2011-JCOMA-lsdyna-sinusoid

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LS-DYNA MAT54 modeling of the axial crushing of a composite tape

sinusoidal specimen

Paolo Feraboli a,, Bonnie Wade a, Francesco Deleo a, Mostafa Rassaian b, Mark Higgins b, Alan Byar b

aAutomobili Lamborghini Advanced Composite Structures Laboratory, Dept. of Aeronautics & Astronautics, University of Washington, Seattle, WA 98195-2400, United Statesb Crashworthiness and Impact Survivability, Applied Structural Methods, Boeing Research & Technology, Seattle, WA, United States

a r t i c l e i n f o

Article history:

Received 30 April 2011

Received in revised form 30 July 2011

Accepted 8 August 2011

Available online 16 August 2011

Keywords:

Crashworthiness

A. Carbon fiber

B. Impact behavior

C. FEA

a b s t r a c t

Thesuitability of a progressive failure material model to simulate the quasi-static crushing of a composite

specimen is evaluated. The commercially available material model MAT54 Enhanced Composite Dam-

age in LS-DYNA is often utilized to simulate damage progression in dynamic failure simulations because

it requires a reduced number of experimental input parameters compared to damage mechanics-based

material models. The composite specimen used for the experiments is a semi-circular sinusoid, and is

comprised of carbon fiber/epoxy unidirectional prepreg tape. Results show that MAT54 can successfully

reproduce experimental results, however the simulation is highly sensitive to changes in model param-

eters, which are either non-physical (i.e. are purely mathematical expedients), or cannot be measured

experimentally. These include element size, contact definition, loadpenetration curve, and crush front

softening parameter, among others. Therefore, achieving successful simulation results requires extensive

calibration of these parameters by trial and error, and a deep understanding of the strengths and chal-

lenges of the selected modeling strategy.

2011 Elsevier Ltd. All rights reserved.

1. Introduction

The behavior of composite materials under crash conditions

poses particular challenges for engineering analysis since it re-

quires modeling beyond the elastic region and into failure initia-

tion 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 todays computa-

tional power it is not possible to capture all of these failure mech-

anisms 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 inte-

gration using explicit rather than standard methods, for example

using the central difference method [4]. 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 mean-

ing. Composites are modeled as orthotropic linear elastic materials

within the failure surface, whose shape depends on the failure cri-

terion adopted in the model [4]. Beyond the failure surface, the

appropriate elastic properties are degraded according to degrada-

tion laws. Depending upon the specific degradation law used, the

constitutive models can be divided into either progressive failure

models (PFM) or continuum damage mechanics models (CDM).

The commercial software package LS-DYNA [6] offers a variety of

material models for composite materials, which include both

PFM (MAT22 and MAT54/55) and CDM (MAT58 and MAT162).

The failure criteria for laminated composites in PFM are typically

strength-based, and use a ply discount method to degrade material

properties. At the failure surface, the values of the appropriate elas-

tic properties of the ply in the material direction are degraded from

the undamaged state, which is 1, to the fully damaged state, which

is typically 0. The material model stressstrain curve does not

require that a specific unloading/softening curve be assigned, and

after the strength of the ply is exceeded the properties are imme-

diately dropped to zero. The so-called progressive failure is

realized through ply-by-ply failure within the laminate, and once

all plies have failed the element is deleted [6].

1359-835X/$ - see front matter 2011 Elsevier Ltd. All rights reserved.doi:10.1016/j.compositesa.2011.08.004

Corresponding author. Tel.: +1 011 206 543 2170; fax: +1 011 206 543 0217.

E-mail address: [email protected] (P. Feraboli).

Composites: Part A 42 (2011) 18091825

Contents lists available at SciVerse ScienceDirect

Composites: Part A

j o u r n a l h o m e p a g e : w w w . e l s e v i e r . c o m / l o c a t e / c o m p o s i t e s a
http://dx.doi.org/10.1016/j.compositesa.2011.08.004mailto:[email protected]://dx.doi.org/10.1016/j.compositesa.2011.08.004http://www.sciencedirect.com/science/journal/1359835Xhttp://www.elsevier.com/locate/compositesahttp://www.elsevier.com/locate/compositesahttp://www.sciencedirect.com/science/journal/1359835Xhttp://dx.doi.org/10.1016/j.compositesa.2011.08.004mailto:[email protected]://dx.doi.org/10.1016/j.compositesa.2011.08.004


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In this paper, the quasi-static energy absorption achieved

through crushing of a composite specimen, consisting of a semi-

circular sinusoid and manufactured with carbon fiber/epoxy unidi-

rectional prepreg tape, is modeled using the PFM material model

MAT54 in LS-DYNA. Details of the specimen design, manufacturing,

and testing procedure have been previously published by the

authors in [7]. The sinusoidal geometry is desirable from a model-

ing standpoint because it is self-stabilizing, i.e. it does not require

potting or a support fixture to prevent buckling during crushing, as

does a flat plate specimen [8], and because it does not have hoop-

fiber constraint, such as a tubular specimen [2,9]. The focus of the

discussion is centered on the analysis approach, and the sensitivity

of the model to parametric variations. Results show that while

MAT54 can be used to successfully simulate the experiment, the

modeling strategy is not truly predictive and several modeling

parameters need to be calibrated by trial and error.

