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High Buckling Strength of Auxetic Carbon
Fiber Composite Laminates
ANTHONY TRICARICO, WENHUA LIN and YEQING WANG
ABSTRACT
This research focused on testing the effect of the negative Poisson’s ratio of a
carbon fiber composite on its critical buckling load. A secondary goal was to
determine the accuracy of simulation compared to the experimental results for carbon
fiber composites. In order to accomplish these two goals, both simulation and
experimental testing were employed. For the simulation, ABAQUS software was
used to determine predicted values for the critical buckling loads of auxetic and non-
auxetic composites as well as the respective nonlinear force behavior of these
composites. These results were then compared to experimental results of four auxetic
and four non-auxetic specimens each experiencing uniaxial compressive tests. The
results of simulation and experimentation showed that the critical buckling loads, and
force sustained in general, of the auxetic composites were about three times higher
than those of non-auxetic composites. While it appears that the negative Poisson’s
ratio has a significant impact on the buckling strength of composite materials, further
testing is required to determine the effects of other factors on the critical buckling
loads. Along with this, the simulation was more accurate for the auxetic composites
than for the non-auxetic composites. Therefore, further testing and simulation are
required to determine the limits of simulation accuracy for composite structures.
Anthony Tricarico, Master student, Department of Mechanical & Aerospace Engineering,
Syracuse University, Syracuse, NY 13244
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 composites have been increasingly used in recent decades to build
structures due to their light weight, high specific strength, and high specific stiffness
compared to conventional materials such as metals [1-3]. These characteristics are an
important consideration for uses in aerospace, wind energy, civil infrastructure,
marine, and high-end sport structures [2-10]. In these applications, the strength of the
composites must be comparable to metals to justify the substitution. Therefore, a goal
for the future of composites is to continue to increase their strength without
compromising their weight-saving benefits. The strength of fiber reinforced
composite materials can be tested by different failure methods [11-16]. One type of
failure that has been rarely tested for composites is the Euler buckling strength of
which Euler buckling occurs when the compressive load on a structure causes out of
plane deformation.
Poisson’s ratio is a material characteristic that affects the Euler buckling behavior
of composites. It is the negative ratio of the change in transverse strain to the change
in axial strain. Most materials are non-auxetic which means that they have a positive
Poisson’s ratio [17]. Theoretically, this means that as the material is compressed
transversely, it expands axially and vice versa [17]. On the other hand, there are fewer
natural materials which possess a negative Poisson’s ratio. They are called auxetic
materials. Theoretically, this means that their axial and transverse strain have a direct
relationship, they either both increase or both decrease [17]. This unique behavior
may suggest that the material could locally flow into the buckling site to enhance the
buckling strength. Therefore, it is expected that the buckling strength of composites
can be increased by designing composites using an auxetic layup vs. an equivalent
traditional non-auxetic layup. This means that changing a carbon fiber composite
from non-auxetic to auxetic should theoretically increase its critical buckling load
while having no significant impact on the weight. In this study, auxetic laminates
were manufactured by using specific layup sequences identified, the non-auxetic
counterparts were designed with layups that would allow them to produce identical
effective modulus in the three principal directions with that of the auxetic specimens.
This will isolate the coupling effect between the stiffness and the negative Poisson’s
ratio [18-21].
Another advancement in engineering is the use of simulation software in the
design process. Whereas in the past, the design process consisted of designing,
manufacturing, testing, and editing, now, simulation eliminates the need for
manufacturing and experimental testing which results in a faster and more efficient
design process [22]. For carbon fiber composites in particular, this speeds up the
process by eliminating the fabrication periods before testing that require long time
periods. As a result, simulation in the field of composite structures can play an
important role in creating a more efficient design process.
EXPERIMENTAL SETUP
Materials and Specimens:
Similar to our previous study [23], the CFRP composite specimens used in this
study were manufactured with unidirectional IM7/977-3 carbon fiber prepregs by
Table I. Comparison of predicted and measured Poisson’s ratio and Young’s modulus of auxetic and
non-auxetic laminates.
Auxetic Laminate
[15/65/15/65/15]
Non-auxetic Laminate
[35/60/-5/60/35]
Predicted Poisson’s ratio
-0.41
0.16
Measured Poisson’s ratio
-0.41 ± 0.012
0.16 ± 0.005
Predicted Young’s modulus (GPa)
51.29
51.29
Measured Young’s modulus (GPa)
52.14 ± 0.896
52.12 ± 0.774
following the recommended cure cycle. Using a layup orientation of
[15/65/15/65/15] for the auxetic specimens and [35/60/-5/60/35] for the non-auxetic
specimens, two 304.8 mm by 304.8 mm auxetic and non-auxetic CFRP plates were
fabricated, respectively. After curing, four specimens with dimensions of 30 mm
wide by 139.7 mm long, and a final thickness of 0.7 mm, were cut from the respective
auxetic and non-auxetic laminates for the uniaxial compressive tests.
