XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
JOURNAL OF
COMPOSITE
M AT E R I A L S
Article
Three-dimensionally woven glass fiber
composite struts: characterization and
mechanical response in tension and
compression
Journal of Composite Materials
0(0) 1–19
! The Author(s) 2015
Reprints and permissions:
sagepub.co.uk/journalsPermissions.nav
DOI: 10.1177/0021998315569751
jcm.sagepub.com
Adam J Malcom1, Mark T Aronson2 and Haydn NG Wadley3
Abstract
Three-dimensionally woven E- and S2-glass fiber textiles have been used in the past to create delamination-resistant
corrugated core sandwich panels. During subsequent out-of-plane loading, the E-glass composite core struts and S2-glass
composite faces are subjected to either compressive or tension loads. This study has investigated the relationships
between the three-dimensional fiber architecture, fiber properties and the mechanical response of representative samples of the core and faces. Using X-ray computed tomography and optical microscopy to characterize the threedimensional fiber architectures, it is found that the in-plane warp and weft fibers suffer significant off-axis displacement
(waviness) due to their interaction with through thickness z-fiber tows. The consequence of this fiber waviness on the
relationships of the in-plane tensile and compressive mechanical properties, along with fiber type, fiber volume fraction,
and strut aspect ratio are experimentally investigated. The large initial misalignment angle of the warp and weft fiber tows
results in a strut compressive strength that is substantially lower than its tensile strength due to compressive failure by
either elastic or localized fiber microbuckling. Simple micromechanical models are used to relate the compressive
strength of the three-dimensional woven composite struts to strut aspect ratio, fiber volume fractions in the three
directions and the three-dimensional fiber architecture.
Keywords
GFRP composite, three-dimensional woven, mechanical response, E-glass, S2-glass, tension, compression, composite,
micromechanical modeling
Introduction
The modulus and strength of fiber reinforced composite
materials are usually optimized by the use of high
modulus and high strength fibers, oriented parallel to
the direction of loading.1 Under bi-axial states of stress,
the fibers are arranged in a variety of in-plane orientations to support each of the principle stress components. Lamination of unidirectional tape is the usually
preferred method of construction for these materials
due to the ease (and lower cost) of this increasingly
automated (robotic) manufacturing processes, and the
ability to modify the ply layup for different loading
configurations.2 However, interest in three dimensionally woven composite structures have continued to
grow because the out-of-plane fibers can be exploited
to reduce the risk of ply delamination, especially under
impact loading conditions.
For long-fiber, unidirectional, plastic composites
loaded in tension in the fiber direction, the modulus is
reasonably well predicted by the Voigt upper predictive
bound while the Reuss relation can be used as a lower
bound for transversely loaded unidirectional composites.3 The Hashin-Shtrikman model provides a more
precise bounding envelope for materials with dissimilar
1
Department of Mechanical Engineering, University of Virginia, USA
DuPont Spruance Plant, New Fibers Group, USA
3
Department of Materials Science and Engineering, University of Virginia,
USA
2
Corresponding author:
Adam J Malcom, Department of Mechanical Engineering, University of
Virginia, 122 Engineers Way, PO Box 400746, Charlottesville, Virginia,
22904, USA.
Email: [email protected]
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
2
Journal of Composite Materials 0(0)
Poisson’s ratios and converges to the rule-of-mixtures
prediction when the Poisson’s ratios of the fiber and
matrix are equal.3 The tensile strength is reached
when either the fiber or matrix reaches its ultimate tensile strength.4,5
Compressive loading in the fiber direction is more
complicated since a variety of failure modes, including
global buckling, inter-ply delamination (splitting),
brooming, and fiber microbuckling6 can be activated.
The weak inter-ply delamination and brooming failure
modes of axially compressed unidirectional and 0 /90
laminated composites can be eliminated in three-dimensional (3D) woven structures by incorporating ‘‘binding’’ fibers-oriented transverse to primary fiber ply
plane.7 Fiber microbuckling then dominates the
response, and the matrix shear strength and fiber misalignment angle affect the compressive failure strength
of the composite, leading to a situation where the fiber
strength is predicted to have no effect upon the compressive strength.8
The use of an out-of-plane, binding fiber strategy
can be implemented by z-pinning, through stitching,
or variations of 3D weaving such as 3D Interlock
Weaving (3DIW) which re-directs a part of the axial
warp yarn to serve as an out-of-place reinforcement,
or 3D Non-Crimp Orthogonal Weaving (3DNCOW)
which is designed to maintain the warp and weft
fibers in an axial configuration while incorporating a
separate (and smaller by volume fraction) z-yarn to
be fully woven through the thickness of the fiber architecture.7,9,10 The out-of-plane fiber tows (z-yarns) in the
non-crimp orthogonal weaving process are woven parallel to the warp tow in a simple [0o/90o]n warp/weft
straight tow laminate, thereby binding the fiber architecture together.
Experimental studies have shown that delamination
cracks brooming failures are partially or (in some cases)
entirely eliminated by 3D weaving, and in some cases
flexural strengths can be double those of conventional
2D laminates.7 Under in-plane compression of the composite, the out-of-plane expansion of the warp and weft
reinforced laminates is inhibited by the z-yarn which is
then placed in tension. While many studies confirm a
significant delamination-resistance benefit of 3D woven
textiles, the fiber waviness created within the in-plane
warp and weft fiber tows increases susceptibility to kink
band formation and microbuckling failure under inplane compressive loading.7,11,12
The improved bending resistance of metallic corrugated (cellular) core sandwich panel structures has stimulated investigations of their underwater impulse
response.13–15 Similar structures made from composite
materials offer a potentially higher specific strength
opportunity, and have therefore attracted interest. A
method for the fabrication of impact-resistant
corrugated composite sandwich panels with 3D woven
composite glass fiber reinforced polymer (GFRP) corrugated cores and faces has recently been described.16
3DNCOW composite E-glass was used to manufacture
the core struts, while the face sheets are made from a
higher strength 3DNCOW S2-glass fiber fabric to provide tensile stretch resistance (While S2-glass exhibits
the high tensile strength needed to resist face sheet
stretching during panel bending, the lower strength Eglass weave was more amenable to folding, allowing the
fabric to be more easily formed into a corrugation core
geometry.), and the through-thickness compressive
response of the structure has been investigated under
both quasi-static16 and dynamic loading17 conditions.
These studies revealed that core strut failure occurred
by either elastic (global) buckling or localized plastic
(fiber) microbuckling.18,19 If a similar composite corrugated core sandwich panel were subjected to a flexural
load, Figure 1, a more complex situation would develop
where some core struts and face sheet members would
be subjected to tensile stresses and others to compression with substantial shear forces at the nodes.20 Here,
the tensile and compressive response of representative
samples of the core struts and faces of structures used in
prior studies16,17 are investigated. It is shown that the
inter-ply delamination and brooming mechanisms
observed in laminated structures are eliminated21,22
and their mechanical response is then related to that
of the fibers, the fiber volume fraction and to the 3D
fiber architecture.
Here we use the same 3D woven fabrics and polymer
matrix as the previous studies16,17 to fabricate E- and
S2-glass fiber composite struts of various aspect ratios
and fiber fractions using a vacuum infusion resin transfer process. We characterize the resulting 3D fiber
architectures using both high-resolution X-ray computed tomography (XCT) and optical techniques, and
investigate the failure mechanisms that govern the
sandwich panel mechanical response. Previously proposed micromechanical models are then used to establish linkages between strut geometry, fiber and matrix
properties, composite fiber structure and the mechanical properties of the struts.
