(
Temperature Dependent Flexural Rigidities and
Thickness Investigation
K. D. WHITE, L. M. DANGORA and J. A. SHERWOOD
ABSTRACT
This paper discusses the characterization of temperature-dependent flexural
rigidities of Dyneema® HB80, a cross-ply thermoplastic lamina. The properties are
then used in the modeling a thermoforming process. A vertical-cantilever
experimental setup is presented to characterize the bending behavior at elevatedtemperature conditions. The material properties derived from the test data are
implemented in a finite element model of the cross-ply lamina. Thickening of the
lamina resulting from shear deformation is investigated and incorporated in the
model. The finite element model uses a hybrid discrete mesoscopic approach, and
deep draw forming of the material is simulated to investigate its formability to a
hemispherical geometry. Simulation results are compared with an experimental
forming trial to demonstrate the capabilities of the model to predict the development
of out-of-plane waves during preform manufacturing and to inform the design of
multiple-ply thermoforming with thickness variation data.
INTRODUCTION
The process of thermoforming fabric-reinforced composites is capable of
producing lightweight, quality parts relatively fast with reasonably low processing
costs [1]. The thermoforming process uses heat and pressure to transform flat sheet
laminates into a desired three-dimensional shape [2]. However, the lack of knowing
if and where defects can develop during the forming process can be a limiting factor
in the widespread use of thermoformed composite parts. A manufacturing defect
such as wrinkling can result in compromised load paths and stress concentrations that
can lead to catastrophic and premature failures [3].
The governing mechanism of deformation of the reinforcement material is inplane shear. The areal coverage of the material decreases when sheared, but the
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University of Massachusetts Lowell, 1 University Avenue, Lowell, MA 01854, U.S.A.
fibers within the ply layers of the stack maintain the same volume; therefore, the
laminate thickness increases with local shear [4]. Thus, as a result of varying degrees
of shear of the material as it deforms to conform to the geometry of the mold results
in thickness variations that can affect the uniformity of pressure distribution between
matched die tooling, allowing weakened, resin-rich areas to form [5] as well as
incomplete consolidation of the ply stack.
Because wrinkling of the composite reinforcement, incomplete consolidation and
resin-rich areas can result in premature failure, it is important that the manufacturing
process be well understood so it can be designed to mitigate formation of such
defects. As a result, the processing parameters will be driven by the forming limits
of the material and the relative complexity of the part geometry. Unfortunately, the
processing conditions that will lead to consolidation problems are not always known
before the development phase. Consequently, correction of adverse product features
is often accomplished with a design-build-test regimen, which can be costly,
wasteful, and time consuming. A simulation tool that could perform the design-buildtest activity in a virtual setting would provide a cost and time-efficient solution to
product development and process design, and ultimately higher confidence in the use
of composites.
Design tools such as Fibersim and CATIA use a “fishnet” algorithm to predict the
deformation of the fiber blank as it conforms to tool geometry [6-10]. Even though
this “fishnet” approach is fast and efficient, it fails to account for the mechanical
behavior of the fabric or the effect of the boundary conditions such as binder pressure.
As a result, process-induced conditions such as wrinkling and thinned and/or
thickened spots will not be captured in the simulation. Therefore, a simulation
method that includes material behavior is necessary to predict the locations and
magnitudes of defects that may develop during manufacture.
Using a discrete mesoscopic finite element model, information regarding fiber
orientations, stresses and strains can be mapped over the preform surface and
monitored throughout the forming process [11]. With a complete set of material
properties for describing the material behavior, the simulation tool is able to identify
potential defects (e.g., in-plane waves, out-of-plane wrinkles, fiber tearing) that arise
during manufacture and compromise the part performance. However, the change in
the local thickness of the laminate due to in-plane shearing is not currently modeled
in the simulation. For many applications, multiple layers of one or more types of
fabrics are used and filler layers may need to be implemented to add material to areas
surrounding the thickened regions. Thus, predicting the regions that require filler
plies is critical in a practical thermoforming process simulation that is going to assist
in the design of a charge of plies that will result in a uniform thickness part. Results
of the finite element analysis (FEA) can therefore be used to guide the selection of
processing parameters (e.g., tool velocity, forming temperature, binder pressure,
material selection, ply geometry, and binder size) such that the resulting preform
satisfies the design constraints (e.g., fiber orientations, uniform thickness and low
seam density) [12].
