LS-DYNA MAT54 modeling of the axial crushing of
composite fabric channel and corrugated section specimens
Bonnie Wade*, Paolo Feraboli
Automobili Lamborghini Advanced Composite Structures Laboratory, Seattle, WA, 98119, United States
*Corresponding author. Tel.: +1 011 206 371 9363. Email: [email protected]
Mostafa Rassaian
Boeing Research & Technology, Seattle, WA, United States
Abstract
The LS-DYNA progressive failure material model MAT54 has previously been used to model both
unidirectional tape and fabric carbon fiber composite material systems in simulations of quasi-static crush
tests using a sinusoidal crush coupon. Experiments have shown that the cross-sectional geometry of
crush specimens has a significant influence on the energy absorption capability of composite laminates.
Using the modeling strategy from the sinusoidal crush simulation, crush experiments of seven different
channel and corrugated coupons are simulated using MAT54 to further evaluate the suitability of this
material model for crush simulation. Results show that MAT54 can successfully reproduce experimental
results of different crush geometries by calibrating only two parameters: the thickness of the crush trigger
elements and the MAT54 SOFT parameter. A linear trend exists between these two parameters, leaving a
single necessary parameter to calibrate the material model for crush simulation.
Keywords: A. Carbon fiber B. Impact behavior C. FEA
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1. Introduction
The behavior of composite materials under crash conditions poses particular challenges for engineering
analysis since it requires modeling beyond the elastic region and into failure initiation and propagation.
Crushing is the result of a combination of several failure mechanisms, such as matrix cracking and
splitting, delamination, fiber tensile fracture and compressive kinking, frond formation and bending, and
friction [1,2]. With today’s computational power it is not possible to capture all of these failure
mechanisms in a single analysis. Models based on lamina-level failure criteria have been used, although
with well-accepted limitations [3], to predict the onset of damage within laminate codes. Once failure
initiates, the mechanisms of failure propagation require reducing the material properties using several
degradation schemes [4]. To perform dynamic impact analysis, such as crash analysis, it is necessary to
utilize an explicit finite element code, which solves the equations of motion numerically by direct
integration using explicit rather than standard methods.
Commercially available codes used for
mainstream crash simulations include LS-DYNA, ABAQUS Explicit, RADIOSS and PAM-CRASH [5].
In general, these codes offer built-in material models for composites. Each material model utilizes a
different modeling strategy, which includes failure criterion, degradation scheme, material properties, and
usually a set of model-specific input parameters that are typically needed for the computation but do not
have an immediate physical meaning. Composites are modeled as orthotropic linear elastic materials
within the failure surface, whose shape depends on the failure criterion adopted in the model. Beyond the
failure surface, the appropriate elastic properties are degraded according to degradation laws.
Previous work by the authors has demonstrated the successful use of the built-in LS-DYNA progressive
failure material model MAT54 to simulate a unidirectional (UD) tape and a plain weave fabric carbon
fiber/epoxy material system in crush and impact simulations [6-8].
This material model is a good
candidate to simulate the dynamic crushing failure of large composite structures due to its relative
simplicity and reduced requirement of experimental input parameters compared to the limited number of
other damage mechanics material models. While successful, this modeling strategy is not truly predictive
2
and some modeling parameters need to be calibrated by trial and error. In particular, a crush front
strength reduction factor called SOFT is critical to the success of crush models and must be calibrated by
matching the simulated results to those of the experiment.
Experimental work has shown that the energy absorption capability of a composite material system is not
a constant material property, and that the cross-sectional geometry of a crush specimen greatly influences
energy absorption [9-11]. For the carbon fiber/epoxy fabric material system under investigation, quasistatic crush tests were performed on flat material coupons [12], three sinusoidal element geometries with
varying curvature [10], as well as five different tubular and channel section geometries [11]. Among
these different experiments, the specific energy absorption (SEA) of the fabric composite ranges from 2378 J/g, indicating that SEA is not a material constant. In this paper, the physical failure and damage
mechanisms which influence the SEA in different crush geometries will be briefly explored. This
information provides insight to better understand the energy absorption capability of composite materials.
The results of the element-level crush experiments will be used to develop a modeling strategy using
MAT54 to simulate the fabric composite material in crush failure for the eight different geometries. The
baseline geometry is a semi-circular sinusoid which has been investigated in previous publications by the
authors, and is the model from which new variant geometry simulations were generated. The discussion
will focus on the analysis approach and the sensitivity of the MAT54 material model to crush specimen
geometry.
2. Experiment
Detailed experimental crush tests results and specifications for the crush specimen design, manufacturing,
and testing procedure of the eight different crush geometries can be found in [10,11]. Composite tube
sections were manufactured using an aluminum square tubular mandrel with a vacuum bag and oven cure.
