Validating Predictive Modeling of Carbon Fiber Composites...

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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


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


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


Figure 1. Adjusting SOFT parameters to obtain desired response in LS-DYNA simulations

(ref.9).

(a)


(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


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.


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.


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.


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).


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.


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].


3. References

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Axial Collapse of CFRP Square Tubes: Finite Element Modeling, Composite Structures,

2006, 74 (2): 213-235.

2. Makhecha DP, Dynamic Fracture of Adhesively Bonded Composite Structures Using

Cohesive Zone Models, PhD dissertation, Virginia Polytechnic Institute and State University,

Blacksburg, VA, 2005.

3. 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 42 (2011)

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4. Hallquist J, Lum LCK, Matzenmiller A, Numerical Simulation Of Post-Failure Crash Of

Composite Tubular Beams, ACC Technical Report, RE EM91-02.

5. Botkin B, Johnson N, Zywicz E, Simunovic S, Crashworthiness Simulation Of Composite

Automotive Structures, 13th annual Engineering Society of Detroit Advanced Composite

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6. Xiao X, Botkin B, Johnson N, Axial Crush Simulation Of Braided Carbon Tubes Using

MAT58 In LS-DYNA, Thin-Walled Structures, 47, 2009, 740-749.

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Wichita, KS.

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