![Photograph of specimens after tensile tests, where A1-A3 are auxetic CFRP composite specimens (laminate layup: [15/65/15/65/15]) and C1-C3 are non-auxetic counterpart CFRP composite specimens (laminate layup: [35/60/-5/60/35]).](https://www.researchgate.net/profile/Yeqing-Wang-3/publication/363808567/figure/fig2/AS:11431281085999319@1664029781745/Photograph-of-specimens-after-tensile-tests-where-A1-A3-are-auxetic-CFRP-composite_Q320.jpg)
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Effect of Negative Poisson’s Ratio on the
Tensile Properties of Auxetic CFRP Composites
WENHUA LIN and YEQING WANG
ABSTRACT
Carbon fiber reinforced polymer (CFRP) matrix composites have become
increasingly popular across industries such as aerospace and automotive industries due
to its outstanding mechanical properties and significant weight saving capability. CFRP
composites are also widely known to be highly tailorable. For instance, different
laminate-level mechanical properties for CFRP composites can be achieved by varying
the individual carbon fiber laminar arrangements, among one of them is the Poisson’s
ratio. Conventional materials have a positive Poisson’s ratio (PPR), visualize any
conventional materials in a 2D block shape, when stretching that material in longitudinal
direction, contraction follows on the transverse direction, whereas for materials with a
negative Poisson’s ratio (NPR), stretching in the longitudinal direction leads to
expansion in the transverse direction. Materials with NPRs have been shown to improve
the indentation and impact resistances, when compared to equivalent materials with
PPRs. However, producing NPRs could potentially compromise other properties, such
as tensile properties, which has not been reported. The current work investigates the
effects of NPR on the tensile properties of CFRP composites. Specifically, a laminate-
level NPR of -0.4094 in the in-plane direction is achieved through ply arrangement of
CFRP composites using classical lamination theory (CLT). The non-auxetic counterpart
CFRP composites are designed to produce an PPR of 0.1598 in the in-plane direction
while simultaneously match their elastic moduli in three directions with those of the
auxetic composites. Results show that the predicted tensile modulus and in-plane
Poisson’s ratio were in excellent agreement with the experiment results. It was found
that the ultimate tensile strength and failure strain or ductility of auxetic specimens were
on average 40% lower than those of the conventional CFRP composites.
_____________
Wenhua Lin, PhD student, Department of Mechanical & Aerospace Engineering, Syracuse
University, Syracuse, NY 13244
Yeqing Wang (corresponding author, email: ywang261@syr.edu), Assistant Professor,
Department of Mechanical & Aerospace Engineering, Syracuse University, Syracuse, NY 13244
INTRODUCTION
Carbon fiber reinforced polymer (CFRP) matrix composites have become
increasingly popular across industries such as in aerospace, automotive, energy, marine,
civil infrastructure, and high-end sports for their high specific mechanical properties and
excellent fatigue and corrosion resistances. These properties translate to significant
weight savings when compared to conventional metallic materials, such as aluminum.
While having superior mechanical performance than conventional metals, CFRP
composites are susceptible to various impact damages, such as tool drop impact, hail
impact, ballistic impact, and bird strike during their service life. These impacts could
lead to various extents of damage modes, such as delamination, matrix cracking, fiber
breakage, and penetration, which results in significant degradations in mechanical
performances of CFRP [1-4]. One solution to mitigate impact damages, especially low
velocity impact damage, for CFRP is to introduce auxeticity or negative Poisson’s ratio
into the CFRP structure [5-9].