Five different channel section geometries were cut from the composite tube, and each cross-section with
dimensions is given in Fig. 1a-e. The corrugated specimens were manufactured by press-molding through
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a set of aluminum matching tools. Details and dimensions of the corrugated specimen geometries are
given in Fig. 2a-c. Each specimen featured a crush initiator, or trigger, which was a 45° single chamfer
on the outside edge as used in many studies to initiate crushing in self-stabilizing structures.
All
specimens were made from the same T700/2510 carbon fiber/epoxy prepreg plain weave fabric supplied
by Toray Composites of America. A summary of the material properties for this material system is
provided in Table 1. The fabric lay-up of the specimens was [(0/90)]4s, yielding an average cured
laminate thickness of 0.07286 in. (1.85 mm) for the vacuum bagged channel sections, and 0.065 in. (1.65
mm) for the press-molded sinusoids.
A minimum of four experimental repetitions were used to obtain average crush data for each geometry
investigated. A summary of the average measured SEA for each geometry is given in Table 2. Fig. 3a–c
shows typical curves for a single test in the following order: the load curve (a), the specific energy
absorption (b), and the total energy absorbed (c) as a function of displacement. The definitions of the
specific energy absorption (SEA) and total energy absorbed (EA) are given in [9]. For the analysis, an
entire representative load–displacement curve (initial slope, peak load, and average crush load) and its
corresponding SEA value were used as benchmarks to evaluate the simulations for all eight geometries.
The representative experimental curves for all eight geometries are shown in Figs. 4a-c. The SEA of each
representative experiment shown was used to calibrate the simulation, rather than the average SEA values
reported in Table 2, which were measured across several experiments as published in [10,11].
Experimental results from the channel section specimens have shown that for this fabric material system,
there is a linear relationship between the SEA and degree of curvature of a coupon, as shown in Fig. 5a
[11].
The higher the degree of curvature of a geometry (defined in [11]), the higher the SEA
measurement. For instance, the small corner features minimal flat segments and produced a relatively
high SEA. The flat flanges of the small corner were elongated to make the large corner, and as a
consequence the measured SEA was lower. When the corrugated elements were added to the trend, an
upper bound of SEA for this material system was shown to be around 75 J/g, Fig. 5b. This result showed
4
that more curvature in the cross-sectional geometry provides a better efficiency in crushing, and that a
threshold exits where increasing the amount of curvature no longer contributes to raising the energy
absorption capability.
In order to better understand the effect of curvature on crush failure, a micrographic analysis was
performed on different crushed specimens: one section taken from the curved sinusoidal specimen and
one section taken from the flat web of the c-channel, Fig. 6. A dye was used in the potting resin which
illuminated under black light and highlighted damaged areas. The differences of the damage and failure
mechanisms between the two geometries can clearly be seen in Fig. 7. The analysis shows that, in the
curved sections, most of the material remained intact and the damage region beyond the crush front was
very small, 0.19 in. (4.8 mm) in the section shown in Fig. 7. Micrographic analysis of the flat sections
revealed the extensive damage, delamination, and long cracks which reached 1.05 in. (26.7 mm) beyond
the crush front in the section shown in Fig. 7.
The micrographic results compliment the failure mechanisms observed in the crushed specimens, which
were noted to be very different between the curved and flat sections, evidenced in the post-failure images
in Fig. 6. The flat sections tended to splay open and the material split along deep cracks into delaminated
segments which bent away from one another. Corner and curved sections of the crush specimens tended
to demonstrate abundant fragmentation and tearing of the material.
These two distinct failure
mechanisms have been identified in previous studies to have different energy absorbing capacity [1,13],
although this difference has not been previously quantified in such a way as it is here. The delamination
failure mode of the flat sections absorbs very little energy as most of the material remains intact while a
large crack propagates between plies causing very little fiber breakage. The fragmentation observed at
the corners, however, absorbs a lot of energy in the process of breaking up the material, both fiber and
matrix, into pieces as small as dust particles. Specimen geometry plays a significant role in that curved
geometries suppress delamination and cracks cannot propagate through the material easily, forcing higher
loads and higher energy to fracture the material at shorter intervals. The greater the delamination
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suppression provided by the geometry, the higher the SEA. The amount of delamination suppression, and
subsequently SEA, can be estimated by considering the degree of curvature of the geometry.
From the element-level crush experiments and investigation completed, the range of energy absorption
capability of a specific carbon composite material system and lay-up has been described through the
development of a relationship between the geometric features of the crush specimen and its expected SEA.
This relationship cannot be derived from a single experimental test, and crush elements with different
degrees of curvature must be tested in order to fully characterize the energy absorbing capability of a
composite material system. This is an important experimental conclusion, as it can be expected that the
development of the composite material model to simulate such a range of crush failure will require some
degree of calibration to match the differing element-level experimental results.
