2016-01-0498

Finite Element Simulation of Compression Molding of Woven Fabric Carbon

Fiber/Epoxy Composites: Part I Material Model Development
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Abstract Multiple types of processing techniques for woven fabric carbon

fiber/epoxy composites are currently being intensively studied by the
automobile OEMs and academia, including resin transfer molding
Woven fabric carbon fiber/epoxy composites made through
(RTM), resin infusion molding (RIM) and compression molding.
compression molding are one of the promising choices of material for
While pros and cons of these technologies have been discussed
the vehicle light-weighting strategy. Previous studies have shown that
elsewhere [4], compression molding remains appealing due to the
the processing conditions can have substantial influence on the
following advantages: shorter cycle time, higher limit on the fiber
performance of this type of the material. Therefore the optimization
weight fraction and better stiffness and strength. A typical
of the compression molding process is of great importance to the
compression molding process is composed of two stages: 1)
manufacturing practice. An efficient way to achieve the optimized
preforming of the woven fabric prepreg and 2) resin curing while
design of this process would be through conducting finite element
being pressed. Simple and straightforward as it may seem, simulation
(FE) simulations of compression molding for woven fabric carbon
of the compression molding is a challenging problem as multiple
fiber/epoxy composites. However, performing such simulation
types of physics are involved, i.e., woven fabric micromechanics,
remains a challenging task for FE as multiple types of physics are
resin property changing during curing and viscoelastic deformation
involved during the compression molding process, including the
mechanism of the resin. Previous studies have been focused on
epoxy resin curing and the complex mechanical behavior of woven
exploration of these physics on separated base and providing isolated
fabric structure. In the present study, the FE simulation of the
solutions for each perspective of the problem. For example, there are
compression molding process of resin based woven fabric composites
extensive discussions over the micromechanics of the woven fabric
at continuum level is conducted, which is enabled by the
structure. Different models have been established by Ishikawa and
implementation of an integrated material modeling methodology in
Chou [5], Naik and Shembakar [6], Chung and Tamma [7], Witcomb
LS-Dyna. Specifically, the chemo-thermo-mechanical problem of
[8], Peng and Cao [9], Tabiei and Jiang [10], and Ivanov and Tabiei
compression molding is solved through the coupling of three material
[11]. On the other hand, the curing kinetics of the epoxy resin have
models, i.e., one thermal model for temperature history in the resin,
been studied by Kamal and Sourour [12], while the models that aims
one mechanical model to update the curing-dependent properties of
at predicting the change of viscoelastic properties of the resin have
the resin and another mechanical model to simulate the behavior of
been provided in DiBenedetto [13], Pascault and Williams [14], Hale
the woven fabric composites. Preliminary simulations of the carbon
et al. [15], which considers the Tg change. There are also works to
fiber/epoxy woven fabric composites in LS-Dyna are presented as a
forecast the influence of the curing degree to the polymer modulus in
demonstration, while validations and models with real part geometry
the framework of generalized Maxwell models, including O'Brien et
are planned in the future work.
al. [16], Menzel [17], Eom et al. [18], and Patham [19]. Despite the
fact that insight has been obtained towards the physics involved,
there is little effort on utilizing and integrating these models to
provide a complete solution to the simulation and modeling of the
1 Introduction compression molding on woven fabric carbon fiber/epoxy composites
to the best knowledge of the authors of this paper, which creates
Among the candidates of light weighting materials for automobile difficulties for the researchers to achieve a modeling toolset with
uses, woven fabric carbon fiber/epoxy composites are widely which the process design can be tested and optimized using
considered to be one of the most promising options because of their simulation methods. Integrated computer aided engineering (CAE)
superior stiffness-to-density ratio. Previous studies on the solution for chopped carbon fiber sheet molding compound is
performance of the woven fabric carbon fiber/epoxy composites provided by a number of the suppliers, including Moldflow by
made through different procedures have shown that the properties of Autodesk and Moldex3D by CoreTech System, in which the resin is
such material system highly depend on the processing conditions [1- regarded as flow with viscosity changing with curing reaction. Yet
3]. Delicate design of the processing procedure can not only produce for the compression molding of woven fabric composites with
parts with few defects and higher quality, but also lead to a continuous carbon fiber, the material flow is rather constrained which
significantly reduced cycle time. Both of these outcomes are highly deviates from the assumption in Moldflow and Moldex3D. An
valued during the mass production in automobile industry which integrated software suite for molding of different types of continuous
stimulates the advancements and innovations in the processing fiber composites is also available in PAM-FORM and PAM-
technology in recent years. However, traditional trial-and-error DISTORTION developed by ESI. However, the integration of the
procedures can hardly fit into the current research and development multidisciplinary physics only occurs after the simulation of an
scheme due to their low efficiency and high cost. Alternatively, individual forming stage is fully completed. For example the curing
modeling and simulation techniques are paid more attention to in the prediction must use the final output of the preforming stage to as
studies of how the processing conditions can affect the final geometric and historical input. The interplay between different types
performance of the material. of physics is not considered at a single time increment, which limits
the effectiveness of the multiphysics solution.
Recently a collaborative effort between Ford Motor Company, LSTC,
The Dow Chemical Company and other partners has been casted in
order to provide a systematic solution for the simulation of carbon
fiber/epoxy composites made with compression molding technique
within the framework of integrated computational materials
engineering (ICME). As part of the project, we develop an integrated
material model capable of handling the multiphysics problem in the
compression molding of woven fabric carbon fiber/epoxy
composites. This model targets at consideration of multidisciplinary
integrated physics taking place during compression molding in the
meantime, including the curing degree, chemical shrinkage, thermal
expansion and the stiffening of the resin during curing process, and
the mechanical behavior of the woven fabric carbon fiber. As a
continuum material model, the homogenization between the resin
matrix and the woven fabric fibers is performed when overall
stiffness matrix of each element is assembled. While this model
keeps the capability of modeling the whole compression molding Figure 1. Schematic of the presented material model in LS-Dyna.
problem, i.e., both the preforming stage and resin curing stage, the
development work and the initial testing runs of the model are 2.1 Thermal Model for Curing Kinetics
specifically focused on the latter one for now.
As has been widely reported, the crosslinking in the resin curing
In the following sections, the framework of this material model will process alters the molecular structure of the resin polymer and
be introduced in details. Some initial testing results will then be consequently leads to property changes at the macroscopic level [13-
presented, followed by discussions and future work to further refine 19]. The extent of this chemical reaction is often quantitatively
the material model. tracked by the curing degree, which reads by definition:

(1)

2 Model Descriptions where HR is the heat released up to time t and H is the heat required
to complete the reaction. There are different models to predict the
While in most of the previous studies, researchers tend to follow a curing degree during the crosslinking reaction. The one used in this
divide-and-conquer strategy, providing solutions for individual model is developed by Kamal and Sourour [12], which is in the form
physics in the compression molding, it may probably lead to an of an n-th order autocatalytic equation:
incomplete consideration of the process and thus the tools developed
can hardly be utilized directly by the engineers while designing and
optimizing the processing parameters. A set of the processing 1 (2)
parameters that is identified as the optimal solution for one type of
the physics may not lead to the best overall performance for the in which m and n are the material parameters obtained from the
whole process. To address such issues and provide tools for the characterization experiments for the epoxy resin and and are
multidisciplinary optimization to achieve the globally optimal reaction rates obtained from
solution, an integrated model is favored with the capability of solving
the multiphysics problem and updating the variables of different
exp (3)
physics at every time increment. The schematic of the material model
is shown in Figure 1, which has been implemented in LS-Dyna. The
chemo-thermo-mechanical problem of compression molding is exp (4)
solved through the coupling of three material models, i.e., one
thermal model for temperature history in the resin, one mechanical
model to update the curing-dependent properties of the resin and where T is the temperature, R is the gas constant, and C1 and C2 are
another mechanical model to simulate the elastic behavior of the the activation energy corresponding to reference reaction rate and
woven fabric composites. The presented modeling framework put , respectively. C1, C2, and are also determined from the
emphasis on encountering the multiple types of physics and capturing resin characterization experiments. The temperature is prescribed the
the major changes of the properties of both woven fabric and resin to presented model, and will be obtained by coupling the thermal solver
provide more reliable and complete solutions. and the mechanical solver together in LS-Dyna in the future, in which
case an independent thermal material in LS-Dyna will be used along
with the developed model to address the heat transfer in the
composites.