The objective of the current research is to demonstrate capabilities of a discrete
mesoscopic finite element model that considers the mechanical behaviors of the
material during a forming simulation. This paper presents the characterization
methodologies used to define the temperature-dependent flexural behavior of
Dyneema® HB80, a thermoplastic cross ply, and discusses the modeling approach
taken to simulate the manufacturing process, including thickness changes resulting
from in-plane shear deformation. A qualitative comparison of out-of-plane wrinkles
in an experimentally formed part and the model prediction is presented and discussed.
MATERIAL CHARACTERIZATION
The specific material considered in this research is Dyneema® HB80, a
thermoplastic cross-ply containing four unidirectional layers oriented in a (0/90)2
initial fiber configuration. Each ply is comprised of ultrahigh molecular weight
polyethylene (UHMWPE) fibers and a thermoplastic polyurethane (TPU) based
matrix comprise the highly fibrous lamina. While the methodology is demonstrated
only for this one material system in this paper, the methodology discussed is
applicable to a wide range of materials. Previous works describe shear [13] and
tensile testing [12] of the material, while the current paper presents flexural rigidity.
Bend Testing
The bending rigidity governs the shapes of the wrinkles that may form during
textile draping and composite forming. Unlike conventional isotropic materials, the
bending stiffness of fibrous materials is not directly related to the tensile modulus; it
must therefore be measured through experimentation [14]. For the purpose of the
research presented in this paper, the simple vertical cantilever test proposed by
Soteropoulos et al. [15] was modified to accommodate characterization at elevated
temperatures.
The test fixture is shown in Figure 1. This fixture heats the sample using radiation
from a concentrated ceramic infrared (IR) element. A feedback control system with
a Type J thermocouple sensor is used to regulate the temperature of the ceramic
elements. An additional thermocouple is added on the surface of the fabric away from
the IR element for monitoring the test-specimen temperature. To enforce the
cantilever boundary condition, a magnetic clamp is used. The ceramic block magnet
has a stability temperature of 250°C and a maximum pull force of 60 N. Such a strong
magnet was selected so the experimental setup could also be used for much thicker
specimens.
The free end of the sample was displaced using a hanging mass on a string,
redirected with a pulley. The test protocol followed the procedures outlined in [15].
While the matrix deformation in bending was presumably governed by shear, this
property was not separately investigated. With the high fiber content, the response of
the lamina in bending was largely dominated by the fiber mechanics; and as the
sample length was significantly larger than the thickness, shearing of the fibers was
considered to be negligible.
Figure 1. Vertical cantilever method setup for experimental evaluation of bending stiffness at
elevated temperatures.
Material Characterization Results and Discussion
The material was tested for temperature-dependent flexural rigidities in
accordance with the aforementioned procedures. The use of these material properties,
in conjunction with the shear behavior and tensile behavior (previously characterized
in [12, 13]), facilitated development of a forming model. Data collected from the
characterization tests are presented in this section and contribute to the finite element
deep-draw simulation results presented in the Forming Simulation section.