3. The MAT54 material model and previous crush simulation findings
A detailed description of the LS-DYNA MAT54 material model and each of its parameters was
developed during an in-depth single element investigation presented in [14]. Definitions of the MAT54
input parameters are reproduced in Table 3. Beyond the elastic region MAT54 uses four mode-based
failure criteria based on Hashin [15] to determine individual ply failure. There is a criterion for each the
tensile and compressive loading case in both the fiber and matrix (axial and transverse) directions. When
one of the criteria is violated in a ply within an element, specific elastic properties of that ply are set to
zero and the stress remains at the value achieved at failure rather than becoming zero. Thus, the strain
energy maintained by a failed element can be very high. The failed ply remains at a constant stress state
until a user defined failure strain (DFAILT, DFAILC, DFAILM, and DFAILS in Table 3) is achieved and
the ply is deleted, at which point stresses are zero. Ply and element deletion are governed by these
maximum strain parameters rather than the stress-based failure criteria, and it has been shown that these
strain parameters have a great effect on the outcome and stability of simulations utilizing MAT54 [6-8,14].
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The MAT54 model for this particular fabric material system requires that the transverse failure strain,
DFAILM, be artificially increased by a factor of four to achieve stable results [7,8]. This is likely a
consequence of using MAT54, which is designed specifically for unidirectional tape laminates that
experience large nonlinear behavior in the transverse direction, to model a fabric material system. For a
fabric material system both the axial and transverse properties are fiber-dominated, and the transverse
strain-to-failure is smaller than that of a unidirectional tape.
Results from crush simulations of sinusoid specimens show that the average crush load and corresponding
SEA value are highly sensitive to the MAT54 SOFT parameter. By itself, this parameter is capable of
dictating whether the simulation is stable or unstable. It can also shift the average crush load above or
below the baseline by at least 30%. This parameter is meant to artificially reduce the strength of the row
of elements immediately ahead of the active crush front. It is a mathematical expedient which allows for
stable crush propagation and inhibits global buckling of the specimen by preventing large peaks in stress.
In the physical world, one could interpret the SOFT parameter as the damage zone ahead of the crush
front, comprised of delaminations and cracks, which reduces the strength of the material. The greater the
physical damage zone observed in an experimental crush specimen, the more the SOFT parameter should
reduce the strength of the simulated material. While this physical interpretation can be made, the SOFT
parameter is not a material property and cannot be directly measured experimentally. It must be found by
trial and error until the load-displacement curve of the crush simulation matches the experimental result.
The average crush load of the sinusoid model was also sensitive to compressive material parameters such
as the compressive fiber strength, XC, failure strain, DFAILC, and compressive matrix strength, YC. For
these MAT54 input parameters, the measured experimental values produced a stable crush simulation of
the sinusoid which matched the experiment.
Outside of the MAT54 material definition, model parameters which influenced the crush model results
included the thickness of the trigger elements and the stiffness of the contact load-penetration (LP) curve.
The trigger element thickness directly affected the initial peak load of the simulation, where a thicker
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trigger caused a higher initial load peak. This parameter could be calibrated such that the initial peak load
of the crush simulation matched that of the experiment. The contact LP curve defines the reaction loads
at the contact surface with respect to contact penetration. LP curves which produced stable crush
simulations were piecewise linear curves with three segments of increasing slope. A very stiff LP curve,
which introduces high loads into the element within a short displacement, can cause global buckling.
Reducing the stiffness and magnitude of the piecewise LP curve can prevent such global buckling.
4. Simulation of other fabric crush specimens
The variation in SEA experimentally measured from the different crush elements is directly dependent
upon the different failure mechanisms experienced, and it is the goal of this numerical investigation to
determine the best way to represent such changes in the simulated crush models.
Following the
parametric investigation of the sinusoid crush element simulations [7], several new crush elements are
simulated using the MAT54 fabric material model. The new crush elements are the seven geometries,
five channel variants and two additional sinusoids, which were experimentally crush tested. The eight
geometry models (including the baseline semi-circular sinusoid) are shown in Fig. 8. The modeling
strategy developed for the fabric semi-circular sinusoid crush element, including mesh size, contact
definition, boundary conditions, material card, etc.; is used as a template to model the seven new
geometries. The nominal dimensions for the channel and sinusoidal specimens are given in Fig. 1-2.
The crush models are comprised of single 0.1 x 0.1 in. (2.54 x 2.54 mm) fully-integrated shell (2D)
elements, which simulate a composite laminate by regarding each lamina through the thickness as an
integration point. A single row of reduced thickness elements at the crush front of the specimen simulates
the crush trigger. Unfortunately, the very failure mechanisms which differentiate the energy absorbing
capability of the different crush elements (e.g. delamination) cannot be directly simulated using this single
shell element approach developed for the sinusoid crush simulations. Without the capability to simulate
delamination, it is expected that simulating different geometries requires changes in the material model
itself even though the material remains constant throughout this investigation.