Materials selection and strut fabrication
Fibers and fabrics
The 3D fiber architecture of 3DNCOW fabrics used to
fabricate the GFRP sandwich panels investigated here
is shown in Figure 2(a). The dry fabrics, Figure 2(b)
and (c), consisted of alternating layers of initially
straight warp and weft fiber tows (Weft tows are also
referred as fillers, warp tows as stuffers, and z-yarn tows
as warp weavers.) held in place by a smaller fraction of
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
Malcom et al.
3
Face sheet in compression
3D woven
fiber
architecture
Weft fiber
direction
Strut in
tension
Strut in
compression
S2-glass
3Weave®
face sheets
Kevlar stitching
Panel
unit cell
Face sheet
in tension
Dual laminate
E-glass
3Weave® struts
Compression
H
hf
l
t
ω
Core unit cell
H130 Divinycell foam
Tension
Figure 1. Schematic illustration of a hybrid polymer foam/corrugated composite core sandwich panel utilizing 3D woven E-glass fiber
textile to create the core struts and S2-glass for the face sheets. When subjected to bending, the face sheets and core struts are loaded
in either in-plane tension or compression. The focus of this study is to investigate the core strut and face sheet when subjected to this
loading.
z-yarns that looped over and under the weft tows. The
z-yarns propagated in the warp tow direction and
bound the warp and weft tows, inhibiting their outof-plane delamination, but at the cost of waviness of
the in-plane tows. In principle, the 3DNCOW fiber
architecture is able to maintain straight warp and
weft fiber tows through the use of a z-yarn squarewave profile that minimally deflects the warp and weft
fiber tows7 while maintaining binding confinement of
these tows. In practice, a quasi-sinusoidal profile is created because tow displacement from tension is applied
during the z-yarn insertion process. The number of
warp and weft layers, the number and type of fibers
per tow, and the spacing between tows in each layer
are variables that effect the composites structure and
mechanical properties.
The 3D laminates used here consisted of a [0 /90 /
0 /90 /0 ] layup of three weft and two warp layers. The
z-yarn looped the outermost weft tows, binding the
entire structure together, thereby increasing the delamination strength.23 The fraction of tow layers in each
direction, the spacing between tows in a layer, and the
number of fibers per tow control the fiber volume in a
composite panel. The fiber fraction and number of tows
in each direction for both the E- and S2-glass woven
fabrics is summarized in Table 1. Approximately 48%
of the fibers were in the warp tows, 48% in the weft
tows with the remaining 4% residing in the z-yarn.
The E-glass fiber used in the core of the sandwich
structure has a high strength and is commonly used in
transportation applications.4 E-glass fibers are composed of silica (54.3 wt%), alumina (15.2 wt%), calcium
oxide (17.2 wt%), magnesium oxide (4.7 wt%), boron
oxide (8.0 wt%), and sodium oxide (0.6 wt%). The
fiber tensile strength of commercial fibers is reported
to range from 1.7 to 2.5 GPa with a Young’s modulus
of 72 to 81 GPa.24 The density of E-glass fiber is
2.54 Mg/m3. The core web was constructed from a
3WeaveÕ fabric (grade P3W-GE045) made by 3Tex,
Inc (Cary, NC) using Hybon 2022 silane sized, Eglass fibers with an average fiber diameter of 18 mm.
There were approximately 2300 fibers in the weft fiber
tows and nearly 3500 fibers in the warp fiber tows. The
mass per unit area of the dry, 1.49-mm thick fabric was
1.86 kg/m2 for the weave pattern used here, Figure 2(b).
In this textile, the z-yarn spacing in the weft and warp
directions was approximately 5.2 mm. Fabric flexibility
was affected by the weave’s z-yarn spacing, z-yarn fiber
tension, and the tow spacing. This fabric was chosen for
use as the core strut fiber material as it provided sufficient flexibility to allow folding in the weft tow direction to create the corrugated core sandwich panels.16,17
S2-glass was selected for the face sheets because of
its higher tensile strength.4 It is composed of silica
(64.2 wt%), alumina (24.8 wt%), magnesium oxide
(10.27 wt%), ferrous oxide (0.21 wt%), sodium oxide
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
4
Journal of Composite Materials 0(0)
(a)
3D Woven Fiber Geometry
Warp fiber tows
Weft fiber tows
z-yarn
Unit cell:
(c) S2-Glass 3Weave®
Warp tows
(b) E-Glass 3Weave®
5.0 mm
5.2 mm
Weft tows
z-yarn
Figure 2. Architecture of 3D woven glass fiber fabrics used in the core struts and face sheets of the corrugated core sandwich
structure. (a) The 3WeaveÕ geometry consisting of three weft tows, two warp tows, and one z-yarn per repeating volume element.
(b) Photograph of the E-glass 3WeaveÕ fabric used for the core struts and (c) the S2-glass 3WeaveÕ used for the face sheets. The Eglass 3WeaveÕ fabric had a larger z-yarn spacing resulting in a looser weave which facilitated fabric folding to form a core corrugation.
(0.27 wt%), barium oxide (0.2 wt%), calcium oxide
(0.01 wt%), and boron oxide (0.01 wt%). S2-glass
fibers have a reported tensile strength of 2.3–3.4 GPa
(in finished product form) and an elastic modulus of
86–93 GPa.4,24 The face sheets used here were constructed from a single-laminate of S2-glass 3WeaveÕ
(grade P3W-GS025) made by 3Tex, from AGY 463
S2-glass roving with an epoxy-silane sizing. The average fiber diameter was 9 mm. The weft fiber tows contained nearly 8000 fiber filaments while the warp fiber
tows contained approximately 11,000 fiber filaments.
The density of S2-glass is 2.49 Mg/m3 and the aerial
density of the 3.6-mm thick dry fabric was 3.39 kg/m2.
The measured inter z-yarn spacing in the warp direction
was approximately 5.0 mm, Figure 2(c). The weave
density was higher than that of the E-glass laminate,
making this fabric much less flexible, and not as well
suited for construction of the core webs.
The Young’s modulus of the E-glass fibers was
obtained by testing warp and weft tows extracted
from the fabric in quasi-static tension utilizing grooved
capstan grips at a strain rate of 10–3 s–1 following test
methods in ASTM D-2343. The fiber tows were
wrapped around the capstan grip, clamped into place,
and pre-tensioned to approximately 10 MPa to remove
fiber slack. The stress–strain response was initially linearly until the onset of isolated fiber failure within the
fiber tow, Figure 3(a). The E-glass fiber elastic modulus
was 74 GPa and lay within the literature range of values
of 72–81 GPa.4 The S2-glass fiber modulus was 82 GPa;
slightly below the literature value of 85 GPa.4 The
virgin fiber strength immediately on formation is
reported to be 3.4 GPa for E-glass and 4.5 GPa for
S2-glass fibers.4 Mechanical processing of the silanecoated and woven fabric is reported to reduce the
tensile strength by 50% dropping the strength of
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
Malcom et al.
5
Table 1. 3WeaveÕ fiber distribution in the warp, weft, and z tows for both E-glass and S2-glass.