Bend tests were performed at 80°C, 100°C, and 120°C. Softening of the material
was apparent with the addition of heat. As the temperature was increased, the sample
experienced a larger deflection under identical loading conditions. Pictures were
taken of the loaded samples and ImageJ, an open-source image analysis software,
was used to measure discrete displacements. A third-order polynomial was fit to the
data, and the curves shown in Figure 2a are the respective fits for an average of three
test samples. The curvature was approximated by taking the second derivative of the
average deflection equation. Because the tip force used to displace the free end of the
cantilever was measured, the moment along the sample was known. This information
was used to plot the moment as a function of curvature (Figure 2b). The bending
stiffness was derived from the slope of the moment-curvature line, and these values
are summarized in Figure 2b. Although the flexural rigidity varied over the
temperature range investigated, all values remained within the same order of
magnitude. Material properties at a processing temperature of 100°C were applied
in the modeling simulation.
Tem perature
Bending
Rigidity
(°C)
80°
100°
120°
(N·m m 2)
380
240
170
Figure 2. Bending test results for Dyneema® HB80 (a) Deflection of strips subject to the same
loading at different temperatures and (b) the moment curvature relation at elevated temperature.
MODELING APPROACH
The modeling performed for this research was accomplished at the mesoscopic
scale using a discrete approach developed by Jauffrès et al. [11] employing a
hypoelastic element description with an explicit formulation. The textile constituents
are modeled using conventional elements available in commercial finite element
software. Linear beam elements incorporate the tensile and flexural properties of the
tows, while shell elements define the shear response of the fabric. For example, a
cross ply is discretized into a mixed-mesh grid where the unit cell consists of four
beam elements and one shell element (Figure 3). The shell element has no tensile
properties and only possesses in-plane shear stiffness that varies with the degree of
shear. The two horizontal beam elements are defined using properties of the 0° fibers,
and the two vertical beam elements are defined using properties of the 90° fibers. A
single node is used to connect the intersecting beam elements at each of the shell
corners. This joining of the beams assumes a “no slip” condition between 0° and 90°
layers which has been demonstrated through the correlation of the model with
experimental data to be an acceptable assumption. This modeling technique has been
successfully applied to a variety of textile architectures including woven,
unidirectional, and non-crimp fabrics.
Figure 3. A representative unit cell for the finite element discretization of a textile reinforcement
For this research, analyses are performed using the explicit solver in Abaqus
which offers capabilities for analyzing large, nonlinear, quasi static problems, such
as deep draw thermoforming. Furthermore, Abaqus/Explicit implements robust
contact algorithms without the need for additional degrees of freedom, and it can
resolve solution discontinuities such as buckling or wrinkling. User-defined material
subroutines are linked to the Abaqus solver to govern beam and shell behaviors.
Accuracy of the simulation depends on the quality of material constants which are
derived from characterization tests that describe the fabric in bending, tension, and
shear.
Thickness Change Implementation
The primary deformation mode of the fabric during the thermoforming process is
in-plane shear. As a consequence of the shear deformation and material
incompressibity, the thickness of the lamina will increase due to conservation of
volume. Because the areal coverage of material decreases when sheared, the fibers
and matrix within the ply layers stack on top of each other and maintain the same
volume. Dangora et al. [4] verified this theory with micrographs taken of laminates
sheared to 0°, 20°, and 60°. Figure 4 shows the calculation of the conservation of
volume approximation compared to experimental data.
Figure 4. A conservation of volume approximation used to calculate the change in lamina
thickness as a function of shear, which correlates well with experimental data [4].
A virtual bias extension model was chosen to demonstrate the modeling of
thickness. In a bias-extension test, there are three fairly distinct shear regions. These
three regions are shown in Figure 5.
Figure 5. Bias extension post-test geometry with three distinct shear regions [16].
The fabric was modeled a plain-weave fabric with an initial thickness of 0.5 mm
and Poisson’s ratio of 0.5, i.e. for incompressibility. In Abaqus, the section thickness
(STH) state variable was chosen as a field output, and the explicit processer settings
were adjusted to calculate the element thickness based on geometry and
incompressibility at each time interval. In this manner, the thickness change as a
function of the current in-plane shear angle was monitored. Figure 6 shows a
schematic for the bias extension model of a plain-weave fabric.