Auxeticity can be introduced into CFRP structures by i) introducing auxetic
inclusions or using auxetic matrix and ii) stacking a specific ply arrangement of
individual anisotropic lamina. For instance, Li and Wang investigated the effects of
auxetic and non-auxetic core materials on the bending behavior of sandwich
composites. A negative Poisson’s ratio of -1.732 was reported for the sandwich
composite with re-entrant honeycomb core [10]. Gunaydin et al. [11] investigated the
energy absorption characteristics of chiral auxetic lattices filled cylindrical composite
tubes under uniaxial and lateral compression. It was found that the chiral auxetic lattices
inserts improved the specific energy absorption by 360% due to the triggered auxetic
deformation. Auxeticity can also be produced by stacking a specific ply arrangement of
individual anisotropic lamina. A well-validated procedure was proposed by Sun and Li
where laminate-level effective moduli, shear moduli, and in-plane and out-of-plane
Poisson’s ratios can be determined according to the Classical Lamination Theory (CLT)
[12]. For instance, researchers have produced laminate-level (or effective) negative
Poisson’s ratios in the in-plane direction (𝜈
) and in the through-thickness direction
(𝜈
) through tuning the layups of the anisotropic layered carbon fiber reinforced
polymer (CFRP) matrix composites [13]. In this study, we focus on auxetic CFRP
structures produced by the latter method, i.e., stacking individual anisotropic lamina
using a specific layup.
Many studies have reported the enhancement of indentation and impact resistances
of auxetic structures, when compared to their non-auxetic counterparts [5-9]. For
example, researchers from the University of Bolton (UK) used IM7/5882 carbon fiber
reinforced epoxy resin prepregs and produced a negative in-plane Poisson’s ratio (i.e.,
𝜈
) of -0.134 with a layup of [±30]6s and a negative through-thickness Poisson’s ratio
(i.e., 𝜈
) of -0.156 with a layup of [0/15/75/15]s [14]. Experimental results of quasi-
static indentation and low velocity impact tests showed consistently a much smaller
damage area (i.e., delamination and fiber breakage) in auxetic composites when
compared to non-auxetic composite laminates with matched stiffnesses. Under an
impact energy of 18 J, the extent of the damage showed a reduction of 27%.
Despite the many studies conducted to investigate the indentation and impact
resistance enhancements for auxetic CFRP composites, effects of negative Poisson’s
ratio on other mechanical properties, such as tensile strength of CFRP composites are
yet to be explored as the imparted negative Poisson’s ratios could lead to adverse effects
to tensile strength, which is the most advantageous characteristics of CFRP structures.
In the current study, we designed CFRP composites with in-plane negative Poisson’s
ratio and matched non-auxetic counterpart CFRP composites with in-plane positive
Poisson’s ratio while ensuring close agreement of the three laminate-level effective
moduli. Tensile tests were performed to determine the experimentally measured in-
plane Poisson’s ratio and tensile modulus and evaluate effects of negative Poisson’s
ratio on the ultimate tensile strength and the failure strain.
LAMINATE-LEVEL EFFECTIVE CONSTANTS
Effective In-Plane Poisson’s Ratio
Given the transversely isotropic nature of the individual unidirectional lamina,
varying lamina stacking sequence of a CFRP laminate could lead to different laminate-
level mechanical properties and the laminate-level in-plane Poisson’s ratio is of interest
of the current study. The laminate-level in-plane effective Poisson’s ratio, 𝜈
, can be
obtained based on the Classical Lamination Theory (CLT),
𝜈
=
(1)
𝜈
=
(2)
where 𝐽, 𝐽, and 𝐽 are elements of the J matrix,
𝐽 = 𝐴 + 𝐴𝐵(𝐷 − 𝐵𝐴𝐵)𝐵𝐴 (3)
where A, B, and D are the extensional stiffness matrix, extensional-bending coupling
matrix, and bending stiffness matrix according to the CLT. Detailed derivation can be
found in author’s previous works in [15,16] and Sun and Li [12].
After obtaining the above expressions, a MATLAB code was developed to identify
the layup sequences that will produce in-plane negative Poisson’s ratio. A final layup
sequence consists of five plies of orientation [15/65/15/65/15] was chosen, which
produces an in-plane Poisson’s ratio of -0.4094.
Effective Moduli
Note that by varying the layup sequence to produce the desired in-plane Poisson’s
ratio, other mechanical properties are affected at the same time. To effectively
investigate the effects of Poisson’s ratio on the tensile properties of CFRP composites
alone, it is important to minimize effects from other apparent mechanical properties,
such as effective moduli in the longitudinal 𝐸
, transverse 𝐸
and out-of-plane
directions 𝐸
. The three laminate-level effective moduli can be calculated using the
Table I. Ply-level engineering constants of an IM7/977-3 CFRP composite lamina [17].
