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Composites: Part A 40 (2009) 289–299

Contents lists available at ScienceDirect

Composites: Part A
journal homepage: www.elsevier.com/locate/compositesa

Notched behavior of prepreg-based discontinuous carbon fiber/epoxy systems

Paolo Feraboli a,*, Elof Peitso a, Tyler Cleveland a, Patrick B. Stickler b, John C. Halpin c
a
Department of Aeronautics and Astronautics, University of Washington, Box 352400, Guggenheim Hall, Seattle, WA 98195-2400, USA
b
Boeing 787 Technology Integration, Boeing Commercial Airplanes, Seattle, WA, USA
c
JCH Consultants, Dayton, OH, USA

a r t i c l e i n f o a b s t r a c t

Article history: The elastic behavior and failure response of discontinuous carbon fiber/epoxy laminates produced by
Received 16 July 2008 compression molding of randomly-oriented preimpregnated unidirectional tape is characterized. Com-
Received in revised form 26 November 2008 mercial applications for this type of material form already exist, such as Hexcel HexMCÒ. Complex rela-
Accepted 17 December 2008
tionships between unnotched and notched tensile strengths are observed, and show this material to be
particularly notch-insensitive. A parametric study on the effect of specimen thickness, width, diameter/
width ratio, and hole size yields fundamental information on the behavior of this material.
Keywords:
Ó 2008 Elsevier Ltd. All rights reserved.
A. Carbon fiber
A. Discontinuous fibers
A. Moulding compounds
B. Fracture
B. Stress concentration

1. Introduction This study, comprised of several parts, investigates the behavior

of a high-performance system that uses discontinuous carbon fi-
Airframe components fabricated from composite materials have ber/epoxy obtained from aerospace-grade prepreg. Prepreg-based
traditionally been a costly alternative to aluminum construction. discontinuous systems are appealing for primary structural appli-
The primary challenge that the aerospace industry faced leading cations as they can be used in low-flow molding conditions, where-
up to the Boeing 787 was to fully obtain the performance benefits by minimal flow and reinforcement redistribution occurs upon
of composite materials while dramatically lowering production molding. Commercial applications for this type of material form al-
costs [1,2]. Recent composite technology research and develop- ready exist, although using different resin systems and fiber types
ment efforts have focused on new low-cost material product forms, and lengths, under various manufacturers and brands (e.g. Quan-
and automated processes that can markedly increase production tum Lytex 4149 and Hexcel HexMCÒ [8,9]). The Boeing 787 Dream-
efficiencies. The interest of the aerospace community for short fi- liner for example makes use of HexMCÒ for the window frames,
ber composites dates back to the 1960s and the pioneering work which are highly loaded structural elements.
of Halpin, Pagano and Kardos [3–7]. Furthermore, Sheet Molding In [10], a manufacturing technique is developed that allows for
Compounds (SMC) secondary and tertiary airframe structures for the manufacturing of randomly distributed chip-reinforced com-
non-interior applications have been in service for several years. posite plates. Good manufacturing procedures show that the plate
SMC are typically used in conjunction with traditional compression contains minimal number of voids, although resin-rich areas are
molding processes, which we can identify as high-flow molding inevitably present due to the flow of the resin during cure. Prepreg
due to the large amount of resin flow and associated fiber orienta- sheets are slit longitudinally and then chopped transversely to
tion. SMC commonly feature 1.0-in. (25.4 mm) long glass fiber form a chip of specified width and length. The study shows that
reinforcements and less than 30–50% fibers by weight. Although chip dimensions, such as aspect ratio, have a strong effect on the
the lower mechanical properties of discontinuous fiber composites measured strength but a negligible effect on the modulus. Tension,
have traditionally limited their airframe applications, relatively compression and flexural tests are carried out for varying chip
large structures such as engine strut fairings have been in service lengths and to highlight fundamental relationships for the size of
for several years even in commercial transport aircraft. In order the unit reinforcement. Noticeable variation in both modulus and
to become attractive for more significant secondary as well as pri- strength data is reported, and it varies according to the loading
mary structures, higher performance fiber, resins and manufactur- conditions and specific property measured. Failure is a matrix-
ing methods are required. dominated event, which occurs by transverse chip cracking, longi-
tudinal chip splitting, and chip disbonding, with little or no fiber
* Corresponding author. Tel.: +1 011 543 2170; fax: +1 011 206 543 0217.
breakage. In general, ultimate strength is noticeably lower than a
E-mail address: feraboli@aa.washington.edu (P. Feraboli). quasi-isotropic continuous baseline, but the modulus is virtually