Material
Fiber fraction (%) warp / weft / Z-yarn
Number of tow layers warp / weft
E-Glass
S2-Glass
48.3 / 47.9 / 3.8
45.9 / 49.6 / 4.5
2/3
2/3
(a)
Fiber Strength
Virgin Fiber
S2-Glass
E-Glass
Silane Coated Fiber
S2-Glass Post Woven
Fiber Tow Measurement
E-Glass Post Woven
Fiber Tow Measurement
(b)
Stress (MPa)
SC-11 Epoxy Strength
composite. It is a two-component, two-phase (rubber
toughened) system developed for shock loading applications, and is intended for use with a vacuum infusion
processes (VIP). The measured density was consistent
with manufacturer specifications of 1.05 g/cm3. The
compressive stress–strain response of the rubber toughened epoxy, measured at a quasi-static strain rate of
10–3 s–1 and an ambient temperature of 25 C is shown
in Figure 3(b). This test conformed to the ASTM D-695
test standard. The compressive yield strength of the
matrix was 47 MPa at a yield strain of 4.5% and its
elastic modulus was 1.35 GPa. A shear test on the
matrix was performed using an Iosipescu shear fixture
following test methods in ASTM D-5379. The shear
stress–strain response is superimposed on Figure 3(b).
The shear strength of the matrix was 22 MPa at a
yield strain of 11.5%. The shear modulus was
210 MPa. For an epoxy system, the tensile strength is
approximately the same as the compressive strength.21
Compression
Composite fabrication
Shear
Engineering Strain
Figure 3. (a) Measured tensile stress–strain responses of Eand S2-glass fiber tows removed from the 3D woven fiber
architectures compared to the theoretical response of ideal
silane-coated fibers used in this fabric. (b) Compressive and shear
stress–strain response for the rubber toughened SC-11 M epoxy
matrix.
silane-coated E-glass and S2-glass fibers to 1.7 GPa and
2.25 GPa, respectively, Figure 3(a). However, the measured tensile strength of the fiber tows extracted from
the woven fabric was smaller; approximately 1.0 GPa
for E-glass and 1.9 GPa for the S2-glass fibers.
Polymer resin
SC-11 epoxy (Applied Poleramic Inc., Benicia,
California) was used for the polymer matrix of this
Single, double and triple layer E-glass 3D woven fabric
was used to create the hybrid laminated 3D woven
cores described earlier.16,17 Laminating 1, 2, or 3
layers of the E-glass fabric resulted in struts with dry
thicknesses of 1.49, 2.98, and 4.47 mm. Core web and
face sheet plates were constructed using a modified VIP
designed to reproduce the thickness and fiber fractions
of the struts/face sheets studied in the corrugated core
sandwich structure,16,17 and yet provide sufficient
coupon length for testing in compression and tension
under ASTM specifications. Construction began with
the dry fabric placed between layers of peel ply to
allow for part detachment after infusion. A layer of
distribution media was placed on the top of the part
to enhance resin flow to all areas of the glass fiber mat
and created a connection for flow between the resin line
inlet, glass fabric, and vacuum line outlet. The vacuum
line was positioned at the far end of the part ultimately
connecting to a resin trap and vacuum system. The
entire setup was sealed underneath a nylon vacuum
bag film and the system was evacuated to pull resin
through the fabric.
After mixing, the epoxy system had a viscosity of 900
cps, sufficient to permit vacuum-assisted infiltration of
a 500 mm 500 mm area in 30 minutes at –94.8 kPa
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
6
Journal of Composite Materials 0(0)
pressure. To ensure complete component infiltration,
the permeability of the distribution media was
increased along the outside edges of the fabric to
enable rapid resin transport around the periphery of
the entire panel and permitted a sufficient resin supply
from the edges inward to provide sufficient time for the
slower infiltration of the interior fabric. A modified VIP
was implemented in which a vacuum-assisted resin
transfer molding (VARTM) process was implemented
inside an autoclave (ASC Process Systems Econoclave
EC3X5) to create struts similar to those used in corrugated core composite sandwich panels.16,17 The modified VIP facilitated better removal of air voids within
the SC-11 epoxy (trapped air pockets during infusion)
and the ability to control the fiber fraction through the
application of external pressure to the vacuum bag. The
pressure differentials achieved by use of the autoclave
allowed for the fabrication of struts with fiber volume
fractions of 25 to 60% to permit investigation of the
effects of fiber fraction on the hybrid laminated struts.
Struts that contained porosity were removed from the
sample test set of this study. Strut lengths were
14 1 mm or 25 1.5 mm and allowed strut thickness-to-length (t/l) ratios to vary from 0.07 to 0.25.
Strut characterization
Fiber waviness results in substantial fiber misalignment
with the applied force during testing, and can adversely
affect a laminates compressive strength.6 We have
therefore characterized the fiber tow architecture
using both XCT and optical microscopy to measure
initial maximum and average fiber tow misalignment
angles. The XCT allowed a 3D reconstruction of the
fiber architecture through the thickness of the part, and
was conducted using a 225 kV microfocus XCT system
with a flat panel PerkinElmer XRD 1621 X-ray detector at Chesapeake Testing (Belcamp, MD). The setup
was maximized for low-energy, high-resolution scanning in order to resolve the individual fibers and the
effective tow waviness. The samples were scanned at
80 kV with a tube current of 45 uA yielding volumes
capable of reconstruction with a final voxel size of
6 mm.
An XCT image of an E-glass single laminate strut is
shown in Figure 4(a). The image shows warp and weft
fiber tows that exhibit significant fiber tow waviness. In
some cases, warp or weft tows that were stacked vertically during the weave process have slid laterally relative to one another and impinged upon neighboring
E-Glass - 1 Laminate
(a)
Warp
z-yarn
Warp F
ibe
2 mm
W
ef
tF
ibe
r
Weft
r
(b)
Warp Fiber Direction
1 mm
B
A
(c)
Weft Fiber Direction
A
B
1 mm
Figure 4. XCT images of a single laminate E-glass strut. (a) The 3D structure illustrates maximum fiber waviness at the point the zyarn tows contacts the weft fiber tows. Cross-sectional slices show the (b) warp and (c) weft fiber tows, respectively. The dotted lines
illustrate the epoxy surface location and the vertical bands A and B indicate planes for which tow misalignment data are presented.
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
Malcom et al.
7
Figure 5. Optical micrographs of the E-glass 3WeaveÕ composite. Both the horizontal warp tows (a) and horizontal weft tows
(b) exhibit waviness resulting from out-of-plane z-yarn compression. (c) Weft tow misalignment was greatest at the position of z-yarn
impingement. (d) The diameter of the E-glass fibers was 18 mm 4 mm for the approximately 2300 fibers within a weft tow.
transversely oriented tows. Weft tow waviness resulted
from the impingement of the z-yarn at contact points
with the weft tows. The warp tows were, in turn,
deflected by the misshaped weft fiber tows.
Rectangular-shaped resin-rich pockets were created in
regions where no fiber tows were placed or had laterally
slid out of alignment during manufacture, Figure 4(b)
and (c). Detailed analysis of the XCT images, Figure 4,
shows that parallel z-yarns are offset in their pseudosinusoidal profile by approximately 5.2 mm (the thickness of a weft tow), Figure 2, which creates a weft tow
misalignment that varies through the width of the strut.
Measurements of the warp and weft fiber tow misalignment at planes A and B were taken to obtain representative misalignment angle distributions through the
thickness and width of a strut. These results are presented and discussed below after presentation of optical
micrographs of the samples.