Elastic moduli (GPa)
𝐸
= 159,
𝐸
=
𝐸
= 9.2,
𝐺
=
𝐺
= 4.37,
𝐺
= 2.57
Poisson’s ratio
𝜈
=
𝜈
= 0.253,
𝜈
= 0.456
Table II. Laminate-level effective constants of auxetic and conventional non-auxetic
IM7/977-3 CFRP composite laminates.
Auxetic CFRP composite Non-auxetic counterpart CFRP
composite
Layup sequence
[15/65/15/65/15]
[35/60/
-
5/60/35]
𝜈
-0.4094 0.1598
𝜈
0.6302 0.3629
𝐸
(GPa)
51.2869 51.2935 (+0.0129%)
𝐸
(GPa)
25.5294 21.0296 (-17.626%)
𝐸
(GPa)
9.9504 10.2613 (+3.125%)
well-validated method proposed by Sun and Li, the detailed formulations can be found
in Ref. [12]. A MATLAB code was developed to calculate the effective moduli of the
specified layup sequence and to identify the layup sequence that could closely match
the three effective moduli and at the same time producing a positive Poisson’s ratio as
counterpart for the auxetic CFRP composite. Table I shows the ply-level engineering
constants of the IM7/977-3 carbon fiber composite lamina (i.e., the specific composite
considered in this study, see the Materials and Specimens Section) that are used to
calculate the effective constants. Table II shows the calculated results of the laminate-
level effective constants for both the CFRP composite and the conventional CFRP
composite. The layup of the conventional non-auxetic CFRP composite is [35/60/-
5/60/35]. In Table II, it can be seen that the longitudinal 𝐸
and out-of-plane 𝐸
effective moduli could be closely matched with percentage errors of 0.0129% and
3.125%, respectively, whereas the transverse effective modulus had the highest percent
error of 17.626%, as it is impossible to match 100% all three effective moduli. Given
the primary focus of tensile properties of this study, matching the longitudinal moduli
was given the higher priority when selecting the layup sequence.
EXPERIMENTAL SETUP
Materials and Specimens
The CFRP composite specimens used in the current study were manufactured with
unidirectional IM7/977-3 carbon fiber prepregs. Following the recommended cure
cycle, a 304.8 mm by 304.8 mm CFRP plate was fabricated using the layup orientation
of [15/65/15/65/15] for auxetic specimens and [35/60/-5/60/35] for conventional
specimens, each having five plies and a final thickness of 0.65 mm. After curing, the
fabricated CFRP plates were trimmed to a dimension of 254 mm by 254 mm. Then, a
254 mm by 25.4 mm region was prepared on both front and back surfaces of the CFRP
plates and on both top and bottom sides according to ASTM D2093 standard [18] and
to be bonded with four 254 mm by 25.4 mm glass fiber tabs using HYSOL EA 9309NA
adhesive. The purpose of using the bonded tabs was to avoid damage by the grips during
tensile tests given the small thickness of specimens. The CFRP plates with bonded tabs
Figure 1. Tensile test grip with loaded specimen prior to testing.
were then cut with a width of 25.4 mm to produce individual specimens which was 254
mm long by 25.4 mm wide and 0.65 mm thick, with four 25.4 mm by 25.4 mm glass
fibers tabs on the two ends of both surfaces, making the gage section of the specimens
with a dimension of 203.2 mm long by 25.4 mm wide as specified in ASTM D3039
standard [19].
Tensile Test Setup
The tensile tests were carried out according to the ASTM D3039 standard [19] on
an MTS testing system with a 100 kN capacity load cell calibrated at 20 kN load, with
a self-tightening tensile grip. The tests were displacement controlled with a
displacement rate of 1.3 mm/min. To measure the laminate-level Poisson’s ratio, two
strain gages were used for each tested specimen, where one strain gage was positioned
vertically on the front surface to measure the longitudinal strain and the other was placed
horizontally on the back surface to measure the transverse strain, both at the center of
the gage section, as shown in Fig. 1.