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The baseline MAT54 input deck for the fabric material model is given in Fig. 9. The baseline MAT54
parameter values were derived from the material properties of the fabric material system given in Table 1,
with the exception of the DFAILM parameter which was artificially increased for stability of the sinusoid
crush model. From the sinusoid crush model all modeling definitions remained the same and only the
geometry was changed. For the square tube element, the change of geometry caused a failure at crush
initiation where several elements were eroded away from the crush front at very high loads, which
directly led to global buckling, Fig. 10. Similar results were obtained from modeling each of the other
seven geometries directly from the baseline sinusoid model. By simply changing the geometry, the crush
simulations of the new shapes are not successful; however this result is not unexpected since the different
energy absorbing failure mechanisms cannot be individually modeled using the current approach. The
continued systematic investigation is focused to discover the best method to simulate the change in SEA
due to change in geometry using the modeling parameters that most influence stability and SEA, as
discovered in the parametric studies of the crush model.
First, the modeling parameters which influence SEA are investigated to discover if the crushing loads can
be reduced enough to achieve stability and the correct simulated SEA. With the intent to reduce the crush
loads, the MAT54 parameters SOFT, DFAILC, and XC are reduced, without acceptable success. It is
observed that the crush models of all of the tubular, channel, and corner geometries are too unstable to
appropriately alter the crushing load without experiencing global failures, such as that shown in Fig. 10.
Next, parameters which influence stability are investigated with the goal to reduce variability and
promote stability such that changes can be made to lower the crushing load. To promote stability,
DFAILS, SC, and YCFAC are raised, in conjunction with lowering the SEA-influencing parameters
DFAILC, XC, and SOFT. All such efforts which have contained changes within the MAT54 card are
unable to provide a significant improvement in the model stability. Finally, the LP curve at the contact is
altered in order to promote stability. A softer contact LP curve, Figure 11, was used to soften the
introduction of the reaction forces transmitted into the crush specimens. This is the same LP curve as was
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featured in the fabric sinusoid crush parametric study in [7]. Implementing only this change in the contact
definition LP curve and applying the baseline sinusoid material model to seven new geometries did not
yield immediate success, as shown in Fig. 12.
While initial results were unstable, changes to the SOFT parameter and the trigger thickness in
combination with the new LP curve generated positive results. Noting from Fig. 12c that failure of the
square tube occurs at the initial load peak, the trigger thickness in this simulation was reduced to 0.011 in.
(0.28 mm) to prevent early failure and enable crush initiation. With a softer LP curve and a lower trigger
thickness, the SOFT parameter was calibrated to a value of 0.145 such that the average crush load
matched that of the experiment, shown in Fig. 13. The trigger thickness was then calibrated to a value of
0.015 in. (0.38 mm) to match the initial load peak of the experimental curve, Fig.. 14. The shape of the
resulting load-displacement curve, initial peak load value, crush load value, and SEA value matched the
experimental results well, Fig. 15, the tube crush baseline simulation. The crush progression, Fig. 16, was
smooth as elements were deleted simultaneously row by row at the crush front.
From the development of the square tube crush simulation, three parameters were discovered to require
adjustment when changing the geometry of the crush specimen from the sinusoid to the tube: the LP
curve for stability, the SOFT value to calibrate the crush load and SEA, and the trigger thickness to
calibrate the initial load peak value. Rather than calibrate the LP curve for each new geometry, the soft
LP curve was used for all of the crush simulations, including the original baseline semi-circular sinusoid
crush model which was retroactively updated to have the new LP curve. In this way, only two parameters,
SOFT and trigger thickness, were necessary to calibrate when changing the geometry of the crush
specimen.
The successful tube crush simulation was modified to simulate each of the remaining seven geometries.
After inserting these specimens into the crush simulation, the SOFT parameter and trigger thickness were
each calibrated in order to match the experimental crush curve. By making only these two changes, all
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geometries were successfully simulated in crush. Crush curves of the LS-DYNA simulations calibrated
to match the experimental load-displacement curves of the seven new geometries (excluding the square
tube, shown in Fig. 15) are shown in Fig. 17. The calibrated SOFT and trigger thickness parameters used
in all eight cases are given in Table 4, along with the simulated SEA results and errors.
5. Discussion
As a result of this investigation, it is possible to generate relations between experimental data and
modeling parameters which would allow crush modeling of various geometries from an initial calibrated
crush model. First, the linear relation between the calibrated SOFT parameter and the experimentally
measured SEA is revealed in their plot, Fig. 18. The SOFT parameter can be interpreted as a utility to
account for the virtual damage that has propagated beyond the crush front. Fig. 18 shows that greater
values of SOFT yield higher SEA in the simulation. The micrographic analysis of crushed specimens
from sections with varying SEA capability, Fig. 7, indicates that the greater the damaged area, the smaller
the SEA. This provides a new interpretation of the SOFT parameter as the degree of damage suppression
provided by the geometry, thickness, lay-up, and material system. Since the thickness, lay-up, and
material system remained constant, in this study we perceive the SOFT parameter as the degree of
damage suppression provided by the geometry of the crush specimen. The higher the SOFT value is, the
higher the crush damage suppression and SEA will be. This relationship provides a link between an
experimental measurement, SEA, and one of the modeling parameters which requires calibration when
the SEA changes, SOFT.