A series of optical micrographs of the E-glass
3WeaveÕ composite, Figure 5, provided a higher resolution characterization of the structure. To obtain optical micrographs, the composite samples were cut and
polished along planes parallel to the warp and weft
fiber tows using a similar procedure to that described
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
8
Journal of Composite Materials 0(0)
(a)
(b)
Warp Tow Misalignment - Position A
(c)
Warp Tow Misalignment - Position B
(d)
Weft Tow Misalignment - Position A
Weft Tow Misalignment - Position B
Figure 6. Initial fiber tow misalignment angles are measured for a single laminate E-glass composite strut. Warp fiber tow misalignment angles are provided for positions (a) adjacent to a ‘‘mid-weft’’ tow (Position A, Figure 4b) and (b) furthest position away from
the weft tow (Position B, Figure 4b). Weft fiber tow misalignment angles are provided for positions (c) adjacent to the z-yarn (Position
A, Figure 4c) and (d) ‘‘mid-warp’’ tow position (Position B, Figure 4c). These positions provide the relative extremes observed in the
fiber waviness along the length of the sample.
by Bartosiewicz and Mencik.26 Optical micrographs
were obtained using a Nikon Epishot inverted microscope equipped with a Nikon D-90 digital camera and a
Hirox KH-7700 digital microscope. The higher resolution micrographs confirm that both the warp and
weft fiber tows in the E-glass composites have significant local variations in fiber waviness. The micrographs
also confirm the presence of small resin pockets
between the impregnated tows as a consequence of
the fiber architecture. The fiber volume fraction
within a tow is therefore higher than that of the overall
composites fiber volume fraction. The maximum fiber
volume fraction of a single tow was measured to be
approximately 76%.
The initial average fiber misalignment angle varied
significantly as a function of position along the length
in both the warp and weft fiber tows. Figure 6 provides
a histogram of measured misalignment angles from the
XCT images along planes A and B for a single laminate
E-glass strut. The positions were chosen to represent
both the straight and wavy positions observed within
the fiber tows (Misalignment angles are defined by the
out plane component of the deflected fiber with respect
to either the warp or weft nominal fiber direction in the
laminate plane, Figure 2(a).). The warp fiber tows exhibit greatest fiber waviness along plane A where the slippage of the center weft fiber tow (ultimately from
z-yarn compressive loading) created a space into
which the warp fiber tows deformed and occupied.
Misalignment at Position A was observed to range
from –9.3 to 7.1 with an average misalignment of –
1.8 . Position B is straighter with measured
misalignment ranging from –1.9 to 5.3 with an average misalignment of 1.6 . The weft tow misalignment
was greatest at the point adjacent to the z-yarn loading
on the weft fiber tow with an observed range from –3.7
to 11.2 with an average misalignment of 1.5 for
Position A. Position B was well balanced with extremes
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
Malcom et al.
9
(a)
S2-Glass - 1 Laminate
Warp
z-yarn
W
ef
tF
ibe
r
Weft
2 mm
Warp F
ibe
r
(b)
Warp Fiber Direction
1 mm
B
A
(c)
A
Weft Fiber Direction
B
1 mm
Figure 7. XCT images of a single laminate S2-glass strut. (a) The 3D structure illustrates maximum warp and weft fiber tow waviness
near the point where the z-yarn tow contacts the weft fiber tows. Cross-sectional slices containing the (b) warp and (c) weft fiber
directions. The dotted lines illustrate the epoxy surface location and the vertical bands A and B indicate planes for which tow
misalignment data are presented.
ranging from –3.2 to 4.0 with an average misalignment of –0.3 .
XCT and optical images of the S2-glass fiber composite strut samples are shown in Figures 7 and 8,
respectively. The S2-glass fiber architecture was maintained in the intended configuration with the warp and
weft tows in vertical alignment throughout the structure, but the region of z-yarn impingement greatly
affected fiber waviness. A histogram of the measured
misalignment angles in a single laminate S2-glass strut
is shown in Figure 9. Measurements are taken along
planes A and B to represent both the extremes of
straight and wavy positions observed within the fiber
tows. The warp fiber tows exhibit greatest fiber waviness along plane A where the slippage of the center weft
fiber tow (ultimately from z-yarn compressive loading)
created a space into which the warp fiber tows
deformed and occupied. Misalignment at Position A
within the warp fiber tows is relatively straight and
observed to range from –2.5 to 2.4 with an average
misalignment of 0.2 . Position B exhibits greater waviness ranging from –10.5 to 14.9 misalignment with an
average of 1.5 . The weft tow misalignment was greatest at the point adjacent to the z-yarn loading on the
weft fiber tow with an observed range from –22.4 to
20.5 with an average misalignment of 1.6 for Position
A. Position B was well balanced with extremes ranging
from –3.0 to 7.0 with an average misalignment of
1.1 . A summary of the misalignment angles for both
E- and S2-glass composite struts is presented in Table 2.
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
10
Journal of Composite Materials 0(0)
Figure 8. Low magnification of optical micrographs of the S2-glass 3WeaveÕ composite illustrate the (a) z-yarn square weave binding
the weft fiber tows and (b) the misalignment of the horizontal weft tows resulting from the localized pressure applied by the binding zyarn. (c) Weft tow misalignment near a z-yarn contact point. (d) The diameter of the S2-glass fibers was 9 mm 1 mm for the
approximately 8000 fibers within a weft tow.
Composite strut mechanical response and
failure modes
The 3D woven composite struts were tested in both tension and compression in the weft tow direction. Tensile
tests conformed to ASTM D3039, with each test coupon
cut to a length of 250 mm and a width of 25.4 mm. Tabs
utilized for gripping were beveled at approximately 15
and epoxied to the gripping surfaces of the sample to
prevent coupon damage from the compressive loading
by the wedge action grips. Retro-reflective tabs were
mounted on each sample to measure strain within the
150 mm gauge length of the test coupons at a strain rate
of 10–3 s–1 at room temperature (25 C).
Tension. The measured tensile (Young’s) modulus and
tensile fracture strengths in the weft fiber direction are
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
Malcom et al.
11
(a)
(b)
Warp Tow Misalignment - Position B
Warp Tow Misalignment - Position A
(c)
(d)
Weft Tow Misalignment - Position A
Weft Tow Misalignment - Position B
Figure 9. Initial fiber tow misalignment angles are measured for a single laminate S2-glass composite strut. Warp fiber tow misalignment angles are provided for positions (a) adjacent to a ‘‘mid-weft’’ tow (Position A, Figure 7b) and (b) furthest position away from
the weft tow (Position B, Figure 7b). Weft fiber tow misalignment angles are provided for positions (c) adjacent to the z-yarn (Position
A, Figure 7c) and (d) ‘‘mid-warp’’ tow position (Position B, Figure 7c). These positions provide the relative extremes observed in the
fiber waviness along the length of the sample.
shown in Figure 10 as a function of fiber volume fraction. The Young’s modulus of the E-glass composite
samples varied from 12 to 17 GPa for fiber volume fractions of 30–54%, while the S2-glass struts varied from
16 to 19 GPa for fiber fractions of 40–52%, Figure
10(a). Within the scatter of the individual measurements, the modulus of both the E-glass and S2-glass
exhibited a linear dependence upon fiber fraction of
the strut. The tensile strength of the E-glass and S2glass composites also exhibited an approximately
linear relation with fiber volume fraction, but their
slopes were different, Figure 10(b). The average
strength of the E-glass composites varied from 210 to
425 MPa for fiber volume fractions of 30–54% while
the S2-glass composite strength increased from 405 to
650 MPa as the fiber fraction increased from 40 to 52%.
Compression. The compressive strength of the E- and
S2-glass composites was measured parallel to the weft
fiber tow direction. The panels tested in compression
used a combined loading compression (CLC) test fixture, and followed the procedure defined in ASTM
D6641. Test specimens were cut to a length of
152.4 mm parallel to the weft direction and tested
with a gage length of 25.4 mm. Typical stress–strain
responses for E-glass struts constructed from 1, 2,
and 3 laminates (nominal t/l ratios of 0.07, 0.12, and
0.18 respectively) with fiber fractions between 54 and
56%, are shown in Figure 11(a).