Figure 6. Finite element model of bias extension test on plain weave fabric.
The bias-extension model was intended to demonstrate the effect of shear
deformation on the thickness of a single fabric ply, but it was also desired to explore
the behavior of a multi-ply stackup. To have a high-fidelity model that is able to
capture the effects of inter-ply friction, each ply is modeled explicitly as opposed to
smearing a number of plies into a single layer of element, the total thickness of
multiple stacked plies cannot be obtained as a single model output, i.e. the sum of the
thickness changes of each layer of elements must be considered and summed to get
the net change in thickness for the part. In the case of a forming simulation, the
variation in fabric thickness would result in a variation in load distribution across a
ply, which could be used to inform the addition of filler plies. However, the general
shell elements used to model the phenomenological shear behavior of the fabric with
the user-material definition do not support through-thickness stress or strain.
Therefore, demonstration of the variation in total thickness of the laminate after shear
deformation was performed by compressing a layer of a relatively soft, i.e. lowmodulus, material between two rigid plates and the fabric, i.e. rigid plate / soft
material / ply stack / rigid material as shown in Figure 7. In general, the surface
definition of conventional shell elements used for contact does not update the section
thickness during the analysis. However, the *THINNING option can be used with
Abaqus/Explicit’s general contact formulation so that the contact surfaces of the shell
elements will update based on the current geometry of the element and Poisson’s
ratio. With the use of thinning, the deformation of the low-modulus material where
the fabric was compressed onto it was expected to mirror the thickness variations in
the fabric.
Figure 7. Finite element model of sheared fabric sandwiched bweteen rigid plates
and low-modulus material to capture thickness changes.
Results and Discussion
The first bias-extension model created was intended to verify that the thickness
of the conventional shell elements used in the mesoscopic fabric model did not, by
default, change based on shear deformation. The section thicknesses of the shells
were prescribed as model outputs and the model results are shown in Figure 8. The
section thickness across the entire fabric ply stayed at its original value of 0.5 mm,
as expected.
Figure 8. Simulation of a bias-extension test of a plain-weave fabric. Note that there is no
change in the thickness.
The bias-extension model was then performed with the Poisson’s ratio manually
changed to 0.5 to simulate a conservation of volume. The results of that simulation
are shown in Figure 9. The contour of section thickness correlates strongly with that
of shear angle, demonstrating the shear-thickening behavior expected from
conservation of volume. The blue regions of Figure 9a have zero shear, and these
correlate with the near-zero change in thickness as depicted in Figure 9b from the
initial thickness of 0.5 mm. The red region of Figure 9a has ~66o of shear, and these
correlate with the 0.7-mm change in thickness as depicted in Figure 9b from the initial
thickness of 0.5 mm.The thickness contours of Figure 9b do not correlate one-to-one
with the green shear contour areas of Figure 9a due to the deformation in these
regions region being a combination of shearing and stretching. The simulation
showed around 120% increase in the section thickness at 66̊ of shear, which is
approximately what was expected from conservation of volume.
(a)
(b)
Figure 9. Bias extension simulation results showing (a) in-plane shear and (b) section thickness.
To demonstrate the capabilities of the *THINNING surface property for
incorporating the changing fabric thickness into a contact simulation, the deformed
fabric was compressed onto the low-modulus material as shown in Figure 7.
Figure 10 shows the deformation of the low-modulus material resulting from the
compression simulation. The into-plane compression contour of the soft material
shows an imprint that very closely correlates with the thickness contour of the
deformed fabric, as was expected. However, the imprint of the fabric on the soft
material did not exactly match the fabric thickness values previously output in the
bias-extension simulations. Although this method could be utilized to estimate the
uniformity of the overall thickness of a multi-ply stackup preform, more work needs
to be done to more capture the thickness vairations with better resolution and
precision.