In addition to the curing degree evolution, the thermal expansion and

chemical shrinkage are also calculated based on the temperature input
and the curing degree. Linear thermal expansion is considered while
the coefficient can change at different curing degree. For the
chemical shrinkage, a second order polynomial is used to describe the
deformation of epoxy caused by the chemical reaction. The
parameters in the LS-Dyna material card need to be obtained from
characterization tests.
2.2 Curing-dependent properties of the resin utilized to simulate the deformation of fabric structures, these models
do not have an explicit consideration of how the epoxy affects the
mechanical behavior of the composites, which is essential for the
Prior to this study, the model that can capture the viscoelastic
prediction of the processing history. In order to address the effect of
property change of the epoxy resin has been discussed by multiple
the resin matrix in the micromechanics calculation, we follow the
researchers [16-18]. It has been demonstrated that the viscoelastic
framework as in ref. 11, with some modifications when processing
behavior of the resin is alternated by the curing degree. Generally, the
the curing dependent properties for the resin matrix. Some of the key
increase of the curing degree, which indicates the increasing
equations are briefly listed below, while details of the
crosslinking density in the resin, gives rise to the stiffening of resin.
homogenization are not shown here.
While for thermoplastic polymers in which the viscoelastic behavior
can be described using the Prony series in a generalized Maxwell
model, for the thermosetting epoxy resin the moduli terms are Firstly the representative volume cell (RVC) element of the woven
functions of , namely, fabrics is symmetrically divided into 4 subcells. In one of the
subcells, the stiffness matrix of the yarn can be expressed using the
direct stress compliance matrix of the yarn and shear stress matrix of
, ∑ 1 exp (5) the yarn, which reads:

In which G(t, ) is the viscoelastic shear modulus, G0( ) is the

instantaneous modulus and Gi( ) is the ith modulus term in the Prony (10)
series and is the inverse of corresponding relaxation time. In order
to characterize the curing dependency of the Prony series, we choose
the similar method as in ref. 18 based on our experimental results on
the resin. At different curing degree, the Prony series modulus terms where is the 6x6 stiffness matrix of the yarn, and is the
are always proportional to the instantaneous shear modulus, i.e., corresponding compliance matrix of the yarn. and are the
partitions of the compliance matrix representing the direct stress
compliance and the shear stress compliance, respectively, which are
(6)
determined from testing of the fiber tow or other simulation
approaches. The stress in the yarn can then be expressed as:
where is the reference curing degree. In practice, we choose
1.0 and thus [ ] (11)

, 1 exp where is the stress of the yarn in a subcell and is the

prescribed iso-strain of the subcell. Note that and are defined
in local coordinate system in the subcell as described in ref. 11. The
= 1 ∑ 1 exp homogenization in the subcell simply follows the rule of mixture,
which is
.
= 1 ∑ 1 exp (7)
. 1 (12)

It can be seen that after this simplification is applied, the , is where is the stress in the matrix phase after consideration of the
determined by the instantaneous shear modulus measured at different thermal expansion, chemical shrinkage, viscoelasticity as well as the
curing degree and the Prony series of the fully cured resin. interaction between yarn and matrix in the subcell. is the volume
fraction of the yarn. The stress of the subcell, , can then be
Likewise, the bulk modulus terms are expressed following the same obtained using Equation 12. The superscript (c) indicates the index of
way: the subcell, numbered from I ~ IV. A coordinate system transform is
.
applied to , such that the stress are expressed in the coordinate
, 1 ∑ 1 exp (8) system of the RVC element. The transformed stress, ′ , of each
.
subcell is then averaged to give the stress of the RVC element, ,
where , is the bulk modulus at a given curing degree and time, i.e.,
and K0 and Ki are instantaneous bulk modulus and the ith term in
Prony series, respectively. The time-temperature superposition of the ∑ ′ (13)
Prony series stills follow the WLF shifting equation:
The input parameters to the woven fabric composites model needs to
ln (9) be measured from the characterization experiments on the fiber tows.
Current formulation of the model only supports 1/1 twill but it can
also be adapted to other weave patterns by modifying the
where aT is the shifting coefficient and A and B are constants
homogenization equations without great effort.
measured from experiments. Note that natural logarithm function is
intentionally used here to be consistent with the internal settings in
the LS-Dyna. 2.4 Integration

2.3 Woven fabric micromechanics The presented model adopts a weak coupling strategy when
integrating the three modules for different physics. Instead of solving
the equations from all types of physics simultaneously which is often
The micromechanical model for woven fabrics has been discussed in
known as “strong coupling”, the weak coupling follows an iterative
the literature for decades [5-11]. Specifically in LS-Dyna, models
manner so that the equations from different physics are solved
have been implemented for both viscoelastic loose woven fabric
sequentially in one time increment defined in LS-Dyna simulation.
(MAT_234) and dry fabric (MAT_235). Effective as they are when
Although in reality the different behavior are coupled and taking
place in the meantime, this is not a feasible solution for engineering
problems. Convergence and extremely high computational costs are
expected if all the equations are combined and solved following a
strong coupling manner. Admittedly advanced strong coupling
algorithm may also be applied for this problem, however, for this
prototype material model, the authors are prioritizing the ease of
implementation and the simplicity in problem formulation over the
possible benefits that may come with these advanced algorithms of
greater complexity. Nevertheless, exploration of usage of these
algorithms remains an interest for our future work.
(a)
The sequence of the variables updates in different physics is as
shown in Figure 1. At the start of one time step, the temperature will
first be evaluated and the curing degree of the resin will then be
determined. The resin viscoelastic properties, thermal expansion and
chemical deformation are then obtained. Subsequently these data are
passed to the woven fabrics micromechanical model to update the
stress and strain of an element as well as the fiber orientation angle in
the element. In case that the strain rate effect is not negligible for the
fabric, corresponding rate dependent parameters are also required as
the input.

