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Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
Validating Predictive Modeling of Carbon Fiber Composites
In Automotive Crash Applications
(09/2012-2/2013)
Xinran Xiao, Danghe Shi, Vahid Khademi, Andy Vanderklok
Michigan State University, East Lansing, Michigan
In this reporting period, the following tasks have been attempted:
Task 13.0 Select commercial models and model components from public domain
Task 13.1 Select progressive crash models in commercial codes
Task 13.2 Select progressive crash models from public domain
1. Task 13.0 Select commercial models and model components from public domain
& Task 13.1 Select progressive crash models in commercial codes
Composite materials models are available in commercial explicit Finite Element (FE) packages
such as LS-DYNA, PAM-CRASH, RADIOSS, and ABAQUS. All composite models are based
on an orthotropic elasticity framework. They differ in the failure criterion and the manner that
properties are degraded upon failure. The two common types of degradation laws are the
progressive failure and damage mechanics based damage evolution.
Table 1 presents a survey of the FE codes used by major automakers in crashworthiness design
in 2012. As shown, LS-DYNA has been adopted by most of the automakers. PAM-CRASH is
used by European aerospace industry. It has considerable activities in composite component
crash simulations. ABAQUS is widely used by the research community, particularly by
academic users. Newly developed composite models are often implemented in ABAQUS first.
RADIOSS is still used by Ford and Renault/Nissan. In recent years, some users have switched
from RADIOSS to other codes.
Table 1. The FE codes used in crashworthiness design by major automakers
Automaker Crash code Comments
General Motors LS-DYNA
Chrysler LS-DYNA
Ford RADIOSS/LS-DYNA Car/Truck
Toyota LS-DYNA used RADIOSS prior 2012
Honda LS-DYNA
BMW LS-DYNA/ABAQUS Evaluated ABAQUS
Daimler AG LS-DYNA Evaluated ABAQUS
Renault/Nissan RADIOSS
Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
Table 2. Composite material models in LS-DYNA
brick shell Degradation Law
22 Composite Damage Progressive failure
54/55 Enhanced Composite damage Progressive failure
58/158 Laminated Composite Fabric Damage evolution
59 Composite Failure Progressive failure
161/162 Composite MSC Damage evolution
1.1 LS-DYNA
Table 2 is a summary of the composite material models in LS-DYNA and the types of element
the models support. Among the eight models shown in Table 2, MAT54/55 [1-3], MAT58 [4-6],
and MAT162 [7,8] are commonly used in crash/impact simulations.
MAT54/55 (Enhanced Composite Damage) is available only for shell. MAT54/55 is a progress
failure model. Its failure surfaces and degradation rules are summarised in Table 3. The variables
and their typical values for a unidirectional carbon/epoxy are listed in Table 4.
MAT58 (Laminated Composite Fabric) is also available only for shell. The failure criteria for
MAT58 were not provided explicitly in the manual. The users are given the choice to select
either a faceted or a smooth (quadratic) failure criterion, which is assumed as Hashin or Tsai-Wu
types. MAT58 is based on damage mechanics. It employs an exponential damage evolution law
(1)
MAT158 (Rate Sensitive Composite Fabric) allows the consideration of rate dependence in the
shear direction through defining a relaxation modulus in the form of Prony series. Otherwise, it
is identical to MAT58.
It is difficult to obtain progressive crash with shell elements. To simulate the progressive crash
behavior, a SOFT parameter is introduced in composite models in LS-DYNA that allows a
predefined percentage reduction in strength for elements being exposed to the crush front [5].
Adjusting the value of SOFT has been used as a mean to obtain the desired response [1,3,9].
Figure 1 shows an example. As seen, three values of SOFT were used for components of three
different shapes: 10% for a C-channel, 20% for a Hat-stiffener, and 15% for an Angle [9]. This
practice is rather common in composite crash simulations.
Modeling the initial contact between the composite component and impact platen is another art.
In LS-DYNA, defining a contact penetration curve to soften the impulse upon impact has been
proven to be critical in obtaining progressive crash for certain components [10]. Figure 2 shows
an example of user defined contact penetration curve. It also compares two simulations
im
ei
)(01
Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
performed with and without a contact penetration curve [9]. Without the contact penetration, the
response was discontinuous with spikes of large value. With the contact penetration, a
continuous response was generated. After filtering, the response was more like what was seen in
the experiment.