Figure 10. Out-of-plane displacement contour of low-modulus material after compression by
bias-extension-deformed fabric.
FORMING EXPERIMENT AND SIMULATION
Hemisphere forming was performed using the experimental setup shown in Figure
11a. The fixture (consisting of a hemispherical punch, an open die, and a blank
holder) was placed in an environmental chamber and mounted on a universal testing
machine. A single sheet of Dyneema® HB80 was heated to a forming temperature of
100°C and drawn to the punch geometry. Approximately 3200 Pa of pressure was
applied to the blank to supply in-plane tension as the sheet was punched.
(a)
(b)
Figure 11. Hemispherical forming: (a) Experimental deep draw setup and (b) associated
configuration for FEA.
Similarly, a deep-draw forming simulation was completed in Abaqus/Explicit
using the configuration shown in Figure 11b. The tensile modulus and bending
stiffness previously measured were used to calculate an effective compressive
modulus (Ec) for implementation in the finite element model. The compressive
modulus at 100°C was calculated to be 215 MPa, and the bilinear modulus was
implemented into the finite element model. Note that the lamina properties were
assigned to the beam elements, not the fiber properties. A summary of the material
constants used in the model are provided in TABLE I.
TABLE I. SUMMARY OF MATERIAL CONSTANTS FOR MODEL INPUT
Property
Value
Tensile Modulus (MPa)
22,000
Compressive Modulus (MPa)
215
Shear Stiffness* (MPa)
23| |
55| |
48| |
Poisson’s Ratio
0.5
*Note that is defined as the shear strain of the composite lamina
17| |
3
The experimental and finite element forming results are shown in Figure 12a and
12b, respectively. The experimentally-formed part developed wrinkling at the front,
back, and sides of the hemisphere (i.e., along the central axes of the planar sheet but
near the bottom of the 3D part). The finite element analysis captured the development
of such out-of-plane defects in these locations. Overall, the initial modeling efforts
show good correlation with wrinkle developed in the physical part during the forming
trial.
(a)
(b)
Figure 12. Dyneema® HB80 sheet formed (a) experimentally and (b) virtually via FEA.
Comparison of the in-plane shear angles in Figure 13 of the formed part with the
corresponding thickness values in Figure 14 show that the simulation can predict the
thickness variations within the part. The contact definitions for the shell sections can
be updated in future studies to allow for multiple layer stackups and increased
thickness values with within the wrinkles and folds.
Figure 13. In-plane shear contour of formed hemisphere from simulation.
Figure 14. Section thickness contour of formed hemisphere from simulation.
CONCLUSION
This paper discussed approaches used to characterize the flexural behavior of
Dyneema® HB80 at typical forming temperatures. An experimental setup was
developed to perform bend testing at elevated temperatures based on the vertical
cantilever method. The material constants derived from experiment were
implemented into a discrete mesoscopic finite element model. Thickness variations
in fabrics due to in-plane shearing were investigated and implemented into the finite
element analysis. A forming simulation was performed using these modeling
techniques, and the analysis results were assessed against a laboratory-formed part.
The combination of shear, tensile and flexural material properties allowed
out-of-plane defects to be captured in the model. Thickening as a result of in-plane
shearing as well as updated contact definitions will allow for multiple layers of
forming material. Good correlation was seen in a visual assessment of the physical
and virtual parts. The current forming simulation model represents a critical step
towards a multiple-layer stackup forming simulation that can optimize binder
pressure, ply geometries and desired fabric properties.
ACKNOWLEDGEMENTS
The authors thank the US Army Natick Soldier Research Development and
Engineering Center (NSRDEC) for funding this research under Contract No.
W911QY-1A-2-0001. The authors would also like to recognize the Harnessing
Emerging Research Opportunities to Empower Soldiers (HEROES) initiative for
establishing this collaboration and thank the Massachusetts Green High Performance
Computing Cluster (MGHPCC) for the computational resources.
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