1359-835X/$ - see front matter Ó 2008 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compositesa.2008.12.012
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290 P. Feraboli et al. / Composites: Part A 40 (2009) 289–299

identical to it. A strong thickness dependence of strength and mod- [12] for open-hole tension (OHT). The specimens are straight-sided
ulus may limit the minimum thickness that can be successfully rectangular specimens with dimensions 12 in.  1.5 in.
molded. In general, tensile strength appears to be the most critical, (305 mm  38 mm). Both tests are performed to identify key geo-
with compression and flexure strengths noticeably higher. metric and scaling interactions associated with the length scale of
In this study, the emphasis of this study is better understanding this material. In particular, for the UNT test, the specimen width is
of the tensile response of unnotched and notched coupons in ten- varied between 0.5, 1.0, 1.5 and 2.0 in. (12.7, 25.4, 38.1 and
sion and compression for a fixed reinforcement chip size. 50.8 mm) and specimen thickness between 0.076 in. (1.9 mm),
0.168 in. (4.3 mm) and 0.220 in. (5.6 mm). For the OHT test, hole
diameter is varied between 0.125, 0.250, 0.375 and 0.500 in. (3.2,
2. Material fabrication and test setup
6.3, 9.5 and 12.6 mm, respectively) and hole diameter (d) to spec-
imen width (w) ratio is also varied with different combinations of d
2.1. Material fabrication
and w. Table 1 offers the details of the full test matrix.
All specimens are loaded to failure at a rate of 0.05 in./min
All discontinuous carbon/epoxy panels are manufactured in the
(1.3 mm/min) in a 2-grip hydraulic tension/compression test
laboratory starting from unidirectional (UD) prepreg. The system is
frame. Glass/epoxy tabs are bonded to the specimen using 3M
a 350 °F cure (177 °C), designated for vacuum bag, autoclave cure,
Scotchweld film adhesive. For the present study, all strength data
and has a resin content of 40% by volume. The detailed procedure
reported in the following sections refers to ultimate strength, cal-
of how the unidirectional prepreg is slit and then chopped in order
culated as the strength corresponding to ultimate load. A total of
to obtain a random chip distribution is reported in [10]. It should
seven specimens per test family have been tested, and Table 1 re-
be noted that the prepreg system used here is not the same as
ports for each family the average strength (gross section ultimate)
the one used in [10]. As it will be shown, for the chip length tested,
and associated coefficient of variation (CoV). Unnotched values for
the average strength is increased and the variation in strength data
elastic modulus are measured by means of a 1.0 in. gage (25.4 mm)
reduced. The chip dimensions on which this study focuses are 2.0-
extensometer.
in. long  0.33-in. wide (50.8 mm  8.4 mm), which gives a good
compromise between mechanical performance and manufacturing
2.2.2. Unnotched and open-hole compression
ability [10].
Specimens are tested using the Boeing standard test method
Prior to machining of the individual specimens, each panel is in-
D6-83079-71 [13] for unnotched compression (UNC) and open-
spected via pulse-echo ultrasound using a 5 MHz sensor. An exam-
hole compression (OHC). The specimens are straight-sided rect-
ple of a good quality panel is shown in Fig. 1. The signal is
angular specimens with dimensions 12 in.  1.5 in. (305 mm 
particularly noisy due to the non-homogeneous nature of the
38 mm). Both tests are performed to identify key geometric
material form, and overlapping chips act as hard points for the sig-
and scaling interactions associated with the length scale of this
nal, which therefore loses its strength. This is not unlike the phe-
material. For UNC tests, the width and thickness of the speci-
nomenon observed for woven or braided fabrics. As an additional
mens are varied similarly to the UNT tests, except that the
method of inspection, a limited set of pulsed thermography inspec-
2.0-in. (50.8 mm) wide specimen cannot be tested since it is
tions are performed, which also show little uniformity in the sig-
wider than the 1.5 in. (38.1 mm) fixture. Spacers are used to
nal, and perhaps even more noise than the ultrasound. However,
provide support for specimen widths that are smaller than the
via microscopy [10] the panel is shown to be defect free by tradi-
1.5-in. (38.1 mm) specimen prescribed by the test standard.
tional standards, with a void content of less than 0.5% in the form
For the OHC tests, hole diameter is varied between 0.125 and
of larger resin-starved areas rather than micro-porosity. In [10] it
0.500 in. (3.2 and 12.6 mm, respectively), and the d/w ratio hole
was shown that these panels exhibit in-plane isotropy, and that
diameter (d) to specimen width (w) ratio is also varied with dif-
the response of specimens machined at 0°, 45° and 90° from the
ferent combinations of d and w, but specimen width is limited
reference axis all exhibited strength values within 20% of each
to 1.5 in. (38.1 mm) and lower. Table 1 offers the details of the
other. This value was consistent with the variation observed in
full test matrix.
the material itself.
All specimens are loaded to failure at a rate of 0.05 in./min
(1.3 mm/min) in a 2-grip hydraulic tension/compression test
2.2. Test setup frame. For the present study, all strength data reported in the fol-
lowing sections refers to ultimate strength, calculated as the
2.2.1. Unnotched and open-hole tension strength corresponding to ultimate load. A total of seven speci-
Specimens are tested using the Boeing standard test method mens per test family have been tested, and Table 1 reports for each
D6-83079-61 [11] for unnotched tension (UNT) and D6-83079-62 family the average strength (gross section ultimate) and associated