3 Tests and results

(b)
The presented material model is tested in several simulations in LS-
Dyna. As the preliminary study, we focus on examining if the Figure 2. Schematic of the single element model in LS-Dyna. The geometry
developed material model can qualitatively capture the physical and the mechanical boundary conditions are shown in (a), while the prescribed
behavior taking place during compression molding. The performance temperature load is shown in (b).
of the material model is examined in three different simulations. To
start with, the single element models are tested with resin-only The results are shown in Figure 3. The curing degree and the lateral
configuration and composites configuration such that the contribution deformation along X axis caused by compression along Z direction
to the deformation from different types of physics can be evaluated are shown in Figure 3a, while a breakdown of the contribution from
and compared. Then a plaque model with more complex stress state the different deformation mechanism is shown in Figure 3b. There
and higher similarity to real-life compression molding set-up is tested are clearly 3 subsequent stages as shown in Figure 3a as a result the
to examine the elastic behavior of woven fabrics predicted by the temperature load in Figure 2b, i.e., heating, holding and cooling.
implemented fabric micromechanical models. During the heating stage, the thermal expansion is the most
significant deformation mechanism, since the chemical shrinkage is
3.1 Single element model with only resin vanishing due before the curing degree builds up to a high value.
During the holding stage, the thermal strain keeps constant while the
deformation mechanism is the competition between chemical
In order to demonstrate the constitutive behavior of this model, a
shrinkage and the Poisson’s effect due to the load along Z axis. In the
single-element geometry with the dimension as 1mm x 1mm x 1mm
third stage the thermal load is removed and thus the thermal
is built as shown in Figure 2a. The boundary condition is set such that
expansion diminishes, yet the continuous mechanical load and the
the bottom surface (Z=0) is fixed along Z direction while the node A
irreversible chemical shrinkage are still taking place. At the end of
is fixed along all the directions. The rotational degrees of freedom are
the simulation time span, the element is expanded as the mechanical
fixed for all the nodes. A uniform compression is applied at the top
strain overcomes the chemical shrinkage. It can be indicated in
surface (Z=1) following ramp displacement control. The material
Figure 3 that the developed model can well capture the complex
properties of the resin are defined based on typical values provided
deformation history for the resin phase.
by Dow Chemical with parameters for Kamal model, thermal
expansion, chemical shrinkage and the curing and temperature
dependent viscoelastic parameters. To make this a resin-only model,
the volume fraction of the woven fabric is set to 0.0 in the material
card. A prescribed temperature load is also applied to activate the
resin curing process as shown in Figure 2b.
 (a) (b)

Figure 4 Boundary condition (a) and the initial fabric configuration (b) in the
single element fabric-only model.

(a)

Figure 5. Output stress strain curve and the fiber angle change. The segment
blue line is the tangent line of the σxx, which is displayed here to show the
nonlinear elastic response due to the change of fabric angle reorientation.
(b)

Figure 3. Output of the single element model with only resin.

3.3 Plaque composite model

A preliminary test is done using the integrated composites model, in

3.2 Fabrics-only single element model which the volume fraction of the carbon fiber is 60%. The geometry,
mechanical boundary condition and prescribed temperature load is
Similarly a single element model to test the micromechanical part of shown in Figure 6. The Z=0 surface is fixed along Z axis, while the
the developed material model is set up in LS-Dyna, as shown in Z=1 surface is pressed towards negative Z direction, following a
Figure 4a. The parameters of the carbon fiber woven fabric are using displacement controlled boundary condition, which ramps up to -0.1
typical values measured from a tow of around 24K continuous carbon mm at the end of simulation. Three reference time points are marked
fibers. The volume fraction of the fabric is set to 1.0, which is in Figure 6b.
equivalent to a fabric-only situation. The initial fabric angle in the
element is shown in Figure 4b. The warp and weft are aligning along
+/- 45o in the XY plane. Back surface (X=0) is fixed while the front
surface (X=1) is stretched along X axis following a displacement
controlled boundary condition. The node A is fixed for all degrees of
freedom.