The elastic modulus of the E- and S2 composite
struts loaded in compression parallel to the weft direction is plotted against fiber volume fraction in Figure
12. The modulus for E-glass composite samples varied
from 15 to 23 GPa, as the fiber volume fraction was
increased from 35 to 60% while the S2-glass composite
samples modulus varied from 12 to 25 GPa for fiber
fractions ranging from 37 to 57%. The modulus of
typical E- and S2-glass strut samples are summarized
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
12
Journal of Composite Materials 0(0)
Table 2. Measured initial average fiber misalignment angles throughout the warp and weft tows in single laminate struts as measured
with XCT imaging corresponding to Figures 4 and 7 for E- and S2-glass, respectively.
Tow misalignment angle (degree)
Material
Tow type
Measurement position
Minimum
Maximum
Average
E-Glass
Warp
A
B
A
B
A
B
A
B
–9.3
–1.9
–3.7
–3.2
–2.5
–10.5
–22.4
–3.0
7.1
5.3
11.2
4.0
2.4
14.9
20.5
7.0
–1.8
1.6
1.5
–0.3
0.2
1.5
1.6
1.1
Weft
S2-Glass
Warp
Weft
(a)
E-Glass Prediction
S2-Glass Prediction
E-Glass Strut Measurement
S2-Glass Strut Measurement
E-Glass
Prediction
S2-Glass
Prediction
(b)
Strength Predictions
E-Glass Strut Measurement
S2-Glass Strut Measurement
S2-Glass
Composite
Measured Tow
Strength Prediction
Silane Coated
Fiber Prediction
E-Glass
Composite
Measured Tow
Strength Prediction
Figure 10. The fiber volume fraction dependence of (a) the
tensile modulus and (b) tensile strength for the E- and S2-glass
composites.
in Table 3 for fiber volume fraction uf & 35 and 55%.
The S2 fiber composite compressive modulus in the
weft fiber direction is practically indistinguishable
from its E-glass counterpart.
The E- and S2-glass composite compressive strength
in the weft fiber direction is plotted versus the struts
thickness to length ratio (t/l) for samples with fixed
uf ¼ 56% in Figure 13. For this fiber volume fraction,
the stubby struts failed by fiber microbuckling, Figure
11(b) and (c) while the most slender strut, Figure 11(d),
failed by elastic Euler buckling. The transition from
Euler to plastic fiber microbuckling was observed at a
thickness to length ratio, t/l, slightly above 0.07. Above
this value the thickness-to-length ratio shows no effect
on failure, with both E- and S2-glass samples failing via
microbuckling. The E-glass composite microbuckling
average failure strength was 225 MPa; almost identical
to that of the S2-glass composite (222 MPa) for samples
with uf & 56%.
The compressive strength data for the E- and S2glass laminates is summarized in Table 3 for low and
high fiber volume fraction samples. The failure
strengths of the E- and S2-glass fiber composite struts
that failed by microbuckling are plotted against fiber
volume fraction in Figure 14. It can be seen that for
both fiber types, the compressive strength is strongly
dependent on the fiber fraction but relatively independent of fiber type. The compressive strength for E-glass
varied from 90 to 300 MPa, as the fiber volume fraction
was increased from 35 to 60% while the S2-glass varied
from 120 to 220 MPa for fiber fractions ranging from
37 to 57%.
It was observed that neither the 3D woven E- nor
S2-glass fiber composite struts fail by either inter-ply
delamination or brooming. Instead, failure occurred
by either elastic buckling (t/l ¼ 0.07) or fiber microbuckling. When failure occurred by elastic buckling,
the structure was observed to reach a maximum
strength followed by lateral displacement associated
with macro-buckling reduced load capability. If the
axial displacement was reversed at this stage, the structure returned to its original length during unloading.
However, when the strain was increased significantly
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
Malcom et al.
13
(a)
Prediction
E-Glass Strut Measurement
S2-Glass Strut Measurement
t/l = 0.18
t/l = 0.12
S2-Glass Prediction
Ef = 82 GPa
t/l = 0.07
E-Glass Prediction
Ef = 74 GPa
Engineering Strain
(b)
(c)
(d)
Figure 12. Measured and predicted Young’s modulus verses
fiber volume for E- and S2-glass composite struts tested in
compression parallel to the weft fiber tows.
5 mm
Figure 11. (a) Compressive stress–strain response of the Eglass struts; (b) and (c) are examples of compressive fiber
microbuckling and (d) Euler elastic buckling failure of E-glass
struts loaded parallel to the weft tow direction with thickness to
length ratios of (b) 0.18 (5.25 mm), (c) 0.12 (3.5 mm), and (d) 0.07
(1.75 mm).
beyond the critical stress, localized fiber kinking and
matrix cracking occurred as secondary failure mechanisms. For samples that failed by fiber microbuckling,
permanent damage to the sample occurred at the critical load. A polished optical micrograph of a two-laminate E-glass strut (nf ¼ 55%, t/l ¼ 0.111) removed from
testing at its critical failure stress, scrit ¼ 198 MPa, is
shown in Figure 15. A double kink band had begun
to form in one of the weft tows at 35 to the loading
direction, Figure 15(a). At higher magnification, Figure
15(b), weft fiber kinking can be seen to be accompanied
by a shear displacement of the fibers in the warp tow.
Mechanical property predictions
While the XCT approach has been used in combination
with textile models to investigate the effects of variability in the yarn dimensions and spacing upon the elastic
moduli of 3DNCOW laminates,27–29 they did not
observe or address the significant warp and weft tow
waviness observed here. The tensile stiffness and
strength of 3D woven composites has also been previously modeled by Cox et al.11 using a simpler isostrain approach. Their model ignored the z-yarn fibers
and assumed the loading was parallel to the axial (weft)
fibers and perpendicular to the transverse (warp) fibers.
This upper-bound composite modulus, Ec, is given by
Ec ¼ Eweft A weft þ Ewarp 1 A weft
ð1Þ
where A weft is the area fraction of axial (weft) fibers in
the composite, Eweft is the modulus of the weft fiber
occupied area, and Ewarp is the modulus of the warp
fiber occupied area. Ignoring the z-yarn component
A weft can be calculated from the data provided in
Table 1 by assuming that the fiber fraction in the weft
and warp fiber occupied areas are equivalent to the
overall fiber fraction of the composite. This gives
A weft ¼ 0.498 or 0.519 for the E- and S2-glass composites, respectively (This assumption is supported by the
visual approximation that the fraction of all fibers in
the weft direction is equivalent to the fraction of the
area occupied by the weft tow laminates on a section
normal to the load axis (as compared with the warp
fibers and warp tow laminate area)). The modulus of
the weft fiber occupied region is given by
Eweft ¼ Ef f þ Em 1 f
ð2Þ
while the modulus of the warp fiber occupied area is
given by
1 f
f
¼
þ
Em
Ef
Ewarp
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
1
ð3Þ
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
14
Journal of Composite Materials 0(0)
Table 3. Typical strength and modulus parameters for the 3D woven E- and S2-glass fabric manufactured at low and high fiber
fractions.