2. Experiment

Specimens are manufactured by press-molding through a set of

aluminum matching tools, and details are given in [7]. The sinusoi-

dal specimen features a semicircular segment, of radius 6.4 mm(0.25 in.), repeated three times at alternating sides with respect

to the midplane, Fig. 1a. The material system is T700 carbon

fiber/2510 epoxy prepreg, supplied by Toray Composites of

America. It is a unidirectional tape 12 k tow, and a 270 F cure resin

(132 C) designated for autoclave or oven-only cure. The lay-up is

[0/90]3s, yielding an average cured laminate thickness of 0.079 in.

(2.0 mm). This material is used extensively for General Aviation

primary structures, and its properties are well documented as part

of the FAA-sponsored AGATE Program (Advanced General Aviation

Transport Experiment) [10,11]. A summary of the material proper-

ties is provided in Table 1. The upper end of the corrugated speci-

men is machined with a single-sided 45 chamfer to favor the

initiation of stable crushing at the chosen end of the specimen,

and to avoid undesired initial spikes in crush loads which may lead

to specimen instability [7]. This chamfer is known as the trigger, or

crush initiator, and is shown in Fig. 1b. Specimens are tested in the

vertical configuration, resting on a polished hardened steel surface,

at a crosshead velocity of 1 in./min (25.4 mm/min.). Seven repeti-

tions are used to obtain average data. Fig. 2ac 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 en-

ergy absorption (SEA) and total energy absorbed (EA) are given in

[7]. For the following analysis section, the entire loaddisplace-

ment curve [12] of Fig. 2a (initial slope, peak load, and average

crush load) and the average SEA value of Fig. 2c (SEA = 67.06 J/g)

are used as benchmarks for comparing the success of the simula-

tion results.

3. Description of the MAT54 material model and other model

input parameters

MAT54 is designed specifically to handle orthotropic materials

such as unidirectional tape composite laminates (not fabric).

Fig. 1. Prepreg tape corrugated specimen (a), detail of the chamfered trigger (b), and typical morphology after crush testing (c).

1810 P. Feraboli et al./ Composites: Part A 42 (2011) 18091825


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Unfortunately, the LS-DYNA theory/user manual [6] does not con-

tain detailed definitions of the input parameters used, so it is

important to provide them here, see Table 2.In the elastic region, the material stressstrain curves in MAT54

for the fiber (1-direction), matrix (2-direction) and shear (12

direction) are given by:

e1 1

E1r1 m12r2 1

e2 1

E2r2 m21r1 2

2e12 1

G12s12 rs312 3

In Eq. (3), the a (ALPH in Table 2) input parameter is a weighingfactor for the nonlinear shear stress term. ALPH cannot be mea-

sured experimentally but needs to be calibrated by trial and error.

Beyond the elastic region, MAT54 uses the Chang-Chang failure

criterion [6,13] to determine individual ply failure as shown in

Eqs. (4)(7). In the following equations: ef, ec, em and ed are called

history variables and they represent (respectively) tension and

compression for the 1-direction and tension and compression for

the 2-direction. XT is the fiber tensile strength, XC is the fiber

compressive strength, YT is the matrix tensile strength, YC is the

matrix compressive strength, and SC is the shear strength of the

unidirectional ply. These input parameters can be measured

through testing of the unidirectional tape lamina. It should be

noted that all of these quantities assume that the 1-direction is

the fiber direction, while the 2-direction is the matrix direction.

For this reason, all calculations in MAT54 assume that the materialis unidirectional tape, and not fabric, where otherwise both the

1- and 2-directions would be fiber directions. The only difference

between MAT54 and MAT55 is that the latter uses the Tsai-Wu

failure criterion.

For the tensile fiber mode where r11P0:

e2f r11Ftu2

!2 b

r12Fsu12

2 ! 1failed< 1elastic

4

Upon failure: E1 = E2 = G12 = v12 = v21 = 0.

The MAT54 shear stress weighing factor b (BETA in Table 2)

allows the user to explicitly define the influence of shear in the

tensile fiber failure mode. For BETA = 1 the Hashin [6] failure crite-

rion is implemented, while setting BETA = 0 reduces Eq. (4) to theMaximum Stress failure criterion. Selecting the right value of BETA

is a matter of preference, and otherwise can be done by trial and

error.