Table I shows the comparison between the predicted and measured Poisson’s
ratio and Young’s modulus of auxetic and non-auxetic laminates. In the current study,
the predicted in-plane Poisson’s ratio for the auxetic laminate with a layup of
[15/65/15/65/15] is -0.41, and for the non-auxetic laminate with a layup of [35/60/-
5/60/35] is 0.16. As can be seen, the predicted and measured Poisson’s ratio and
Young’s modulus are in good agreement with each other. Note that the layup of the
non-auxetic laminate is specifically chosen to produce the same Young’s modulus
with the auxetic laminate. By doing so will allow us to investigate only the effect of
Poisson’s ratio on the critical buckling loads of composite laminates by avoiding
differences in the respective Young’s modulus.
Figure 1. Schematic of the composite specimen using shell model in ABAQUS
[15/65/15/65/15] for the auxetic model and [35/60/-5/60/35] for the non-auxetic model.
139.7 mm
30 mm
Fixed BC
Fixed BC
Except Y
Applied Traction
Simulation Setup:
The research in this discipline consisted of two separate procedures to compare the
critical buckling loads of auxetic and non-auxetic carbon fiber composites. For the
simulation, the finite element analysis software ABAQUS was employed. Prior to
running the simulation, models were developed in the ABAQUS software for the
auxetic and non-auxetic composite beams that were made for the experimental tests,
as shown in Fig. 1. The model started out as a rectangular shell model with the same
length and width as the testing specimens, i.e., 139.7 mm by 30 mm. Next, the elastic
material properties of the IM7/977-3 unidirectional prepreg were assigned. Finally,
using that material, a conventional shell composite layup was employed with 5 layers
of the composite material each with a thickness of 0.14 mm and with layups of
[15/65/15/65/15] for the auxetic model and [35/60/-5/60/35] for the non-auxetic
model.
The first procedure is a simulation of the computational model to determine the
theoretical results. First, a step is added for a linear perturbation procedure type of
“Buckle”. For this step, the number of eigenvalues requested was 5, the vectors used
per iteration is 10, and the maximum number of iterations was 300. Next, the
boundary conditions were applied as depicted in Fig. 1. At the bottom edge, a fixed
boundary condition is applied with no linear movement or rotation in any direction.
At the top edge, the model was allowed to move in the y-direction, but movement
was fixed in all other linear directions and in all rotational directions. Lastly, at the
top edge, a compressive shell edge load was applied with a uniform distribution and
a magnitude of 1. After this, a uniform mesh was applied to the model with a global
size of 2 mm2. Finally, a job was created to compile the results. Note that up to this
point, the model only represented the results for linear buckling.
For nonlinear buckling behavior, the created model was modified by editing the
keywords in the input file to include the imperfections in the subsequent nonlinear
model. Next, the simulation step was changed to a general procedure type of “Static,
Riks”. For incrementation, the maximum number of increments was 100, the arc
length increment had an initial value of 0.01, a minimum of 1e-5, and a maximum of
1e36, and the estimated total arc length was 1. Due to the change of simulation step,
the boundary conditions and loads needed to be reapplied to the second model, with
the only change being that the magnitude of the load is now equal to the value of the
eigenvalue from the linear buckling results. After this, a second job was created for
the nonlinear buckling model. Following this, the keywords for the second model
were also modified to include an imperfection for the nonlinear model. Now the job
can be run for nonlinear results. This process was done for both the auxetic and non-
auxetic composite structures.
Uniaxial Compressive Test Setup:
The setup for the experimental test required a universal testing machine to apply
the load and a fixture to be attached to the testing machine to impose the boundary
conditions. Fig. 2 shows the uniaxial compressive test setup. The in-house fixture
consists of two steel rectangular base pieces each with two sliders on one face that
can be adjusted by tightening or loosening the two bolts inserted through each slider
Figure 2. Uniaxial compressive buckling testing setup.
into the base, this allows accommodation for testing specimens with various
thickness if desired.
For the experimental tests, first, the bases of the fixtures were attached to the top
press and bottom cylinder of the testing machine. Next, the crosshead was lowered,
and the sliders were put in place loosely, allowing the beam to be inserted between
the top and bottom slider, and then the sliders were tightened around the beam so that
the beam cannot move forwards, backwards, or to the side. This represents the fixed
boundary conditions on the top and bottom edges. The compressive tests were
performed with displacement control with a rate of 1 mm/min and were performed
on four specimens each for both auxetic and non-auxetic specimens.
Figure 3. Predicted buckling shapes for (a) auxetic and (b) non-auxetic composites from FEA
simulation.
(a)
(b)
Table II. Comparison of critical buckling loads between simulated and experimental results.