Material
Number of laminates
vf (%)
t/l
sstrut (MPa)
Estrut (GPa)
E-glass
1
E-glass
2
E-glass
3
S2-glass
1
33
54
31
55
35
56
37
57
0.074
0.066
0.141
0.107
0.212
0.171
0.166
0.108
88
106
92
228
113
225
140
222
14.1
20.8
12.2
20.3
13.1
21.2
16.4
24.7
Microbuckling
Euler Buckling
Clamped Ends
K=0.5
Pin Jointed Ends
K=1
E-Glass Strut Data
S2-Glass Strut Data
Model Predictions
(vf = 56% only)
measured tensile modulus of the E-glass and S2-glass
fiber composites are within 10% of the predictions and
consistent with the arguments of Cox et al. that an
empirical knockdown parameter is needed to account
for fiber waviness effects.
The tensile strength of a composite loaded in the
weft tow direction, sc, can be estimated by assuming
the weft fibers and matrix are equally strained at failure. The warp and z-yarn fibers are assumed to have a
negligible effect in tension12 as the critical strength of a
high-strength fiber/epoxy system operating in series is
limited by the lower strength matrix. This leads to a
rule-of-mixtures predicted strength given by
c ¼ f fA þ m 1 fA
Figure 13. Measured and predicted compressive strength for
E- and S2-glass composite struts loaded parallel to the weft fiber
tows. At low ratios of t/l < 0.07 the struts failed by Euler (elastic)
buckling. As t/l increased, strut failure occurred by fiber
microbuckling.
where Ef is the modulus of the glass fiber, Em is the
modulus of the matrix, and f is the fiber fraction of
the composite.
However, 3D woven composites contain sufficient
fiber waviness to reduce the modulus under initial loading7. Provided that the modulus of the fiber is significantly higher than the matrix, and the matrix is
sufficiently compliant to preclude matrix failure
before the fiber tows straighten, the measured tensile
modulus will approach the predicted modulus as
wavy fiber tows straighten. While highly dependent
upon the materials and manufacture method of the
weave, Cox et al.11 predicted a 10–20% higher modulus
than experimental measurements for heavily compacted
samples of similar weave geometry.
Using the measured modulus of the E-glass and S2glass fibers (Materials Selection and Strut Fabrication:
Fibers and Fabrics), the predictions of equation (1) are
compared with experimental data in Figure 10(a). The
ð4Þ
where fA is the fiber fraction of only the axial (weft)
fibers in the composite, f is the fiber strength, and m is
the matrix strength. Tensile strength predictive bounds
for the composite is calculated using both the measured
fiber tow strength (lower bound) and theoretical ‘‘asmanufactured’’ silane-coated fiber strength (upper
bound) within equation (4) for both E and S2-glass
fiber composites and is plotted in Figure 10(b) for comparison with experimental data. The experimental data
for both composites falls close too, or between these
predicted bounds.
In compression, the modulus of a 3D woven composite is expected to be lower than a laminated unidirectional fiber composite due to the higher fiber waviness11
imparted by the z-yarn. The compressive modulus of
the weft laminates in a 3D woven composite loaded
parallel to the weft fiber direction can again be approximated by a rule-of-mixtures expression, equation (2).
Likewise, the transversely loaded warp tow laminates
can be predicted using a constant stress model prediction,3 equation (3), where the stress in both the fiber
and matrix is assumed equivalent. The overall elastic
modulus of the composite in compression would then
be given by equation (1) with an unknown knockdown
related to fiber waviness. Using the data presented in
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
Malcom et al.
15
Weft Tow Laminate Failure Prediction
Warp Tow Laminate Failure Prediction
E-Glass Strut Measurement
S2-Glass Strut Measurement
ф = 0.5˚
S2-Glass Prediction
E-Glass Prediction
ф = 1.5˚
ф = 2.5˚
ф = 5.0˚
Figure 14. Dependence of compressive strength upon fiber
volume fraction for E- and S2-glass composite struts with
t/l > 0.07 loaded parallel to the weft fiber tows. Failure of weft
tow laminates is dependent upon the fiber misalignment angle,’,
but independent of the fiber strength, while failure of the warp
tow laminates is dependent upon the fiber strength but independent of the fiber misalignment angle.
Table 1 together with the measured fiber and matrix
elastic modulus, the measured modulus values are in
moderate agreement with the predictions, Figure 12
with an empirical knockdown parameter up to 40%,
consistent with the observations of Cox et al.11
In compression, the failure mechanism is not material
yielding (as in tension), but rather buckling. Thin struts
are observed to fail initially by elastic (Euler) buckling, a
geometry-dependent failure mode. Struts tested with a
low aspect ratio (t/l ¼ 0.7) have strengths consistent with
the Euler buckling mode failure prediction.
Euler ¼
2 Ec t2
12K2 l
ð5Þ
where K is an end clamping condition dependent coefficient (K ¼ 1/2 for fully clamped ends, 1 for pin jointed
ends), and Ec is the elastic modulus of the composite
strut. As the thickness-to-length ratio was increased,
the failure transitioned from elastic buckling to plastic
microbuckling. Once in the microbuckling regime, the
strut geometry, at a fixed fiber volume fraction, had no
effect upon the compressive strength, Figure 13.
To predict the plastic microbuckling strength, the 3D
woven architecture can be approximated by a multilaminate system shown in Figure 16 with the weft fiber
tows in the (axial) loading direction and the warp fiber
tows (separated by resin pockets) in the transverse direction. In the warp fiber tow region, the critical failure
strength of the warp fiber laminates can be simply
taken to be the epoxy compressive strength. Strut failure
Figure 15. (a) Optical micrographs of an E-glass strut that
failed by microbuckling under compressive load. (b) Fiber fracture in weft tows and matrix shear in warp tows accompany the
double kink microbuckling mechanism.
was observed, Figure 15, to coincide with double kink
band initiation in the warp fiber tows, consistent with
other studies on 3D woven composites.30
Argon’s predicted plastic microbuckling fiber failure
stress8 can be used to predict the unidirectional composite failure strength
f ¼
m
ð6Þ
where is the fiber misalignment angle (in radians) and
m is the matrix shear strength. Fleck30 argues that a
rule-of-mixtures approach can be utilized with Argon’s
unidirectional composite microbuckling prediction to
predict the fiber volume fraction-dependent compressive strength of a unidirectional composite. The weft
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
16
Journal of Composite Materials 0(0)
Compressive loading
Epoxy
Resin
Pockets
occurs in the warp laminate, the compressive strength is
given by
33crit
Weft Tow Direction
Warp fiber
tows
33crit
Thickness direction
Figure 16. Illustration of the iso-strain loading diagram for the
micromechanical model of a single laminate 3D woven strut. The
micromechanical model assumes including equal tow spacing,
equal tow sizes, and the absence of the z-yarn.
laminate critical microbuckling strength would then be
given by
PL
AE
ð8Þ
where P is the applied force, A the laminate cross sectional area, L the laminate length, and E the Young’s
modulus of each laminate. By equating equation (8) for
each laminate, the force supported by the weft laminates can be found
Pweft
Aweft Eweft
¼ Pwarp
Awarp Ewarp
ð9Þ
The weft strength can then be written
weft ¼ warp Eweft
Ewarp
Awarp Ewarp
weftcritical Aweft
¼
1þ
Atotal
Aweft Eweft
ð10Þ
The critical compressive strength will be determined
by failure of either the warp or weft laminates. If failure
ð12Þ
With the assumption that the overall fiber volume
fraction is equivalent in both the warp and weft laminates, and assuming no porosity within the strut, the
area fraction will be equal to the weft and warp fiber
fractions, fweft and fwarp, within the 3D weave. The
directional fiber fractions are given by
fweft ¼
Aweft
Atotal
ð13Þ
fwarp ¼
Awarp
Atotal
ð14Þ
and
ð7Þ
where the weft fiber volume fraction is given by f and
m is the compressive strength of the matrix.