The result is shown in Figure 5. The stress-strain relation is observed

to be nonlinear, as the solid curve deviates from its tangent at origin
point. The dotted line in Figure 5 is the fiber angle data calculated by
the developed model. In our formulation, the fabric angle change is
considered when generating the stiffness matrix of the element at
each time increment. With the stretching along X direction, the warp
and weft reorients from the initial configuration and moves towards
the X axis. The woven fabric is thus stiffer along X direction as the
strain increases and consequently leads to a nonlinear stress-strain (a)
curve. The results in Figure 5 indicate that the developed model can
well capture the changing modulus of the woven fabric when the
fibers are reorienting. This nonlinearity is minimal when the strain
level is lower than 5% yet not negligible at high strain level.
 (b)

Figure 6. Plaque composites model (a) in LS-Dyna and the boundary

condition configuration (b). Three time points are marked up in (b). The angle
distribution between the yarn and X axis at these time points is shown in
Figure 7. Figure 7. Distribution of the angle (φ), between the yarn direction in each
element and the global X axis. A, B and C are the three reference time points
marked in Figure 6b. The color represents the value of φ. As shown in the
The simulations results in Figure 7 indicate how the fabric angle bottom right schematics, φ higher than 45o indicates that the yarn is rotating
reorients during the compression molding process. The angle of the towards Y axis while φ lower than 45o indicates the yarn is rotation towards X
yarn along +45o is shown for the plaque part in the Z=0 plane. As can axis.
be observed, the fiber angle distribution in this plaque is not uniform
and also evolves with the increasing press strain level along Z
direction, which is due to the consideration of the nonlinear effects
caused by fiber reorientation and the thermos- and curing-dependent
deformations in the resin phase. The Poisson’s effects and thermal 4 Discussions
expansion makes plaque to expand along X and Y direction. And the
45o tends to align with the direction of expansion, as discussed in As discussed above, the compression molding of the woven fabric
section 3.2. As a result, the angle between the yarn and the X axis, φ, carbon fiber composites is a complex multi-physics problem. In order
decreases where expansion along X direction is preferred and to better simulate this process and thus provide adequate
increases while Y direction deformation is preferred, as is the case in microstructural information to the prediction of the part performance,
Figure 7. Though generally small in value since the carbon fiber tow the presented material model is developed in LS-Dyna, aiming at a
is stiff, the change of the angle is more obvious at high temperature more complete solution to this problem. The single-element tests on
when lateral thermal expansion in the resin is more significant, as the resin- and fabric-only material in section 3.1 and 3.2 can capture
shown in the top right contour taken at time point B during the the different physics expected during compression molding
temperature holding stage. Again the developed composites model qualitatively. The chemical shrinkage and thermal expansion of the
captures the deformation mechanism qualitatively well. Nevertheless, resin and the fabric angle reorientation of the fabric are well observed
it is also noted that the distribution of φ is not fully symmetric in B, in the simulation results. Additionally section 3.3 shows that the
which might be an indication of numerical issues in the material woven fabric carbon fiber composites model works generally well in
model and further investigations are needed. Follow-up quantitative the plaque geometry, despite some numerical issues that call for
validations are required to assess the accuracy of prediction of the further investigation. A more exhaustive quantitative benchmark is
woven fabrics micromechanical model, which is discussed in Section still ongoing, which requires precise characterization on the resin and
4. fabric, respectively, and an accurate translation of the processing
conditions into the boundary condition configurations in LS-Dyna
used in the validation experiments.

In the current examples, the temperature settings are all using

prescribed temperature load in LS-Dyna, which circumvents the
usage of the thermal solver. The heat transfer in the composites is
thusly neglected in these preliminary tests. However, when complex
part geometry is defined in practice, the temperature field inside the
composites may not be homogeneous. Special cautions are needed
while building such thermal models since carbon fiber typically
yields a much higher thermal conductivity compared to resin phase
and thus the heat transfer can be anisotropic.

Also excluded from the preliminary tests is a separate viscoelastic

relaxation test to verify the viscoelastic module in the presented
model. Due to the lacking of validation data, this test is not
considered at this stage. Once characterization and validation
experimental data are both ready, the viscoelastic behavior of the
resin-only case and the composites will be examined and compared
quantitatively with the experimental validations.
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Acknowledgements
The authors sincerely acknowledge the funding support by
Department of Energy (DE-EE0006867) and the insightful discussion
with Dr. Ala Tabiei at University of Cincinnati, Cincinnati, OH and
Dr. Deep Wang at Dow Automotive Systems, The Dow Chemical
Company, Shanghai, China.