Fig. 1. Non-destructive inspection of good quality panels via pulse-echo ultrasound (left) and pulsed thermography (right).
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P. Feraboli et al. / Composites: Part A 40 (2009) 289–299 291

Table 1
Global test matrix for this study: * indicates continuous quasi-isotropic (25/50/25) reference values.

Family Test Width Thickness D d/w No. tested Avg. gross strength CoV Avg. modulus CoV
type mm [in.] mm [in.] mm [in.] MPa [ksi] [%] GPa [Msi] [%]
A UNT 38.1 4.19 – – 7 257 9 44.0 19
[1.5] [0.165] [37.3] [6.38]
B UNT 25.4 4.34 – – 7 262 4 46.9 13
[1.0] [0.171] [38.0] [6.81]
C UNT 38.1 5.59 – – 7 280 9 47.4 9
[1.5] [0.220] [40.6] [6.88]
D UNT 38.1 1.93 – – 7 234 19 47.0 15
[1.5] [0.076] [33.9] [6.82]
E UNT 12.7 4.45 – – 7 284 13 44.5 11
[0.5] [0.175] [41.2] [6.45]
F UNT 50.8 4.27 – – 7 231 14 43.9 9
[2.0] [0.168] [33.5] [6.37]
G OHT 38.1 4.32 3.18 0.083 7 262 8 – –
[1.5] [0.170] [0.125] [38.0]
H OHT 38.1 4.27 6.35 0.167 7 239 10 – –
[1.5] [0.168] [0.250] [34.6]
I OHT 38.1 4.32 9.53 0.250 7 203 8 – –
[1.5] [0.170] [0.375] [29.4]
J OHT 38.1 4.32 12.7 0.333 7 188 9 – –
[1.5] [0.170] [0.500] [27.3]
K OHT 25.4 4.32 6.35 0.250 7 235 8 – –
[1.0] [0.170] [0.250] [34.1]
L OHT 25.4 3.86 3.18 0.125 7 273 6 – –
[1.0] [0.152] [0.125] [39.6]
M OHT 50.8 3.96 12.7 0.250 7 194 8 – –
[2.0] [0.156] [0.500] [28.1]
N OHT 50.8 3.81 6.35 0.125 7 231 5 – –
[2.0] [0.150] [0.250] [33.6]
O UNC 38.1 4.19 – – 7 349 3 44.2 13
[1.5] [0.165] [50.6] [6.41]
P UNC 38.1 5.59 – – 7 354 5 43.1 14
[1.5] [0.220] [51.4] [6.26]
Q UNC 38.1 1.93 – – 7 295 9 41.5 12
[1.5] [0.076] [42.8] [6.02]
R UNC 25.4 4.19 – – 7 285 10 N/a N/a
[1.0] [0.165] [41.4]
S UNC 12.7 4.19 – – 7 257 8 N/a N/a
[0.5] [0.165] [37.3]
T OHC 38.1 2.11 3.18 0.083 7 308 5 – –
[1.5] [0.083] [0.125] [44.7]
U OHC 38.1 4.19 6.35 0.167 7 247 5 – –
[1.5] [0.165] [0.250] [35.8]
V OHC 38.1 4.19 9.53 0.250 7 222 4 – –
[1.5] [0.165] [0.375] [32.2]
W OHC 38.1 4.19 12.7 0.333 7 181 6 – –
[1.5] [0.165] [0.500] [26.3]
X OHC 25.4 4.19 6.35 0.250 7 209 11 – –
[1.0] [0.165] [0.250] [30.3]
Y OHC 25.4 4.19 3.18 0.125 7 291 7 – –
[1.0] [0.165] [0.125] [42.2]
AA* UNT 38.1 1.52 – – N/a 605 N/a 49.6 –
[1.5] [0.060] [87.7] [7.2]
BB* OHT 38.1 1.52 6.35 0.167 N/a 359 N/a – –
[1.5] [0.060] [0.250] [52.0]
CC* UNC 38.1 1.52 – – N/a 481 N/a 45.5 –
[1.5] [0.060] [69.7] [6.6]
DD* OHC 38.1 1.52 6.35 0.167 N/a 276 N/a – –
[1.5] [0.060] [0.250] [40.0]