An iso-strain analysis of the model composite,
Figure 16, can then be used to determine the effective
compressive strength of the 3D woven composite. Since
the compressed warp and weft fiber laminates will be
elastically strained an identical amount, the displacements in the warp and weft laminates (weft and warp),
will be equal, and given by Hooke’s law
¼
ð11Þ
If failure occurs in the weft laminates first the critical
stress is
Weft fiber
tows
weftcritical ¼ f f þ m ð1 f Þ
m Awarp
Aweft Eweft
¼
1þ
Atotal
Awarp Ewarp
If we ignore the presence of the z-yarn, the warp and
weft directional fiber fractions are approximately 50%
for both E- and S2-glass, Table 1. Equations (11) and
(12) can be rewritten to give
0
33crit
1
Ef f þ Em 1 f
f
weft
A
¼ m fwarp @1 þ
f
ð1f Þ
fwarp
þ
Ef
ð15Þ
Em
and
33crit ¼ fweft f f þ m 1 f
0
1
f
ð1f Þ
þ
f
Ef
E
warp
m
A
@1 þ
fweft Ef f þ Em 1 f
ð16Þ
Equations (15) and (16) predict the overall critical failure of the strut when ply failure is initiated in either the
warp or weft laminates, respectively.
The predicted strength based upon weft and warp
tow initiated failure are shown in Figure 14. The weft
tow initiated failure strengths are shown for fiber misalignment angles ranging from 0.5 to 5 . The model
shows that failure can be initiated in either warp or weft
tow laminates. Failure within the weft tow laminates is
dependent upon the fiber misalignment angle, but independent of the fiber strength. Conversely, failure of the
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
Malcom et al.
17
warp tow laminates is dependent on the fiber strength
but independent of the fiber misalignment angle. The
model predicts that with an initial fiber misalignment
angle of 1.5 or greater, failure will be initiated in the
weft tow laminates. However, as the misalignment
angle is reduced, failure transitions to an initiation by
the warp tow laminates. If the overall initial average
fiber misalignment can be reduced to 0.5 , the model
predicts that for all fiber volume fractions, failure either
initiates within the warp tow laminate or occurs simultaneously with weft tow laminate failure. Comparison
with experimental data indicate that the average initial
fiber misalignment angle ranged from 1.5 to 2.5 and
failure always initiated in the weft tow laminates.
Discussion
By combining 3D woven fiber fabrics that utilize z-yarn
fibers to inhibit delamination with vacuum infusion of a
rubber toughened epoxy, a wide range of composite
struts have been fabricated with both the thicknessto-length ratio (t/l) and fiber volume fractions varied.
The 3D structure of the composites has been characterized and samples have been tested in tension and compression parallel to the weft fiber tow direction. The
moduli and strengths in tension and compression are
found to be well predicted by previously proposed
micromechanical models and thereby provide a linkage
between mechanical properties and fiber architecture.
The compressive strength of slender struts (t/l 0.07)
was governed by elastic buckling and therefore the critical elastic buckling strength is dependent upon the
struts aspect ratio, fiber volume fraction, and fiber
type. Stubby struts with aspect ratios that are sufficiently
low to avoid elastic buckling, fail by plastic microbuckling during compressive loading. This has been predicted
to be dependent upon the fiber misalignment angle,
matrix shear strength, and fiber volume fraction. The
matrix shear strength and fiber volume fractions were
measured for the struts tested in this study. Using
XCT images, the misalignment angles of the weft (axially loaded) tows in the 3D woven composites were
found to be widely distributed with maximum misalignment angles as high as 11.2 and 22.4 for E- and S2glass, respectively. While the maximum misalignment
angles measured in the fiber tows where significantly
higher than average values, fibers with the biggest misalignment angles were observed to be isolated, and infrequently measured within a composite sample.
The micromechanical model strength model developed in this study for axially loaded 3D woven composites, Figure 14, predicts failure with an effective
misalignment angle of 1.5 to 2.5 degrees. This suggests
that failure is not driven by a localized highly misaligned fiber tow, but rather by the much higher fraction
of tows with close to the average tow misalignment
angle. The XCT measurements (Figures 6 and 9) indicated that the (strength governing) axially loaded weft
tows had average tow misalignments of 1.5 and 1.6
degrees for the E- and S2-glass struts, respectively at the
positions of greatest waviness within the laminates (the
most likely location of failure). We therefore conclude
that the average tow misalignment governs the compressive strength in the struts investigated in this
study. Experimental results show that struts made
from E- or S2-glass fibers resulted in similar compressive strengths and were insensitive to the tensile
strength of the individual fibers, consistent with previous micromechanical models.6
At high fiber fractions (55% < nf < 60%), the microbuckling governed compressive strength of the struts
approached 225 MPa for both E- and S2-glass composite struts. At similarly high fiber fractions, the tensile
strength of E-glass composite was & 450 MPa while
that of the S2-glass fiber composite (made with stronger
fibers) was closer to 650 MPa. The strut tensile strength
in both fiber systems was therefore 2–3 times that measured in compression, because of the substantial fiber
misalignment present in the 3D woven composites.
In the center-loaded sandwich panel application
motivating the study, Figure 1, the core’s compression
resistance will be governed by collapse of the compressively loaded struts, since those placed in tension by the
bending deformation are equally stressed but have much
higher failure strength, as discussed above.31 While there
is a clear advantage to using higher strength fibers in
tensile loading situations (such as the face sheets)
where failure is governed by fiber fracture, the fiber
strength is much less important under compression loading where microbuckling dominates the response. In that
case, inexpensive E-glass fibers could be substituted for
more costly, high-strength S2-glass fibers while maintaining similar structural properties.
Finally, we note that while the use of z-yarns was
successful in eliminating the weak delamination
mechanism of compressive failure, this was achieved at
the cost of significant fiber misalignment, and therefore
reduced compressive strength. The development of an
improved 3D weave technique that reduced warp and
weft tow bending, and thus the average misalignment
angle near z-pinning crossings, could lead to substantial
improvements (a factor of 2–3) in the crush resistance of
sandwich panels of the type motivating this study.
Conclusions
The main conclusions from this study are as follows:
1. The bending of GFRP sandwich panels with corrugated cores results in both compressive and tensile
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
18
2.
3.
4.
5.
6.
Journal of Composite Materials 0(0)
stresses developed within the core struts. For out-ofplane panel displacements exceeding the panel thickness, the face sheets are placed in a state of tension.
The regions of the panel loaded in tension have a
strength and modulus that is directly controlled by
those of the fibers and matrix, the fiber volume fraction, and the fiber architecture. However, regions
subjected to compressive loads have a mechanical
response that is also sensitive to the fiber misalignment (within the microbuckling limit) and the delamination resistance of the strut.
The use of a 3DNCOW weaving approach was
found to successively eliminate the low strength delamination failure mechanism, but introduced significant fiber waviness in the warp and weft tows
through weave geometry limitations. This fiber waviness resulted in a substantial reduction in the compressive strength of this class of material.