Table 3. MAT54/55 failure criteria and degradation rules
Table 4. MAT54/55 material properties and input values for unidirectional carbon/epoxy
Fiber tensile 0,01)()( 12211221
122112
GEESX
ecT
f
Fiber
compression 0,01)( 12211
2112
EX
ec
f
MAT54 Chang matrix failure
Matrix
tensile 0,01)()( 21122122222
GE
SYe
cT
m
Matrix
compression cc
ccc
c
c
d YXGESYS
Y
Se 2,0,01)(]1)
2[()
2( 1221122
2122222222
MAT55 Tsai-Wu criterion for matrix failure
01
)()()( 222122222
Tc
Tc
ccT
mdYY
YY
SYYe
Description Variable Value
Longitudinal modulus (GPa) E11 112.3
Transverse modulus (GPa) E22=E33 7.58
Minor Poisson’s Ratio 21 0.209
Shear modulus (GPa) G12=G23=G31 3.4
Bulk modulus of failure material (GPa) K 4.0
Longitudinal tensile strength (MPa) XT 2070
Longitudinal compressive strength (MPa) XC 1317
Transverse tensile strength (MPa) YT 61
Transverse compressive strength (MPa) YC 205
In-plane Shear strength (MPa) SC 112
Maximum matrix strain DFAILM 0.008
Maximum shear strain DFAILS 0.032
Maximum fiber tensile strain DFAILT 0.0168
Maximum fiber compressive strain DFAILC -0.012
Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
Figure 1. Adjusting SOFT parameters to obtain desired response in LS-DYNA simulations
(ref.9).
(a)
Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
(b) (c)
Figure 2 (a) A user defined contact penetration curve in LS-DYNA. Simulations without (b) and
with (c) the contact penetration curve (ref.9).
MAT161/162 (Composite MSC) is a user defined material model available in LS-DYNA with
additional license fee. MAT161/162 has been implemented for solid. Based on the principle of
Hashin failure criterion, MAT162 has 6 failure modes for laminate and 7 failure modes for fabric
composites. The strain rate dependence can also be considered. MAT162 is a damage mechanics
based model. The damage evolution law has an exponential form [6]
A unique feature of MAT162 is its options for element deletion. An element may erode by three
ways: (1) erosion by strain limit as in other models; (2) erosion by compressive relative volume
(ratio of current volume to initial volume); and (3) erosion by expansive relative volume. These
options provide more rational element deletion. MAT162 appear to be more stable in progressive
crash simulations.
1.2 PAM-CRASH
Johnson and Kohlgrüber used a bi-phase model in PAM-CRASH to simulate the crash behavior
of composite components for helicopters [11]. The bi-phase model appears to be a damage
mechanics model implemeted for shell. Its compliance matrix is given as
Figure 3 depicted the damage evolution law and the resulted stress-strain curve. Figure 4
presents a comparison of simulations with experiment.
)1(1
1
m
jre m
i
1212
221
12
1
12
11
)1(
100
0)1(
1
0)1(
1
Gd
EdE
EEd
S
Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
Figure 3 PAM-CRASH bi-phase model. The damage evolution law and the resulted stress-strain
curve.
Figure 4 Simulations using PAM-CRASH bi-phase model and experimental results [11].
Johnson et al have implemented Ladeveze’s composite damage mechanics model in PAM-
CRASH for shell [12] and incorporated cohesive interfaces to simulate delamination [13], Figure
5. The damage-plasticity model together with delamination modeling appeared to be inadequate
to model the axial crash cases in CMH-17 numerical round robin. To improve the correlation,
different triggers were used for composite components of different shapes [13], as shown in
Figure 6.
Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
Figure 5 Mesoscale modeling of delamination for crash simulation (Johnson, 2011).
Figure 6. Different triggers were used in the chamfer area in order to correlate with experimental
results (Johnson, 2011).
1.3 RADIOSS
The composite model that has been reported in crash simulations is COMPSH (25) [14,15].
Unlike any other composite models, COMPSH is based on an anisotropic plasticity framework
with Tsai-Wu criterion to define yield and work hardening, Figure 7. The model also employs a
set of linear damage laws to describe the softening response above the failure strain. It may
model either elastic failure or plastic failure, as shown in Figure 8. COMPSH is available for
both shell and solid. RADIOSS simulations tend to be more stable than those using other codes.
Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
Figure 7. RADIOSS COMPSH has a yield surface and work hardening defined by Tsai-Wu
criterion.
Figure 8. The stress-strain response described by RADIOSS COMPSH.
1.4 ABAQUS
ABAQUS Explicit has been used in crash simulations of composite components. Composite
material models are often in the form of VUMAT, user material model for explicit ABAQUS.