coefficient of variation (CoV). Unnotched values for elastic modu- laminate analogy, the Mori–Tanaka inclusion model, and others
lus are measured by means of a 1.0 in. gage (25.4 mm) [14,15]. Predicting the magnitude of strength is a much more diffi-
extensometer. cult challenge, and one that has eluded the composite community
for decades. This is, in a way, no different that for continuous fiber
3. Results composite, where the failure theories devised to date have only
partially if not insufficiently addressed the physics of composite
The discussion will focus on the modulus and strength results failure. However, for discontinuous fiber composites there is the
collected during this experimental investigation. It has been previ- added complexity that the fiber orientation is not repeatable and
ously shown that several analytical methods exist by which the self-similar, and it cannot be predicted a priori, hence the stress
elastic properties of a discontinuous fiber reinforced composite state can vary dramatically between specimens due to the local
can be successfully predicted. These include the Halpin–Pagano meso-structure.
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Fig. 2. Representative load–displacement (left) and stress–strain (right) curves for the UNT specimens.

3.1. Tension rates in two halves (Fig. 4). The fracture surface becomes evident
as does local chip and fiber failure.
UNT specimens fail in a brittle fashion, in a combination of chip For the baseline UNT specimen configuration, Family A, an aver-
disbonding/pullout and chip fracture. The load–displacement age gross strength of 37 ksi (255 MPa) is achieved, with only 9%
curve exhibits some non-linearity (Fig. 2, left), however the variation. This value corresponds to roughly 40% of the continuous
stress–strain curve is perfectly linear up to catastrophic failure quasi-isotropic UNT strength (Family AA*). For modulus it can be
(Fig. 2, right). In the figure, the deflection is given by cross-head seen that the discontinuous and continuous quasi-isotropic values
displacement, and the modulus is measured by a single extensom- are within 10% of each other. However, it is important to observe
eter located at mid-gage of the specimen. that the amount of variation observed during the measurement
Unlike the observations reported in [10], where failure was of modulus for the discontinuous specimens is as high as 19%,
mostly matrix dominated, the material used in this study achieves which is much greater than the typical variability observed for
better shear transfer between resin and fibers, and fails in a com- continuous fiber composites, and nearly twice that observed for
bination of fiber fracture and matrix shearing between the chips.
After failure, the specimen retains a large part of its apparent integ-
rity (Fig. 3), and only upon further extension the specimen sepa-

Fig. 5. UNT strength variation with specimen width.

Fig. 3. Representative UNT specimen failure morphology (top, side, bottom).

Fig. 4. Failure surface of UNT specimen shows extensive fiber failure. Fig. 6. UNT strength variation with specimen thickness.
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P. Feraboli et al. / Composites: Part A 40 (2009) 289–299 293

Fig. 7. (a-c) OHT 3/8-in. diameter specimen failed in the net section (a), with close-up images of failure zone (b and c).