RESULTS AND DISCUSSION
Tensile Test Results
Figure 2 shows the photograph of all tested specimens, where A denotes the auxetic
specimen group and C denotes the counterpart conventional specimen group. It can be
seen that both groups have specimen failure towards the end of the gage section instead
of at the center and both specimen groups failed predominantly with matrix cracking at
the surface plies, at 15° orientation for auxetic specimens and 35° orientation for
conventional specimens, along with fiber breakage at embedded plies.
Optical microscopy images of specimens A3 and C3 shown in Figs. 3 and 4 give a
better representation of the failure mechanisms. For auxetic specimen A3, clean matrix
cracking along the 15° surface plies can be observed. The embedded 65° plies also failed
by matrix cracking along with fiber breakage at the exposed edges where the 15° plies
failed. Whereas for conventional specimen C3, both the 35° surface plies and embedded
plies with 60° and -5° orientation failed with both matrix cracking and fiber breakage.
In the microscopy images of the cross section of the tip regions of specimens A3 and
C3, delamination between the surface and adjacent plies can be observed in specimen
A3. This could be caused by the combined effect of negative Poisson’s ratio in the in-
plane direction and higher Poisson’s ratio in the out-of-plane
Figure 2. Photograph of specimens after tensile tests, where A1-A3 are auxetic CFRP composite
specimens (laminate layup: [15/65/15/65/15]) and C1-C3 are non-auxetic counterpart CFRP composite
specimens (laminate layup: [35/60/-5/60/35]).
Figure 3. Optical microscopy of auxetic CFRP composite specimen A3 (laminate layup:
[15/65/15/65/15], 𝜈
= -0.3901, 𝐸
=50.92 GPa, see Table III below).
Figure 4. Optical microscopy of conventional non-auxetic counterpart CFRP composite specimen C3
(laminate layup: [35/60/-5/60/35], 𝜈
= 0.1441,
𝐸
=54.44 GPa, see Table III below).
Table III. Experimental and predicted mechanical properties of auxetic (i.e., A1-A3) and non-auxetic
(i.e., C1-C3) CFRP composite specimens.
Specimen
#
Tensile
Modulus
Predicted
(GPa)
Tensile
Modulus
Measured
(GPa)
Poisson’s
Ratio
Predicted
Poisson’s
Ratio
Measured
Ultimate
Tensile
Strength
Measured
(MPa)
Failure
Strain
Measured
(mm/mm)
A1
51.2869
50.45
-0.4094
-
0.4055
323.31
0.00651
A2
50.93
-
0.4189
317.62
0.00633
A3
50.92
-
0.3901
278.31
0.00553
Average — 50.75
(± 5.67)
— -0.4048
(± 0.0144)
— —
C1
51.2935
54.30
0.1598
0.1283
558.36
0.01032
C2
55.56
0.1286
576.02
0.01048
C3
54.44
0.1441
567.72
0.01039
Average — 54.79
(± 5.43)
— 0.1337
(± 0.009)
— —
direction of auxetic specimen than conventional specimen. With the layup sequence of
[15/65/15/65/15] for auxetic specimen, the in-plane Poisson’s ratio (𝜈
) is -0.4094 and
the out-of-plane Poisson’s ratio (𝜈
) is 0.6302, in comparison with the in-plane
Poisson’s ratio (𝜈
) of 0.1598 and out-of-plane Poisson’s ratio (𝜈
) of 0.3629 of
conventional specimen with layup sequence of [35/60/-5/60/35]. The combined effect
of negative Poisson’s ratio in the in-plane direction and higher Poisson’s ratio in the out-
of-plane direction of auxetic specimen indicates that during tensile loading, the in-plane
direction is expanding in both longitudinal and transverse direction while the thickness
direction is contracting and could lead to even greater extent of strain mismatch than
conventional specimens, thereby causing the delamination.
Figure 5. Stress vs. Strain curves for all tested specimens, where A1-A3 are auxetic CFRP composite
specimens (laminate layup: [15/65/15/65/15]) and C1-C3 are non-auxetic counterpart CFRP composite
specimens (laminate layup: [35/60/-5/60/35]).