The only other modeling parameter which requires calibration when the geometry (and SEA) of the crush
element changes is the trigger thickness. The thickness of the trigger elements is reduced to facilitate
crush initiation, and the reduced cross-section of the trigger elements ensures these elements fail at a
lower applied force than the full thickness elements. In this way, the trigger thickness is a strength
knockdown factor for the initial row of elements, which are not subject to the SOFT knock-down since
the crush front is established only after failure of the initial element row. Plotting the calibrated SOFT
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against the ratio of the reduced trigger thickness to the total element thickness generates another linear
relationship, Fig. 19. The fact that this linear relationship is nearly 1:1 suggests that the trigger row of
elements has nearly the same strength knockdown, by virtue of reducing the cross-sectional area, as that
which was applied by SOFT to the rest of the elements. This implies that the correct trigger thickness
value can be determined from the calibrated SOFT, and that changing the geometry of the crush element
only is dependent on only a single variable.
For this fabric material system, if the average experimental SEA for a given crush geometry is known, the
calibrated values of SOFT and trigger thickness can be estimated which will produce a fair simulated
crush curve and SEA. This approach is not predictive, but can provide a good starting point for trial-anderror model calibration that is near the solution which best matches the experimental results.
Since these simulations are not predictive, a structural crush specimen at this level of complexity should
be interpreted as an element-level test, from which the analysis model can be successfully calibrated for
each material system. It is expected that the material model is fully calibrated following the calibration at
the element level of structural complexity, and it is suitable to use in models of higher levels of
complexity. For every crash element with a different thickness, geometry, or lay-up, additional elementlevel testing and model calibration is required.
6. Conclusions
It has been shown that the energy absorbing capability of a carbon fiber/epoxy crush specimen is strongly
influenced by specimen geometry due to the amount of damage propagation suppression provided by the
curvature of the specimen geometry. Using the existing MAT54 material model, several simulations of
crush elements with various cross-sectional geometries have been successfully calibrated to match the
experimental results well. In this MAT54 crush modeling approach it is not possible to simulate different
specimen geometries without making changes to the material model since specific damage and failure
mechanisms (such as delamination) cannot be modeled individually. Some relationships have been
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established which link experimental parameters (SEA) to important modeling parameters (SOFT, trigger
thickness), thus greatly reducing scope of, and providing guidance to the trial and error calibration
process.
Ultimately, this modeling approach requires a comprehensive set of experimental element-level
crush data which fully characterizes the energy absorbing capability of the composite material system
such that trial-and-error calibration of the SOFT parameter can be executed to develop a good crush
model.
7. Acknowledgements
The research was performed at the Automobili Lamborghini Advanced Composite Structures Laboratory
(ACSL) at the University of Washington. Funding for this research was provided by the Federal Aviation
Administration (Dr. Larry Ilcewicz, Allan Abramowitz, Joseph Pellettiere, and Curt Davies), The Boeing
Company (Dr. Mostafa Rassaian and Kevin Davis), and Automobili Lamborghini S.p.A. (Maurizio
Reggiani, Luciano DeOto, Attilio Masini).
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8. References
[1]
Carruthers JJ, Kettle AP, Robinson AM. Energy absorption capability and crashworthiness of
composite material structure: a review. Applied Mechanics Reviews 1998; 51:635-49.
[2]
Farley GL, Jones RM. Crushing characteristics of continuous fiber-reinforced composite tubes.
Journal of Composite Materials 1992; 26(1):37-50.
[3]
Hinton MJ, Kaddour AS, Soden PD. A comparison of the predictive capabilities of current
failure theories for composite laminates, judged against experimental evidence. Composite
Science and Technology 2002;62(12-13):1725-97.
[4]
Xiao X. Modeling energy absorption with a damage mechanics based composite material
model. Journal of Composite Materials 2009;43(5):427-44.
[5]
Feraboli P, Rassaian M. Proceedings of the CMH-17 (MIL-HDBK-17) Crashworthiness
Working Group Numerical Round Robin, Costa Mesa, CA, July 2010.
[6]
Feraboli P, Wade B, Deleo F, Rassaian M, Higgins M, Byar A. LS-DYNA MAT54 modeling
of the axial crushing of a composite tape sinusoidal specimen. Composites: Part A, 2011;
42:1809-25.
[7]
Wade B, Feraboli P, Rassaian M. LS-DYNA MAT54 modeling of the axial crushing of a
composite fabric sinusoidal specimen. Composites: Part A, in review, September 2013.
[8]
Feraboli P, Deleo F, Wade B, Rassaian M, Higgins M, Byar A, Reggiani M, Bonfatti A, DeOto
L, Masini A. Predictive modeling of an energy-absorbing sandwich structural concept using
the building block approach. Composites: Part A, 2010; 41:774-786.
