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 1 

Proceedings of IMECE2009 

2009 ASME International Mechanical Engineering Congress and Exposition 

November 13-19, Lake Buena Vista, Florida, USA 

IMECE2009-11926 

MODELING THE EFFECT OF FLUID-STRUCTURE INTERACTION ON THE IMPACT 

DYNAMICS OF PRESSURIZED TANK CARS 

Hailing Yu 

MacroSys Research and Technology 

55 Broadway, Cambridge, MA 02142, USA 

Hailing.Yu@dot.gov 

Yim H. Tang 

Volpe National Transportation Systems Center 

55 Broadway, Cambridge, MA 02142, USA 

Yim.Tang@dot.gov 

Jeffrey E. Gordon 

Volpe National Transportation Systems Center 

55 Broadway, Cambridge, MA 02142, USA 

Jeffrey.Gordon@dot.gov 

David Y. Jeong 

Volpe National Transportation Systems Center 

55 Broadway, Cambridge, MA 02142, USA 

David.Jeong@dot.gov 

ABSTRACT 

This paper presents a computational framework that 

analyzes the effect of fluid-structure interaction (FSI) on the 

impact dynamics of pressurized commodity tank cars using the 

nonlinear dynamic finite element code ABAQUS/Explicit. 

There exist three distinct phases for a tank car loaded with a 

liquefied substance: pressurized gas, pressurized liquid and the 

solid structure. When a tank car comes under dynamic impact 

with an external object, contact is often concentrated in a small 

zone with sizes comparable to that of the impacting object. 

While the majority of the tank car structure undergoes elasticplastic deformations, materials in the impact zone can 

experience large plastic deformations and be stretched to a state 

of failure, resulting in the loss of structural integrity. 

Moreover, the structural deformation changes the volume that 

the fluids (gas and liquid) occupy and consequently the fluid 

pressure, which in turn affects the structural response including 

the potential initiation and evolution of fracture in the tank car 

structure. 

For an event in which the impact severity is low and the 

tank car maintains its structural integrity, shell elements 

following elastic-plastic constitutive relations can be employed 

for the entire tank car domain. For events in which the impact 

severity is higher and the tank car is expected to be punctured, 

an equivalent plastic strain based fracture initiation criterion 

expressed as a function of stress triaxiality is adopted for the 

material in the tank car’s impact zone. The fracture initiation is 

implemented for ductile, shear and mixed fracture modes and 

followed by further material deterioration governed by a strain 

softening law. Multi-layered solid elements are employed in 

the impact zone to capture this progressive fracture behavior. 

The liquid phase is modeled with a linear Us–Up Hugoniot 

form of the Mie-Grüneisen equation of state, and the gas phase 

is modeled with the ideal gas equation of state. Small to 

moderate amounts of fluid sloshing are assumed for an 

impacted tank car in this study. As such, the FSI problem can 

be solved with the Lagrangian formulation of ABAQUS, and 

appropriate contact algorithms are employed to model the 

multi-phase interactions. The force, displacement and impact 

energy results from the finite element analysis show good 

correlations with the available shell (side) impact test data. The 

puncture energy of a tank car in a shell impact scenario is 

further analyzed. It is demonstrated that the FSI effect needs to 

be adequately addressed in an analysis to avoid overestimating 

the puncture resistance of a tank car in an impact event. 

INTRODUCTION 

Pressurized commodity tank cars are commonly employed 

in the railroad industry to transport liquefied goods including 

hazardous materials (hazmat) such as compressed flammable 

(e.g., propane) or toxic gases (e.g., chlorine). Severe impacts 

in some railroad accidents compromised the structural integrity 

of tank cars, released hazmat into the surrounding environment 

and caused human fatalities and injuries, environmental 

damage and economic losses [1-3]. Thus improving the 

structural integrity of railroad tank cars is of great importance, 

and it requires improved tank car designs based on a better 

understanding of the dynamics of individual tank components 

and their interactions [4]. To achieve these goals, 
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 2 

Fig. 2: Illustration of solid, liquid and gas phases comprising a loaded tank car 

computational methods such as finite element analysis (FEA) 

have proven to be a powerful tool that complements 

experimental approaches. 

Under normal operating conditions, both liquid and vapor 

forms of a substance being transported coexist in a tank car. 

The pressure of a gaseous vapor in dynamic equilibrium with 

its liquid form at a given temperature is called vapor pressure. 