Using high-resolution XCT and optical imaging, we
have conducted a detailed characterization of the
fiber architecture in 3DNCOW E- and S2-glass
fiber composites that were fabricated using a
vacuum-assisted resin transfer process. These characterization techniques have enabled the determination of the fiber misalignment angle distribution at
various regions, and within different tows of the
composite system.
Using previously proposed micromechanical models,
a simplified model has been assembled to predict the
tensile and compressive response of the laminates
and enabled the effects of fiber properties, the fiber
volume fractions assigned to the three tow types, and
the fiber misalignment angles in each tow type to be
predicted. Good agreement exists between the simplified model predictions and the experimental data
for the 3D weave composites investigated in this
study.
It was found that while the use of higher strength S2glass fibers increases the tensile failure strength of
3D woven composites, they offer no benefit when
used in compression because of the high fiber average misalignment angle. As a result, lower strength
(less costly) E-glass fibers are sufficient for manufacture in corrugated core struts that would only be
exposed to compressive loading.
Reduction of the misalignment angle in the E-glass
3D woven laminates has the potential to increase the
compressive strength of a corrugated core sandwich
structure by a factor of 2–3. If the misalignment
angle could be sufficiently reduced, it is possible
that tensile failure of the strut might become the
predominate failure mode if the core is placed in
bending. This condition would lead to a scenario
where higher tensile strength fibers would then
become advantageous.
7. Additional improvements in core properties might
be achieved by the use of unbalanced 3D laminates
in which a larger fraction of the fibers in a strut are
aligned in the direction of axial compressive loading.
Acknowledgements
We are grateful to Vikram Deshpande and Kumar
Dharmasena for their helpful discussions with this research.
Conflict of interest
None declared.
Funding
This work was supported by the Office of Naval Research
(ONR) under grant number N00014-07-1-0764 (Program
manager, Dr. David Shifler).
References
1. Gay D and Hoa SV. Composite materials: design and
applications, 2nd ed. Boca Raton, Fl: CRC Press, 2007.
2. Strong AB. Fundamentals of composites manufacturing:
materials, methods, and applications, 2nd ed. Dearborn,
MI: Society of Manufacturing Engineers, 2008.
3. Mortensen A. Concise encyclopedia of composite materials, 2nd ed. Oxford, UK: Elsevier, 2007.
4. Agarwal BD, Broutman LJ and Chandrashekhara K.
Analysis and performance of fiber composites, 3rd ed.
Hoboken, NJ: John Wiley & Sons, 2006.
5. Kaw AK. Mechanics of composite materials. Florida,
USA: Boca Raton, CRC Press, 1997.
6. Fleck NA. Compressive failure of fibre composites. Adv
Appl Mech 1997; 33: 43–119.
7. Tong L, et al. 3D fibre reinforced polymer composites. 22:
Elsevier, 2002.
8. Argon AS. Fracture of composites. Treatise Mater Sci
Technol 1972; 1: 79–114.
9. Mohamed MH and Bogdanovich AE. Comparative analysis of different 3D weaving processes, machines and
products. In: Proceedings of 17th international conference
on composite materials (ICCM-17), Edinburgh, UK July
27–31, 2009.
10. Bogdanovich AE and Mohamed MH. Three-dimensional
reinforcements for composites. SAMPE J 2009; 45: 8–28.
11. Cox BN, et al. Failure mechanisms of 3D woven composites in tension, compression, and bending. Acta
Metallurgica et Materialia 1994; 42: 3967–3984.
12. Cox BN, et al. On the tensile failure of 3D woven composites. Compos A 1996; 27A: 447–458.
13. Dharmasena K, Queheillalt D, Wadley H, et al. Dynamic
response of a multilayer prismatic structure to impulsive
loads incident from water. Int J Impact Eng 2009; 36:
632–643.
14. Wadley HNG, Dharmasena KP, O’Masta MR, et al.
Impact response of aluminum corrugated core sandwich
panels. Int J Impact Eng 2013; 62: 114–128.
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015
XML Template (2015)
[11.2.2015–12:27pm]
//blrnas3.glyph.com/cenpro/ApplicationFiles/Journals/SAGE/3B2/JCMJ/Vol00000/150006/APPFile/SG-JCMJ150006.3d
(JCM)
[1–19]
[PREPRINTER stage]
Malcom et al.
19
15. Wadley HNG, Borvik T, Olovsson L, et al. Deformation
and fracture of impulsively loaded sandwich panels.
J Mech Phys Solids 2013; 61: 674–699.
16. Malcom AJ, Aronson M, Deshpande VS, et al.
Compressive response of glass fiber composite sandwich
structures. Compos A Appl Sci Manuf 2013; 54: 88–97.
17. Russell BP, Malcom AJ, Wadley HNG, et al. Dynamic
compressive response of composite corrugated cores.
J Mech Mater Struct 2010; 5: 477–493.
18. Deshpande VS and Fleck NA. Collapse of truss core
sandwich beams in 3-point bending. Int J Solids Struct
2001; 38: 6275–6305.
19. Calladine CR. Understanding imperfection sensitivity in
the buckling of thin walled shells. Thin Walled Struct
1995; 23: 215–235.
20. Zenkert D. The handbook of sandwich construction.
Worcestershire, UK: EMAS Publishing, 1997.
21. Finnegan K, Kooistra G, Wadley HNG, et al. The compressive response of carbon fiber composite pyramidal
truss sandwich cores. Int J Mater Res 2007; 98: 1–12.
22. Russell B, Deshpande V and Wadley H. Quasi-static
deformation and failure modes of composite square honeycombs. J Mech Mater Struct 2008; 3(7): 1315–1340.
23. Pochiraju K and Chou TW. Three-dimensionally woven
and braided composites. II: an experimental characterization. Polymer Compos 1999; 20: 733–747.
24. Granta Design Limited. E-glass fiber information. CES
EduPack. 2011, Version 7.0.0.
25. Littell J, et al. Measurement of epoxy resin tension, compression, and shear stress-strain curves over a wide range
of strain rates using small test specimens. J Aerospace
Eng 2008; 21(Special Issue): 162–173.
26. Bartosiewicz L and Mencik Z. An etching technique to
reveal the supermolecular structure of crystalline polymers. J Polymer Sci 1974; 12: 1163–1175.
27. Desplentere F, Lomov SV, Woerdeman DL, et al. MicroCT characterization of variability in 3D textile architecture. Compos Sci Technol 2005; 65: 1920–1930.
28. Lomov SV, Bogdanovich AE, Dmitry SI, et al. A comparative study of tensile properties of non-crimp 3D
orthogonal weave and multi-layer plain weave e-glass
composites. Part 1: materials, methods and principal
results. Compos A 2009; 40: 1134–1143.
29. Lomov SV, Bogdanovich AE, Dmitry SI, et al.
Comparative study of tensile properties of non-crimp
3D orthogonal weave and multi-layer plain weave eglass composites. Part 2: comprehensive experimental
results. Compos A 2009; 40: 1144–1157.
30. Fleck NA, Jelf PM and Curtis PT. Compressive failure of
laminated and woven composites. J Compos Technol Res
1995; 17: 212–220.
31. Wang J, Evans AG, Dharmasena K, et al. On the
Performance of truss panels with Kagome cores. Int J
Solids Struct 2003; 40: 6981–6988.
Downloaded from jcm.sagepub.com at UNIV OF VIRGINIA on March 31, 2015