[9]
Farley GL, Jones RM. Analogy for the effect of material and geometrical variables on energyabsorption capability of composite tubes. Journal of Composite Materials 1992; 26(1): 78-89.
[10] Feraboli P. Development of a corrugated test specimen for composite materials energy
absorption. Journal of Composite Materials 2008;42(3):229-56.
[11] Feraboli P, Wade B, Deleo F, Rassaian M. Crush energy absorption of composite channel
section specimens. Composites: Part A, 2009; 40:1248-1256.
[12] Feraboli P. Development of a modified flat plate test and fixture specimen for composite
materials crush energy absorption. Journal of Composite Materials, 2009; 43:1967-1990.
[13] Hull, D. A unified approach to progressive crushing in fibre reinforced composite tubes.
Composite Science and Technology, 1991; 40:337-422.
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[14] Wade B, Feraboli P, Osborne M, Rassaian M. Simulating laminated composite materials using
LS-DYNA material model MAT54: Single element investigation. FAA Technical Report
DOT/FAA/AR-xx/xx, in review, September 2013.
[15] Hashin Z. Failure criteria for unidirectional fiber composites. Journal of Applied Mechanics
1980; 47: 329-334.
[16] T700SC 12K/2510 Plain Weave Fabric. Composite Materials Handbook (CMH-17), Vol. 3.
Rev G.
15
9. Tables and Figures
Table 1. Material properties of T700/2510 plain weave fabric as published in the CMH-17 [16]
Property
Symbol LS-DYNA Experimental value
parameter
Density
ρ
RO
1.52 g/cc
Modulus in 1-direction E1
EA
8.09 Msi
Modulus in 2-direction E2
EB
7.96 Msi
Shear modulus
G12
GAB
0.609 Msi
Major Poisson’s ratio
v12
0.043
Minor Poisson’s ratio
v21
PRBA
0.043
Strength in 1-direction,
XT
132 ksi
tension
Strength in 2-direction,
YT
112 ksi
tension
Strength in 1-direction,
XC
103 ksi
compression
Strength in 2-direction,
YC
102 ksi
compression
Shear strength
SC
19.0 ksi
Table 2. Average SEA results of the fabric material system from each of the eight geometries crush tested,
in addition to the flat material coupon [12]
Geometry
Average SEA
[J/g]
Flat coupon
23
Semi-circular sinusoid
78
High sinusoid
76
Low sinusoid
70
Square tube
37
Large corner
32
Small corner
62
Large c-channel
37
Small c-channel
43
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Table 3. MAT54 input parameter definitions.
Name
Definition
Material identification number
MID
Mass per unit volume
RO
Axial Young’s modulus
EA
Transverse Young’s modulus
EB
Through-thickness Young’s modulus
EC
Type
Measurement
Computational
N/A
Experimental
Density test
Experimental
0-deg tension test
Experimental
90-deg tension test
(Inactive)
0-deg tension test with biaxial strain
measurement
PRBA
Minor Poisson’s ratio v21
Experimental
PRCA
PRCB
GAB
GBC
GCA
KF
Minor Poisson’s ratio v31
(Inactive)
Major Poisson’s ratio v12
(Inactive)
Shear modulus G12
Experimental
Shear modulus G23
(Inactive)
Shear modulus G31
(Inactive)
Bulk modulus
(Inactive)
AOPT
XP,YP,ZP
A1,A2,A3
MANGLE
V1,V2,V3
D1,D2,D3
Local material axes option
Computational
Used for AOPT = 1
(Inactive)
Vector ‘a’ used for AOPT = 2
Computational
N/A
Angle used for AOPT = 3
Computational
N/A
Vector used for AOPT = 3
Computational
N/A
Used for AOPT = 2, solid elements
(Inactive)
Elastic shear stress non-linear factor
Shear factor in tensile axial failure
criterion
Shear factor
None; Default 0.1 recommended
Shear factor
None; Default 0.5 recommended
DFAILT
DFAILC
Axial tensile failure strain
Experimental
0-deg tension test
Axial compressive failure strain
Experimental
DFAILM
Transverse failure strain
Experimental
DFAILS
EFS
TFAIL
Shear failure strain
Effective failure strain
Experimental
Optional
0-deg compression test
90-degree tension and compression
tests;
May require adjustment for stability
Shear test
Combination of standard tests
Time step failure value
Axial tensile strength factor after 2dir failure
Material strength factor after
crushing failure
Axial compressive strength factor
after 2-dir failure
Axial tensile strength
Computational
Derived from numeric time-step
Damage factor
None; Default 0.5 recommended
Damage factor
None; Requires calibration
Damage factor
None; Default 1.2 recommended
Experimental
0-deg tension test
Axial compressive strength
Experimental
0-deg compression test
Transverse tensile strength
Experimental
90-degree tension test
Transverse compressive strength
Experimental
90-degree compression test
Shear strength
Experimental
Shear test
Specification of failure criterion
Computational
N/A; Requires value of 54 for MAT54
ALPH
BETA
FBRT
SOFT
YCFAC
XT
XC
YT
YC
SC
CRIT
17
Shear test
N/A
Table 4. Summary of modeling parameters varied for each geometry to match the experimental curves
shown in Figs. 8 and 10a-g.
