J. Reinf. Plast. Compos., 2, 2-17.
15. Chai H (1984). The characterization of mode I delamination failure in non-woven multidirectional
laminates. Composites, 15, 277-290.
16. Schapery RA, Goetz DP, Jordan WM (1986). Delamination analysis of composites with distributed damage
using a J integral. Proc. Int. Symp. on Compos. Mater. Struct., Beijing, 543-549.
17. Laksimi A, Benzeggagh ML, Jing G, Hecini M, Roelandt JM (1991). Mode I interlaminar fracture of
symmetrical cross-ply laminates. Compos. Sci. Technol., 41, 147-164.
18. Robinson P, Song DQ (1992). A modified DCB specimen for mode I testing of multi-directional laminates.
J. Compos. Mater., 26, 1554-1577.
19. Choi NS, Kinloch AJ, Williams JG (1999). Delamination fracture of multidirectional carbon-fibre/epoxy
composites under mode I, mode II and mixed-mode I/II loading. J. Compos. Mater., 33, 73-100.
20. Ozdil F, Carlsson LA (1999). Beam analysis of angle-ply laminate DCB specimens. Compos. Sci. Technol.,
21. Benyahia AA, Benzeggagh ML, Gong XL (2000). Initiation and bifurcation mechanisms of cracks in multi-
directional laminates. Compos. Sci. Technol., 60, 597-604.
22. Rhee KY, Koh SK, Lee JH (2000). Mode I fracture resistance characteristics of graphite/epoxy laminated
composites. Polym. Compos., 21, 155-164.
23. Davidson BD, Krüger R, König M (1996). Effect of stacking sequence on energy release rate distributions
in multidirectional DCB and ENF specimens. Eng. Fract. Mech., 55, 557-569.
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 10
24. Nairn JA (2000). Energy release rate analysis for adhesive and laminate double cantilever beam specimens
emphasizing the effect of residual stresses. Int. J. Adhesion and Adhesives, 20, 59-70.
25. Raju IS, Crews JH, Aminpour MA (1988). Convergence of strain energy release rate components for edge-
delaminated composite laminates. Eng. Fract. Mech., 30, 383-396.
26. Qian W, Sun CT (1997). Calculation of stress intensity factors for interlaminar cracks in composite
laminates. Compos. Sci. Technol., 57, 637-650.
27. Narayan SH, Beuth JL (1998). Designation of mode mix in orthotropic composite delamination problems.
Int. J. Fract., 90, 383-400.
28. Chow WT, Atluri SN (1997). Stress intensity factors as fracture parameters for delamination crack growth
in composite laminates. Composites, 28B, 375-384.
29. Robinson P, Javidrad F, Hitchings D (1995). Finite element modelling of delamination growth in the DCB
and edge delaminated DCB specimens. Compos. Struct., 32, 275-285.
30. Morais AB, Moura MF, Gonçalves JPM, Camanho PP (2003). Analysis of crack propagation in Double
Cantilever Beam tests of multidirectional laminates. Mech. Mater., 35, 641-652.
31. Chai H (1990). Interlaminar shear fracture of laminated composites. Int. J. Fract., 43, 117-131.
32. Polaha JJ, Davidson BD, Hudson RC, Pieracci A (1996). Effects of mode ratio, ply orientation and
precracking on the delamination toughness of a laminated composite. J. Reinf. Plast. Compos., 15, 141-173.
33. Ozdil F, Carlsson LA, Davies P (1998). Beam analysis of angle-ply laminate end-notched flexure
specimens. Compos. Sci. Technol., 58, 1929-1938.
34. Tao JX, Sun CT (1998). Influence of ply orientation on delamination in composite laminates. J. Compos.
Mater., 32, 1933-1947.
35. Choi NS, Kinloch AJ, Williams JG (1999). Delamination fracture of multidirectional carbon-fiber/epoxy
composites under mode I, mode II and mixed-mode I/II loading. J. Compos. Mater., 33, 73-100.
36. Hwang JH, Kwon O, Lee CS, Hwang W (2000). Interlaminar fracture and low velocity impact of
carbon/epoxy composite materials. Mech. Compos. Mater., 36, 195-214.
37. Morais AB, Silva JF, Marques AT, Castro PT (2002). Mode II interlaminar fracture of filament wound
angle-ply specimens. Appl. Compos. Mater., 9, 117-129.
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 11
Figure 1. Scheme of the DCB test.
GIc (J/m2 )
0 20 40 60
(a - a 0 ) (mm)
Figure 2. Typical R-curves obtained in DCB tests of C/PEEK5 and C/epoxy6 UD specimens.
GI (normalise d)
0 5 10 15 20
width-wise distance (mm)
Figure 3. Distribution of GI along the width of C/epoxy UD specimens6. GI values were
normalised by the width-wise average.
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 12
Figure 4. Alternative crack initiation criteria1,2.
GIc (J/m2 )
Film Precrack Propagation
Figure 5. Results of DCB tests on C/epoxy UD specimens according to the various initiation
criteria6. Propagation values are also included.
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 13
Figure 6. Schematic representation of the proposed mode II specimens.
GIIc (J/m2 )
Film Mode II Pc Mode I Pc Wedge Pc
Figure 7. Results of ENF tests on glass/epoxy UD specimens: influence of the starter defect
(film, mode I, mode II and wedge precracks) and of initiation criteria8.
A. B. de Morais, C. C. Rebelo, P. T. de Castro, A. T. Marques, P. Davies 14
GIc (J/m2 )
0 10 20 30 40 50 60
(a - a 0 ) (mm)
Figure 8. Typical R-curves of C/epoxy [(0º/90º)6//(0º/90º)6] and [0º12//0º12] specimens6.
Figure 9. Scheme of crack propagation in [(0º/90º)6//(0º/90º)6] specimens6.
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