For this type of material form, where the dimensions of the unit
reinforcement (chip) are of the scale as the dimensions of the test
specimen itself, length scale relationships may become of impor-
tance. Four specimen widths are tested, and results show that
there is a small but definite trend of increasing strength with
decreasing specimen width (Fig. 5), with the 0.5-in. specimen
(12.7 mm) about 20% stronger than the 2.0-in. specimens
(50.8 mm). With regards to thickness the trend is less distinct, pos-
sibly due to the high variation observed for the thinner specimens,
but there still appears to be a 16% decrease in strength between the
0.220-in. (5.6 mm) and the 0.076-in. (1.9 mm) thick laminates
(Fig. 6). For families B thorough F it can be seen that there is still
noticeable variation in the measured modulus, as observed for
Family A, but the average remains constant around 6.5 Msi
(44.8 GPa) regardless of specimen configuration.
In order to determine the strength reduction associated with
the presence of a circular hole, a series of OHT tests is conducted
varying hole diameters and d/w ratios. This investigation allows
Fig. 8. Variation of OHT strength with hole diameter (calculated using gross section
area), highlighting net vs. gross section failures. for the development of an understanding of the characteristic
length scale of the material, which in the case of discontinuous fi-
bers may be finite. OHT strength values are calculated using the re-
tensile strength. Explanations of this behavior are reported in a fu- mote applied stress and the gross section area, consistent with
ture study. industry practice [12,13,16]. It can be seen that for the standard
The focus of the study on UNT strength is to isolate geometric 0.250-in. (6.3 mm) diameter hole (Family H), the decrease in OHT
relationships between test specimen size and measured strength. gross section strength from the UNT value (Family A) is 7% and

Fig. 9. OHT 0.375-in. diameter specimen failed at gross section (a), also with close-up of failure area (b).
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294 P. Feraboli et al. / Composites: Part A 40 (2009) 289–299

34% from the continuous quasi-isotropic benchmark (Family BB*). greater complexity then for continuous fiber composites. It should
Interestingly, for 0.125-in. hole (3.1 mm) the average OHT value is be noted that in Figs. 10 and 11 all strength values are calculated as
lightly higher than the UNT value, which is an artifact of the lim- gross section strengths, regardless of their failure location, and that
ited set of test repetitions at each hole diameter. Nonetheless, it finite width effects have been neglected.
indicates that for such a small hole there is no decrease in gross
section strength. 3.2. Compression
A typical specimen that fails around the hole can be seen for a
0.375-in. (9.4 mm) hole in Fig. 7, and its shows the failure mode UNC specimens also fail in a brittle fashion, in a combination of
to be of the same kind of chip pullout and fracturing seen in the chip disbonding and wedging, as well as chip/fiber kinking and
UNT tests. However, this kind of failure is not the most typical to fracture (Fig. 12). The load–displacement curve exhibits an initial
occur. The majority of coupons containing small holes do not fail nonlinear region typical of most compression test (Fig. 13, left),
at the tip of the hole, where classical mechanics predict the highest however the stress–strain curve is perfectly linear up to cata-
concentration to occur, but in the gross section, away from the strophic failure (Fig. 13, right).
hole. This phenomenon is not common in traditional isotropic or For the baseline UNC specimen configuration, Family O, an aver-
continuous fiber composite materials, where the stress concentra- age gross strength of 50 ksi (690 MPa) is achieved, with a variation
tion in proximity of the hole inevitably generates failure in the net of only 3%. This value corresponds to roughly 70% of the continuous
section area. As the hole diameter increases, the number of speci- quasi-isotropic UNC strength (Family CC*). For modulus it can be
mens that fail in the net section increases, Fig. 8. For the 0.125-in. seen that the discontinuous and continuous quasi-isotropic values
(3.2 mm) hole 4 of 7 specimens fail in gross section, for the 0.250- are nearly identical.
in. (6.3 mm) hole 3 of 7, for 0.375-in. (9.5 mm) hole only 1 of 7, and The focus of the study on UNC strength is also to isolate geomet-
finally all specimens fail in the net section for the 0.500-in. ric relationships between test specimen size and measured
(12.7 mm) hole (Fig. 8). This atypical behavior is likely attributable strength. Three specimen widths are tested, and results show that
to the non-homogeneous nature of this type of material form, there is a clear trend of decreasing strength with decreasing speci-
which features strong discontinuities in stress distributions at men width (Fig. 14), with the 0.5-in. specimen (12.7 mm) over 25%
the chip intersections, with high stress concentrations at the chip less strong than the 1.5-in. specimens (38.1 mm). UNC results are
ends. To that extent Fig. 9 shows also shows a 0.375-in. hole therefore more marked and in direct antithesis with those observed
(9.5 mm) specimen, which however precipitated failure away from for UNT (Fig. 5), and suggest that the stability considerations have a
the hole and away from the grips, exactly in mid-gage. A similar re- predominant effect over the measured strength than the length-
sponse was reported by Kardos et al. for short fiber composites [6],
and by Feraboli [17] for oriented strand board wood composite.
Results shown in Fig. 10 refer to five families with varying
widths and hole diameters, which are grouped into two sets having
the same d/w. It is interesting to observe that for the same d/w ra-
tio, the specimens with smaller holes or narrower widths tend to
exhibit higher strength. Fig. 11 on the other hand contains seven
families with varying widths and d/w ratios, which are grouped
into three sets by hole diameter. It appears that for the same hole
size, the specimens tend to exhibit contradicting trends with vary-
ing d/w ratio, with either greater or lower strength for higher or
lower d/w. It appears therefore that there are non-trivial interac-
tions between specimen geometry and strength, of the same or

Fig. 11. Variation of OHT strength (calculated using gross section area) with
specimen width and d/w ratio, for three given values of hole diameters.