Geometry
Trigger
Thickness [in]
SOFT
Single Test
SEA [J/g]
Numeric SEA
[J/g]
Error
SC Sinusoid
High Sinusoid
Low Sinusoid
Tube
Large Channel
Small Channel
Large Corner
Small Corner
0.044
0.045
0.040
0.015
0.021
0.023
0.022
0.030
0.580
0.540
0.450
0.145
0.215
0.220
0.205
0.310
88.98
77.84
75.01
34.55
28.93
42.49
33.71
62.11
89.08
77.28
74.13
34.99
28.33
42.49
33.43
62.44
0.1%
-0.7%
-1.2%
1.3%
-2.1%
0.0%
-0.8%
0.5%
18
I. Tube
IV. Small Corner
II. Large Channel
III. Small Channel
V. Large Corner
Figure 1. Sketch of cross-section shape and dimensions for the five specimens considered.
19
(a)
(b)
(c)
Figure 2a-c. Detailed geometry of the (a) low sinusoid, (b) high sinusoid, and (c) semi-circular sinusoid
crush specimens
20
8000
7000
Load [lb]
6000
5000
4000
3000
2000
1000
0
0
0.5
(a)
1
1.5
Displacement [in]
2
2.5
2
2.5
2
2.5
40
35
SEA [J/g]
30
25
20
15
10
5
0
0
0.5
(b)
1
1.5
Displacement [in]
1600
1400
EA [J]
1200
1000
800
600
400
200
0
0
(c)
0.5
1
1.5
Displacement [in]
Figure 3. Experimental load (a), specific energy absorption (b), and energy absorbed (c) as a function of
displacement from a representative tube crushing experiment.
21
6000
SC Sine
Load [lb]
5000
High Sine
Low Sine
4000
3000
2000
1000
0
0
0.5
(a)
1
1.5
Displacement [in]
2
2.5
8000
7000
Load [lb]
6000
5000
Tube
4000
Lg. Corner
3000
Sm. Corner
2000
1000
0
0
(b)
0.25 0.5 0.75 1 1.25 1.5 1.75
Displacement [in]
6000
Lg. Channel
Load [lb]
5000
Sm. Channel
4000
3000
2000
1000
0
0
(c)
0.5
1
1.5
2
Displacement [in]
2.5
Figure. 4a-c. Representative experimental load-displacement curves for the eight crush geometries,
separated into three plots for clarity.
22
70
90
IV
60
80
70
40
II
30
20
I
SEA [J/g]
SEA [J/g]
50
III
V
50
40
30
flat
10
20
Tubular
10
Corrugated
0
0
0
(a)
60
0.1
0.2
Degree of Curvature, φ
0
0.3
(b)
0.2
0.4
0.6
0.8
Degree of Curvature, φ
1
Figure 5a-b. Experimental SEA vs. degree of curvature relationship of the flat material coupon with (a)
the five tubular shapes I-V represented in Figure 1, and (b) all eight geometries represented in Figures 1-2.
A
A
A
A
B
B
B
B
Figure 6. The micrographic section used to study the curved crush coupon, section A-A, and the flat crush
coupon, section B-B.
23
(a)
(b)
Figure 7. Micrographic analysis of the (a) curved and (b) flat specimens, showing the length of damage
propagation from the crush front.
24
(a)
(b)
(c)
(d)
(f)
(e)
(g)
(h)
Figure 8a-h. Eight LS-DYNA crush specimen models with different geometries: (a) semi-circular
sinusoid, (b) high sinusoid, (c) low sinusoid, (d) tube, (e) large c-channel, (f) small c-channel, (g) large
corner, and (h) small corner.
25
Figure 9. Baseline MAT54 input deck for the fabric material model with DFAILM and SOFT values
calibrated to generate a good match with the crush experiment of the semi-circular sinusoid.
Simulation
Tube
Experiment
25000
Load [lb]
20000
15000
10000
5000
0
0
1
2
3
Displacement [in]
Figure 10. Simulated load-displacement crush curve and simulation morphology from changing only the
specimen geometry from the sinusoid baseline to that of the tube element.
26
Original LP curve
New LP curve
5000
Load [lb]
4000
3000
2000
1000
0
0
0.1
0.2
Penetration [in]
0.3
Figure 11. Original and new Load-Penetration curves defined in the contact deck.