Specimen Type
Simulation (N)
Experimental (N)
(average)
Percent Error (%)
Auxetic
127.33
116.37
8.61
Non-Auxetic
43.84
37.84
13.69
Figure 4. (a) Auxetic and (b) non-auxetic composites after uniaxial compressive buckling testing.
RESULTS AND DISCUSSION
From the FEA simulation, the predicted buckling shapes for the auxetic and non-
auxetic specimens were found to be similar to each other, as shown in Figs. 3(a) and
3(b) which are the contour plots for the unified out-of-plane displacement for the
auxetic and non-auxetic models, respectively. The critical buckling loads calculated
are shown in Table II. The critical buckling load for the auxetic specimen was found
to be 127.3 N which was approximately three times higher than the non-auxetic
specimen, with a critical buckling load of 43.8 N.
From the uniaxial compressive tests, the main failure for the composite specimens
after experimental tests occurred at the edges of the sliders where the composites met
the fixture at both the top and bottom as shown in Figs. 4(a) and 4(b), this could be
due to the extended amount of displacement applied during loading. In addition to
the physical change in shape and damage, the critical buckling loads were also
determined. The experimental critical buckling load for each specimen was found by
finding the point of interaction for the stable loading path and the post buckling
equilibrium path from the Load vs. Displacement curves generated during the tests.
The critical buckling loads from the experimental tests are presented also in Table II.
For the experimental tests, the average critical buckling load of the four tests for the
auxetic specimens was 116.37 N while the average for the non-auxetic specimens
was 37.84 N.
For the graphs of Load vs. Displacement, the FEA simulations of both the auxetic
and non-auxetic have steep slopes to their respective critical buckling loads, after this
point, the forces increase much slower as the vertical displacement increases, as
displayed in Fig. 5. For the experimental test results for the auxetic specimens,
(a)
(b)
specimens 1 and 4 increased steeply then both increased much slower until they
flattened out as the vertical displacement increased with specimen 1 stalling just
above 120 N and specimen 4 stalling just above 100 N. Specimens 2 and 3 increased
to much higher values, then their forces increased much slower as the vertical
displacement increased until the force for specimen 2 flattened out around 120 N and
the force for specimen 3 flattened out above 120 N. These results are presented in
Fig. 6. For the experimental test results for the non-auxetic specimens, the forces for
all 4 specimens increased steeply. As the vertical displacement increased, the forces
for all specimens increased slowly and then samples 1, 2, and 4 flattened out around
35 N while sample 3 flatted out around 30 N. These results are presented in Fig. 7.
Figure 5. Simulation Load vs. Displacement results for auxetic and non-auxetic specimens.
Figure 6. Load vs. Displacement curves from experimental tests for auxetic specimens.
0
20
40
60
80
100
120
140
160
0 0.5 1 1.5 2
Load (N)
Vertical Displacement (mm)
Non-Auxetic Auxetic
0
20
40
60
80
100
120
140
160
0 0.5 1 1.5 2 2.5
Load (N)
Vertical Displacement (mm)
Sample 1 Sample 2
Sample 3 Sample 4
Simulation
Figure 7. Load vs. Displacement curves from experimental tests for non-auxetic specimens.
CONCLUSION
During this project, the effectiveness of auxetic composites under buckling loads
in comparison to non-auxetic composites was investigated. Using the obtained
experimental test results, the accuracy of simulation results for composite materials
was also studied. The experimental results were obtained using an MTS universal
testing machine to apply compressive loads while the simulation results were
performed in Abaqus. In both the experimental and simulated tests, the critical
buckling loads for the auxetic composites were about 3 times higher than the critical
buckling loads for the non-auxetic composites. Despite this, more research is needed
to determine if other factors were contributing to the increased critical buckling loads.
Specifically, for the auxetic composite, there was higher accuracy between the
simulated critical buckling load and the average experimental load than for the non-
auxetic composites. Along with this, the experimental results for the auxetic
specimens were much more scattered than for the non-auxetic specimens. Therefore,
more testing and simulation are needed to determine whether the difference between
the two results lies in the simulated model, the implementation of the FEA
simulations, or the experimental testing. Along with this, the inaccuracy of the
nonlinear behavior in simulation compared to the nonlinear behavior in testing shows
that the simulation may not be able to accurately predict how the composite will react
once it enters its nonlinear region. Altogether, more testing and simulation work is
required to determine the true effect of auxeticity on the critical buckling load of
composite materials.
ACKNOWLEDGMENTS
The authors would like to acknowledge the financial support from National
Science Foundation under Award No. CMMI-2202737.
0
10
20
30
40
50
60
0 0.5 1 1.5 2 2.5
Load (N)
Vertical Displacement (mm)
Sample 1 Sample 2
Sample 3 Sample 4
Simulation
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