0.000 0.002 0.004 0.006 0.008 0.010 0.012
0
100
200
300
400
500
600
Stress (MPa)
Strain (mm/mm)
A1
A2
A3
C1
C2
C3
Figure 5 shows the stress vs. strain curves for all the tested specimens, it can be
observed that all specimens exhibit a brittle failure where the stress vs. strain curves for
all specimens increased linearly up to the failure point and immediately dropped to zero
beyond the failure point. Table III shows the predicted and experimental mechanical
properties data for the auxetic and conventional specimens, the tensile modulus is
calculated by finding the slope of the stress vs. strain curves and the Poisson’s ratio is
calculated by finding the slope between the transverse strain vs. longitudinal strain
curves for each specimen. The overall tensile modulus was found to be 50.75 GPa with
a standard deviation of 5.67 GPa for auxetic specimens and 54.79 GPa with a standard
deviation of 5.43 GPa for conventional specimens. The average in-plane Poisson’s ratio
was found to be -0.4048 with a standard deviation of 0.0144 for auxetic specimens and
0.1337 with a standard deviation of 0.009 for conventional specimens. Note that the
predicted and measured tensile modulus are in excellent agreement where the predicted
tensile modulus is 51.2869 GPa for auxetic specimens and 51.2935 GPa for
conventional specimens, which have a percent difference of 1.05% and 6.82% from the
measured values, respectively.
Even though both layup sequences had similar tensile modulus, the failure strain
and ultimate tensile strength of the auxetic specimens on average were only around 60%
of those of the conventional specimens, where the average failure strain for conventional
specimen was around 1.04%. Note that IM7/977-3 lamina (i.e., a single ply of IM7/977-
3, not the laminate) was reported to have a tensile failure strain of 1.61% [20]. The lower
ultimate tensile strength and failure strain could also be due to the combined effect of
negative Poisson’s ratio in the in-plane direction and higher Poisson’s ratio in the out-
of-plane direction of auxetic specimen where the strain mismatch in the in-plane and
out-of-plane directions caused premature delamination and impaired the interface
bonding strength between plies causing the lower ultimate tensile strength and failure
strain of the auxetic specimens.
CONCLUSION
Auxetic structures were shown to improve the indentation and impact resistances in
existing studies. However, producing auxeticity could potentially compromise other
properties, such as the tensile properties. The current study investigated the effect of in-
plane negative Poisson’s ratio on the tensile properties of CFRP composites by
designing layup sequence that would produce in-plane negative Poisson’s ratio (𝜈
=
-0.4094) and then matching counterpart conventional laminates with in-plane positive
Poisson’s ratio (𝜈
= 0.1598) while matching the three laminate-level effective moduli
between the auxetic and conventional laminates. Tensile tests were conducted to
evaluate the tensile performance of auxetic and conventional non-auxetic specimens
followed by photography and optical microscopy to document the failure mechanisms
exhibited.
It was found that both auxetic and conventional specimen groups failed in a brittle
manner where the stress vs. strain curves increased linearly up to failure point and
immediately dropped to zero beyond the yield point. The tensile modulus and the in-
plane Poisson’s ratio were found to be in excellent agreement with the predicted values.
However, the ultimate tensile strength and failure strain or ductility of the auxetic
specimens were found to be 40% on average lower than those of the conventional
specimens which could be attributed to the combined effect of negative Poisson’s ratio
in the in-plane direction and higher Poisson’s ratio in the out-of-plane direction of
auxetic specimen where the greater strain mismatch in the in-plane and out-of-plane
directions led to premature failure.
This study suggests that considerations need to be given when designing CFRP
structures with negative Poisson’s ratio by weighing the desired properties of improved
impact resistance and lowered tensile strength. In the future work, we will continue by
obtaining the delamination and impact resistances of the two proposed layup sequences.
A new auxetic layup sequence will also be investigated which will have good agreement
of laminate-level effective moduli with the current layup schedules, but with a lower in-
plane negative Poisson’s ratio to further investigate the effect of varying the in-plane
negative Poisson’s ratios on the ultimate tensile strength and ductility of CFRP
composites.
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