Fig. 10. Variation of OHT strength (calculated using gross section area) with hole
diameter and specimen width, for two given values of d/w ratio. Fig. 12. Representative UNC specimen failure morphology (left and right sides).
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P. Feraboli et al. / Composites: Part A 40 (2009) 289–299 295

Fig. 13. Representative load–displacement (left) and stress–strain (right) curves for the UNC specimens.

(6.3 mm) diameter hole (Family U), the decrease in OHC gross sec-
tion strength from the UNC value (Family O) is 29%, but only 11%
from the continuous quasi-isotropic benchmark (Family DD*).
All OHC specimens failed at the hole as in Fig. 16, which shows
the failure mode to be of the same kind of chip shearing, wedging
and fracturing seen in the UNC tests. As the hole diameter in-
creases, the gross section strength decreases in a linear fashion
(Fig. 17).
Results shown in Fig. 18 refer to two families with different
widths and hole diameters, but having the same d/w ratio. It is
interesting to observe that the family with smaller hole or nar-
rower width tends to exhibit lower strength. Fig. 19 on the other
hand contains four families with varying widths and d/w ratios,
which are grouped into two sets by hole diameter. It appears that
for the same hole size, the OHC specimens with higher d/w appear
Fig. 14. UNC strength variation with specimen width. to have lower strength, as evidenced in the case of OHT for
D = 0.25 in. (6.3 mm) and D = 0.375 in. (9.5 mm). Once again it ap-
pears that there are non-trivial interactions between specimen
scale effects. With regards to thickness, the trend is consistent with geometry and strength, where the influence of the hole and its size
that observed for UNT (Fig. 6), and there still appears to be a 17% de- may have contrasting or reinforcing effects with respects to the ef-
crease in strength between the 0.220-in. (5.6 mm) and the 0.076-in. fects caused by other length scales (such as width). It should be
(1.9 mm) thick laminates (Fig. 15). For Families P and Q it can be noted that in Figs. 18 and 19 all strength values are calculated as
seen that there is still noticeable variation in the measured modu- gross section strengths, regardless of their failure location.
lus, as observed for Family O, but the average remains constant
around 6.5 Msi (44.8 GPa) regardless of specimen configuration.
4. Discussion
In order to determine the strength reduction associated with
the presence of a circular hole, a series of OHC tests is conducted
When calculating the OHT strength of composite materials,
varying hole diameters and d/w ratios. OHC strength values are cal-
where stress concentration factors depend on the stacking se-
culated using the remote applied stress and the gross section area,
quence and the local stress state in the vicinity of the notch is
as in the tension case. It can be seen that for the standard 0.250-in.
not clearly defined due to the heterogeneity of the material, two
approaches can be used. The first calculates the net strength rNOHT
of the material as the maximum sustained load P divided over
the net section, and is defined as
P
rNOHT ¼ ð1Þ
ðw  dÞ  t
where w is the width of the specimen and d is the hole diameter,
while t is the specimen thickness. The other approach employs
the gross strength rinf
OHT , as in the case of unnotched strength rUNT,
regardless of the presence of the hole, and is defined as:
P
rinf
OHT ¼ rUNT ¼ ð2Þ
wt
The latter method is commonly preferred in advanced compos-
ite design, such as in the generation of allowable strength values in
the aerospace industry. The effect of the presence of the hole is to
effectively reduce the value of the maximum load to failure, thus
Fig. 15. UNC strength variation with specimen thickness. reducing the calculated strength.
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296 P. Feraboli et al. / Composites: Part A 40 (2009) 289–299

Fig. 16. OHC 1/4-in. diameter specimen, with close-up images of failure zone.