(a)
8000
Experiment
Simulation
Load [lb]
6000
4000
2000
0
0
0.5
1
1.5
Displacement [in]
2
2.5
27
(b)
6000
Experiment
Simulation
Load [lb]
5000
4000
3000
2000
1000
0
0
0.5
1
1.5
2
Displacement [in]
2.5
(c)
25000
Experiment
Simulation
Load [lb]
20000
15000
10000
5000
0
0
0.5
1
1.5
2
Displacement [in]
2.5
28
(d)
12000
Experiment
Simulation
Load [lb]
9000
6000
3000
0
0
0.5
1
1.5
2
Displacement [in]
2.5
(e)
10000
Experiment
Simulation
Load [lb]
8000
6000
4000
2000
0
0
0.5
1
1.5
2
Displacement [in]
2.5
29
(f)
10000
Experiment
Simulation
Load [lb]
8000
6000
4000
2000
0
0
0.5
1
1.5
2
Displacement [in]
2.5
(g)
2500
Experiment
Simulation
Load [lb]
2000
1500
1000
500
0
0
0.5
1
1.5
2
Displacement [in]
2.5
Figure 12. Undesired crush simulation results compared against the experimental curve when only the
geometry is changed from the semi-circular sinusoid baseline model: (a) high sinusoid, (b) low sinusoid,
(c) square tube, (d) large c-channel, (e) small c-channel, (f) large corner, and (e) small corner elements.
30
20000
18000
16000
Experiment
12000
SOFT = 0.58
10000
SOFT = 0.2
Load [lb]
14000
SOFT = 0.145
8000
SOFT = 0.1
6000
SOFT = 0.05
4000
2000
0
0 0.25 0.5 0.75 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Displacement [in]
Figure 13. SOFT parameter calibration of the tube simulation using new contact LP curve.
10000
Load [lb]
8000
t = 0.016
t = 0.015
t = 0.013
t = 0.011
Experiment
6000
4000
Load [lb]
8000
10000
6000
4000
2000
2000
0
0
0
0.5
1
1.5
2
2.5
Displacement [in]
0
3
0.25
0.5
Displacement [in]
Figure 14. Trigger thickness calibration of the tube simulation using new contact LP curve.
31
9000
Experiment, SEA = 34.55 J/g
Simulation, SEA = 34.99 J/g
8000
7000
Load [lb]
6000
5000
4000
3000
2000
1000
0
0
0.25 0.5 0.75
1
1.25 1.5 1.75 2
Displacement [in]
2.25 2.5 2.75
3
Figure 15. Load-displacement curves from simulation and experiment of the tube specimen crush.
[d = 0.00 in]
[d = 0.30 in]
[d = 0.60 in]
[d = 0.90 in]
[d = 1.20 in]
[d = 1.50 in]
Figure 16. Time progression of the crushing simulation of the square tube baseline.
32
6000
Experiment, SEA = 89.0 J/g
Simulation, SEA = 89.1 J/g
5000
Load [lb]
4000
3000
2000
1000
0
0
0.5
(a)
1
1.5
Displacement [in]
2
2.5
6000
Experiment, SEA = 77.84 J/g
Simulation, SEA = 77.28
5000
Load [lb]
4000
3000
2000
1000
0
0
0.5
(b)
1
1.5
Displacement [in]
2
2.5
6000
Experiment, SEA = 75.01 J/g
Simulation, SEA = 74.13 J/g
5000
Load [lb]
4000
3000
2000
1000
0
0
(c)
0.5
1
1.5
Displacement [in]
33
2
2.5
6000
Experiment, SEA = 28.93 J/g
Simulation, SEA = 28.33 J/g
5000
Load [lb]
4000
3000
2000
1000
0
0
0.5
(d)
1
1.5
Displacement [in]
2
2.5
6000
Experiment, SEA = 42.95 J/g
Simulation, SEA = 42.50 J/g
5000
Load [lb]
4000
3000
2000
1000
0
0
0.5
(e)
1
1.5
Displacement [in]
2
2.5
6000
Experiment, SEA = 33.71 J/g
Simulation, SEA = 34.31 J/g
5000
Load [lb]
4000
3000
2000
1000
0
0
(f)
0.5
1
1.5
Displacement [in]
34
2
2.5
6000
Experiment, SEA = 62.11 J/g
Simulation, SEA = 62.44 J/g
5000
Load [lb]
4000
3000
2000
1000
0
0
0.5
(g)
1
1.5
Displacement [in]
2
2.5
Figure 17a-g. Load-displacement crush curve results comparing simulation with experiment for seven
crush specimen geometries: (a) semi-circular sinusoid, (b) high sinusoid, (c) low sinusoid, (d) large cchannel, (e) small c-channel, (f) large corner, and (g) small corner.
140
y = 134.13x + 10.77
R² = 0.92
120
SEA [J/g]
100
80
60
40
20
0
0
0.2
0.4
0.6
0.8
1
SOFT
Figure 18. Linear trend between calibrated MAT54 SOFT parameter and the experimental SEA.
35
1
Trigger thickness/total thickness
y = 0.94x + 0.10
R² = 0.98
0.8
0.6
0.4
0.2
0
0
0.2
0.4
0.6
0.8
1
SOFT
Figure 19. Linear trend between the calibrated SOFT parameter and the ratio of trigger thickness to
original thickness.
36
37