For the compressive fiber mode where r1160:

e2c r11Fcu1


5

Upon failure: E1 = v12 = v21 = 0.

For the tensile matrix mode where r22P0:

e2m r22Ftu2

!2

r12Fsu12


6

Upon failure: E2 = v21 = G12 = 0.

Table 1

Material properties of T700/2510 Unidirectional tape as published in the CMH-17

[10,11].

Property Symbol LS-DYNA

parameter

Experimental

value

Density q RO 0.055 lb/in.3 (1.52 g/cm3)

Modulus in 1-direction E1 EA 18.4 Msi (127 GPa)

Modulus in 2-direction E2 EB 1.22 Msi (8.41 GPa)

Shear modulus G12 GAB 0.61 Msi (4.21 G Pa)Major Poissons ratio v12 0.309

Minor Poissons ratio v21 PRBA 0.02049

Strength in 1-direction,

tensionFtu1 XT 319 ksi (2.20 GPa)


tensionFtu2 YT 7.09 ksi (48.9 MPa)


compression

Fcu1 XC 213 ksi (1.47 GPa)


compression

Fcu2 YC 28.8 ksi (199 MPa)

Shear strength Fsu12 SC 22.4 ksi (154 MPa)

Fig. 2. Experimental loaddisplacement curve (a), specific energy absorption (b),

and total energy absorbed (c) as a function of displacement.

P. Feraboli et al./ Composites: Part A 42 (2011) 18091825 1811


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For the compressive matrix mode where r2260:

e2d r22

2Fsu12

2

Fcu22Fsu12

1

r22Fcu2

r12Fsu12


7

Upon failure: E2 = v21 = v12 = 0 = G12 = 0.

When one of the above conditions is exceeded in a ply within

the element, all specified elastic properties of that ply are set to

zero. Matrix failure corresponds to first ply failure. The FBRT andYCFAC strength reduction parameters in Table 2 are used to de-

grade the pristine fiber strengths of the remaining plies once ma-

trix failure takes place. This strength degradation is applied using

the following equations:

XT XT FBRT 8

XC YC YCFAC 9

The FBRT factor acts as a percentage reduction of the tensile

fiber strength from its pristine value, therefore its value may only

be in the range [0, 1]. The YCFAC factor uses the pristine matrix

strength YC to determine the damaged compressive fiber strength,

which means that the upper value of YCFAC is not 1 but

XC/YC = 7.4. The input value for the two parameters FBRT and

YCFAC cannot be measured experimentally and need to be

determined by trial and error.

In addition to these strength-based criteria, failure can also

occur if the strains exceed the strain-to-failure for each ply. For a

unidirectional tape, the DFAILT and DFAILC parameters are the ten-

sile and compressive failure strains in the fiber direction, while

DFAILM is the failure strain in the matrix direction. By definition,

DFAILT must be positive and DFAILC must be negative. If DFAILT,

DFAILC or DFAILM are set to zero, the code ignores the parameters

altogether and failure can only occur by the Chang-Chang failure

criterion. If DFAILT, DFAILC and DFAILM are non-zero, failure can

occur if one of the strains exceeds the strain-to-failure. An addi-

tional strain-to-failure, DFAILS for shear, is used in the code but

it does not appear as a criterion for failure. This means that if the

shear strain exceeds the assigned value of DFAILS, failure does

not occur. All strains-to-failure can be measured through cou-

pon-level tests of the unidirectional lamina, however if they are

not known LS-DYNA gives the user the possibility to employ a gen-

eric parameter EFS (effective failure strain). If EFS is greater than

zero, failure occurs if the effective strain is greater than EFS. If

EFS is set to zero, the parameter is ignored. This parameter is not

truly a physical property, and can only be estimated by trial and

error.

Element deletion can also occur if the element time step TFAIL

is exceeded. The value of TFAIL determines whether or not the sim-

ulation considers a minimum time step for element deletion, and

what that minimum time step is. This option is useful only in cases

where the computational cost of the simulation is driven up byhighly distorted elements that no longer carry load but do not fail

from the prescribed element deletion criterion. It is necessary that

these costly elements have very small time steps to handle the

high degree of distortion. By defining a minimum allowed time

step using TFAIL, these costly but useless distorted elements can

be eliminated. TFAIL is defined as follows:

TFAIL 0 : No element deletion by time step size

0 < TFAIL 0:1 : Element is deleted when its time step

is smaller than TFAIL

TFAIL>

1:

Element is deleted when

current time step

original time step

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2011-JCOMA-lsdyna-sinusoid