Remote strength rOHTinf (Eq. (2)) is used to generate the plot of duced section area capable of carrying load. It should be noted that
Fig. 8, which shows the variation of strength with increasing hole the d/w ratio is not held constant for the specimens used to gener-
diameter. In general, the trend observed is of decreasing strength ate Fig. 8, since all specimens are 1.5-in. wide (38.1 mm) regardless
with increasing hole size, which is to be expected given the re- of the hole size. As pointed out earlier, a rather unusual feature of
the plot in Fig. 8 is that for the smaller hole sizes tested the major-

Fig. 17. Variation of OHC strength with hole diameter (calculated using gross Fig. 18. Variation of OHC strength (calculated using gross section area) with hole
section area), showing all net section failures. diameter and specimen width, for the same value of d/w ratio.
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P. Feraboli et al. / Composites: Part A 40 (2009) 289–299 297

Fig. 22. Variation of OHT and OHC strength (calculated using gross section area)
Fig. 19. Variation of OHC strength (calculated using gross section area) with
with d/w ratio, plotted against the notch-insensitive line.
specimen width and d/w ratio, for three given values of hole diameters.

ity of the failure locations occurs in the gross section of the speci- enon observed can be found in the non-homogenous nature of the
men, away from the hole. A possible explanation for the phenom- discontinuous fiber composite. Its meso-structure (more appropri-
ately referred to rather than a micro-structure) is such that the
geometric stress concentration due to the presence of the hole
may have less influence on failure than an ‘‘inherent material”
stress concentration. This material Kt for non-homogeneous mate-
rials, such as short fiber composites, has been attributed to the
presence of high stress concentration at the end of the randomly
distributed reinforcing fibers [18]. In the case of this material form,
the chips effectively act as the reinforcements, and the mismatch
in elastic properties between the chip and the surrounding matrix,
as well as the neighboring chips that may be oriented in different
directions, may generate local peak stresses that lead to failure.
Given the fact that such a high percentage of failures occurs at
the gross section even for specimens with large holes, the strength
data of Fig. 8 can be rearranged in Fig. 20 to differentiate the
strength calculation according to the failure location. Strength
can be re-calculated by dividing the load at failure by the actual
cross-section area where failure occurred, which means the net
section (Eq. (2)) for the specimens that fail at the hole tip, and
the gross section area (Eq. (1)) for the ones that fail away from
the hole, it is possible to derive the plot shown in Fig. 20. Strength
appears then to become constant around a mean value of 38 ksi
Fig. 20. Variation of notched strength with hole diameter (calculated using gross
(262 MPa), with an upper an lower bound of ±8 ksi (55 MPa). This
section and net section area accordingly), highlighting net vs. gross section failures.
result would seem to suggest that the strength of this type of dis-
continuous fiber material does not decrease with the presence of

Fig. 21. Variation of OHT strength (calculated using gross section area) with d/w
ratio, showing classic behaviors for notch-sensitive, notch-insensitive, and typical Fig. 23. Determination of average characteristic dimension d0 for the OHT and OHC
continuous fiber quasi-isotropic experimental data points [16]. load cases over the range of hole diameters tested.
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298 P. Feraboli et al. / Composites: Part A 40 (2009) 289–299