Examples are the micromechanics model for braided composites developed by Stanford (solid)
[16,17], and ABAQUS internal VUMAT for fabric reinforced composites (shell) [18]. Often
these models are proprietary.
Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
CZone [18], developed by Engenuity for crash simulations, is worth mentioning. CZone is an
add-on product with ABAQUS. Similar to the contact penetration in LS-DYNA, CZone is
defined at where a structure makes contact with rigid bodies or stiff structures. CZone allows an
element to pass through the contact zone with a constant crush stress before being eliminated
from the model, as illustrated in Figure 9. The crush stress is measurable using a special crush
test rig, as shown in Figure 10. CZone is very stable such that the crash response of a structure of
constant cross-section becomes a straight line, as shown in Figure 11.
Figure 9. CZone approach - element passes through the contact zone with a constant crush stress
before being eliminated from the model (ref.18).
Figure 10. The testing rig for CZone crash force calibration and some typical results (Ref.18).
Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
Figure 11. Crash force-displacement curves obtained by CZone simulations for six composite
components (ref.18).
In summary, crash simulations of composite components have been attempted with both
progressive failure models and damage mechanics based models. The recent development
appears to favor damage mechanics based models.
Constitutive models alone are not sufficient to model the progressive crash of composite
components. The element type is also important. The solid element representation allows a
volume of material being crashed as in reality but it is computational expensive. Shell elements
are highly efficient in representing the in-plane stretching and out-of-plane deformation but they
are inadequate under large in-plane compressive deformation. With shell, it is difficult to capture
the progressive failure behavior, particularly at the beginning of the crash. This presents a unique
challenge in composite component crash simulations. To simulate the progressive crash,
different triggering or softening mechanisms have been developed, such as the CZone, contact
penetration, SOFT parameter, and various ways to model the chamfer, etc. These interventions
are needed for the sake of simulations but some of them may not represent the real physics.
Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
2. Task 13.2 Select progressive crash models from public domain
Ladevèze model, also called Cachan model has been selected.
Cachan model, developed by the research group of Ladevèze at LMT Cachan, France [19-28], is
one of the most widely used approaches of continuum damage mechanics models for fiber
reinforced composites based on energy potentials. They introduced the concept of meso-model,
which contains two constituents: single-ply and the interface. Single plies are used to represent
intralaminar failure mechanisms (MDF and FF), while two-dimensional interfaces are used to
transmit tractions from one layer to the next, for the modeling of delamination. The state of
damage is uniform within each meso-constituent. [21, 29] Cachan model has been adopted by
several other authors [12, 30-33] and shows good agreement with experimental results.
Cachan model takes into account stiffness recovery and inelastic strains [29]. As shown by Xiao
[35], material models that do not take into account the plastic features of composites failures
might underestimate the energy absorption capacity of composite structures. Cachan model is
sufficient to describe the nonlinear or plastic behaviour that some thermoset or thermoplastic
composites might exhibit, especially under transverse and shear loading [30].
Unlike some other models that are only able to provide valuable insight into some particular
forms of damage, Cachan model are not limited to a specific loading and configuration. Phillips
et al. [31] demonstrated that Cachan model was able to predict damage regardless of fiber
orientations.
From a practical point of view, the difficulty of most damage models is to characterize a great
number of parameters needed to describe the damage behavior. All the parameters needed in the
elementary ply of a Cachan model can be measured by experiment as listed in ref [20]. Johnson
et al [14,15,32] used Cachan model to model the impact and crash behavior of fabric reinforced
composites and showed that the delamination modeling strategy works well.
Cachan model has been developed for more than 20 years. In some later work, it is extended to
consider additional phenomena, like damage in fiber direction in the same fashion as in other
directions, the influence of ply damage variables on out-of-plane moduli E3, G13, and G23
[22,23] and damage-delay in moderately dynamic analyses [28]. In order to get a better
understanding and prediction of fracture, the modified Cachan model is even able to connect the
micromechanics and mesomechanics of laminate composites [23].
Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
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Protected Rights Notice These Protected Data were produced with funding provided under agreement no. DE-EE0005397 with the U.S. Department of Energy and may not be published, disseminated, or disclosed to others outside the Government until five (5) years from the date Protected Data is produced, unless express written authorization is obtained from Plasan Carbon Composites, Inc. Upon expiration of the period of protection set forth in this Notice, the Government shall have unlimited rights in this data. This Notice shall be marked on any reproduction of this data, in whole or in part.
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