the hole, and hence it could be classified as exhibiting notch-insen- 2ðR þ d0 Þ4 rUNT
sitive behavior. A truly notch-insensitive material is shown in the rinf
OHT ¼ 2 3 4
ð4Þ
6R þ 10R d0 þ 13R2 d0 þ 8Rd0 þ 2d0
4 3
dark solid straight line, where the reduction in load-carrying capa-
bility is linearly proportional to the reduction in available cross- It is then possible to calculate an average value of d0 = 0.192 in.
section area. To better clarify this concept, Fig. 21 [16] gives a sum- (4.9 mm) for tension and d0 = 0.091 in. (2.3 mm) in compression, as
mary of the traditional behaviors, and it represents the ratio of shown in Fig. 23. It should be noted that typical d0 values for con-
notched (OHT) to unnotched (UNT) strength as a function of d/w tinuous carbon/epoxy quasi-isotropic laminates [19,20] fall in the
ratio. The three behaviors observed include purely notch-sensitive range 0.02–0.08 in. (0.5–2.0 mm). It appears then that the value
(1/Kt curve), purely notch-insensitive (1:1 straight line), and typi- for compression, although high, appears to be in the range of ex-
cal continuous fiber composite laminates. These latter ones are pected values, while the one in tension is much greater than any-
known to exhibit a response, which is neither purely notch-sensi- thing observed before. Such a large d0 value signifies that this
tive nor insensitive, and they are represented as experimental data material is much more tolerant to open holes. Also to be noted is
points, to which a curve is fitted via the Point Stress Criterion (PSC), that the plot of Fig. 23 lacks a data point corresponding to the
also known as the Whitney–Nuismer criterion [19,20]. If a similar 0.125-in. (3.2 mm) hole diameter on the tension curve, for which
plot is built for the discontinuous fiber composites considered in the PSC loses value since the OHT strength is equal or slightly
this study, it is possible to observe that both tension and compres- greater than the UNT strength. Finally, the predicted strength using
sion results exhibit linear relationship, Fig. 22. However, while the the PSC with a d0, calibrated using the 0.250-in. (6.3 mm) hole
compression data falls right onto the 1:1 straight line for notch- strength, is plotted in Fig. 24 over the measured values, and shows
insensitive materials, the tension data seems to be shifted to the good agreement for both tension and compression.
right to d/w = 0.084. This is consistent with previous observations Using the characteristic dimension d0, Waddoups et al. [21] sug-
that for the 1/8-in. (3.2 mm) diameter holes there is no reduction gested, for advanced polymer composites, that it is possible to cal-
in strength, and that only for the next hole size (1/4-in. or culate the stress concentration factor Kt:
6.3 mm hole diameter) there is a measurable decrease in strength. sffiffiffiffiffiffiffiffiffiffiffiffiffiffi
It also seems to support the observation of an inherent ‘‘material” d þ d0
Kt ¼ ð5Þ
stress concentration, due to the non-homogeneous meso-structure d0
(the word micro-structure is not appropriate to define the random
Referring to Fig. 8, the number of specimens that fails at the
chip distribution).
hole is 28% for d = 0.125 in. (3.2 mm), 50% d = 0.250 in. (6.3 mm),
The PSC, formulated by Whitney and Nuismer to predict the
while 100% of specimens fail at the hole for d = 0.500 in
notched strength of advanced polymer composites, relies on the
isotropic stress concentration expression and modifies it by intro-
ducing the concept of the characteristic dimension d0. If we specify
the index I as the ratio of applied remote stress r over the unnot-
ched tensile strength rUNT,
r
I¼ ð3Þ
rUNT
the Point Stress Criterion specifies that failure will occur when I
reaches the value of unity at a location distant d0 from the hole,
known as characteristic dimension. This d0 has been shown to be
constant for a given material type, stacking sequence, and loading
type for advanced polymer composites. Setting R as the hole radius,
we can write:

Fig. 25. UNT and OHT probability density functions.

Fig. 24. Point Stress Criterion predictions of OHT and OHC strengths using the d0
calibrated with the 0.250 in. (xxx mm) experimental data point, show good
agreement with other data points. Fig. 26. UNC and OHC probability density functions.
 Author's personal copy

P. Feraboli et al. / Composites: Part A 40 (2009) 289–299 299

(12.5 mm). Therefore it is somewhere between 0.375 in. (9.5 mm) methods used for homogenous materials, independent from their
and 0.500 in. (12.5 mm) that the geometric Kt always exceeds the orthotropic nature, cannot be used to predict notched strength va-
inherent material Kt. lue and location due to the complex stress state in the meso-struc-
Using Eq. (5) and d0 = 0.192 in. (4.9 mm) for tension, Kt = 1.90 ture. Specimen size appears to have important effects on the
for d = 0.500 in. (12.5 mm). If we make the analogy that the inter- measured strength, particularly the width of the specimen, but
nal stress concentration. If we define as the pristine strength the unfortunately tension and compression loads generate opposite
UNT strength of the continuous fiber quasi-isotropic composite, trends. Modulus appears to be relatively constant among the vari-
and as the notched strength the UNT strength of the discontinuous ous families of specimens tested, although it manifests high varia-
fiber composite, the: tion, often greater than that observed for strength.
rOHT rUNTcont 1
¼ ¼ ¼ 0:53 ð6Þ Acknowledgments
rUNT rUNTdiscont K t
This would suggest that this discontinuous material form could The authors wish to acknowledge Dr. Alan Miller (Director, Boe-
achieve only 53% of the theoretical strength of the parent quasi- ing 787 Technology Integration) for supporting this study. For the
isotropic composite. Experimental results appear to show that for thermography inspections the authors would like to thank Thermal
the given test geometry and material form, the ratio of average Wave Imaging Inc.
strength of Family A to Family AA* is only 0.42, which is sensibly
lower but could justified by the several approximations and References
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