For instance, the Antoine equation calculates the vapor pressure 

as follows 

 ln(P)=A-B/(T+C) (1) 

where P is vapor pressure, T is temperature and A, B and C are 

Antoine coefficients. Figure 1 shows the vapor pressures of 

water and chlorine over a range of temperatures according to 

Eq. (1), with the Antoine coefficients obtained from 

http://www.cheresources.com/data.xls. While vapor pressures 

of water appear to be negligible at normal temperatures, those 

of chlorine are more significant. Figure 2 depicts three 

interacting phases in a tank car loaded with chlorine: solid 

structure, liquid and gas. The liquid and gas phases are also 

referred to as fluid phases. 

0

50

100

150

200

250

300

350

400

-50 0 50 100 150 200

Water

Chlorine

Vapor pressure (psi)

Temperature ( F) O

Fig. 1: Vapor pressures of water and chlorine as 

functions of temperature 

A tank car structure responds to external impact loading 

with elastic-plastic deformations that ultimately can be 

stretched to a state of failure. In a tank car with liquefied 

lading such as chlorine, the fluid pressure also transmits forces 

to the inner wall and balances with the internal forces of the 

tank container. This is a typical fluid-structure interaction 

(FSI) phenomenon because the fluid pressure affects the 

structural deformation and vice versa. Simplified 

computational approaches have avoided explicitly modeling 

one or both fluid phases by replacing them with prescribed, 

constant inner wall pressure and/or lumped fluid mass. A more 

realistic computational model of a loaded tank car, however, 

needs to include multiple phases: solid structure, pressurized 

liquid and pressurized gas. 

This paper presents a computational study of the multiphase interactions in a tank car during a dynamic event using 

the commercial FEA software ABAQUS. Provided that the 

degree of fluid sloshing is small to moderate, the FSI problem 

can be solved within the ABAQUS Lagrangian framework. 

The paper is organized as follows. First, shell (or side) impact 

tests on full scale tank cars are described. Second, a 

computational multi-phase approach is presented. Third, the 

computational method is applied to simulate the FSI effects in 

the shell impact tests, and the simulation results are verified 

with the experimental data. Fourth, tank car puncture is 

predicted with the multi-phase FEA framework. Last, 

conclusions are drawn from the study, and additional 

applications of the method are discussed. 

EXPERIMENTAL STUDY 

The main structure of a tank car consists of two ellipsoidal 

ends (or heads) connected by a cylindrical shell. An object hits 

anywhere on the shell in a shell impact scenario, and it hits 

anywhere on the heads in a head impact scenario. Head impact 

tests on full-scale tank cars were conducted in as early as the 

1970’s [5] and then during the 1990’s [6-7], whereas head 

component tests were done more recently. In 2007, full-scale 

shell impact tests were conducted at the Transportation 

Technology Center in Pueblo, Colorado. These tests were 

mainly aimed at evaluating the crashworthiness performance of 

existing tank cars. Moreover, the test data can help to develop 
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 3 

and verify computational models [8]. 

Figure 3 shows typical tank and ram cars used in the shell 

impact tests in Pueblo, Colorado. For obvious safety reasons 

the tank car was filled with water in lieu of liquid chlorine, to 

89.4% of its capacity (i.e., 10.6% outage). In addition, clay 

slurry was added in the water, and the mixture had the 

approximate density of liquid chlorine. Air occupied the rest of 

the tank volume and was pressurized initially to 100 psi to 

simulate the condition in a tank car loaded with liquid chlorine. 

The tank car assembly weighed about 263,000 pounds with its 

liquid content, a steel jacket and other accessories. It was 

placed with one side against a concrete wall and the other side 

exposed to impact from the ram car. The ram car was a 

ballasted flatcar that weighed 286,000 pounds and had a 

protruding beam to which an impactor was attached. Two 

impactors were employed in the shell impact tests, and their 

surface geometries are illustrated in Fig. 4. Impactor I had a 

17′′x23′′ face (approximately the size of a draft sill crosssection) whose edges were rounded with 1′′ radius, and 

Impactor II had a smaller, 6′′x6′′ face (approximately the size of 

a coupler shank cross-section) whose edges were rounded with 

0.5′′ radius. 

Accelerometers on the ram car yielded data to calculate 

impact forces and impactor displacements. Displacement 

transducers were mounted on the interior tank wall, providing 

tank indentation data. Pressure transducers were also placed on 

the interior tank wall to monitor the liquid pressure at selected 

locations. No data channel was available for monitoring the air 

pressure. 

An assurance test was first conducted with limited 

instrumentation, followed by two fully instrumented tests (Test 

1 and Test 2). Impactor I was employed in Test 1 and Impactor 

II in Test 2. In both tests, the ram car ran the impactor 

perpendicularly to the center of the tank shell (at 14 mph in 

Test 1 and 15.1 mph in Test 2). The tank car was dented a 

maximum 26 inches but maintained its structural integrity in 

Test 1. The tank car was punctured and the fluids escaped in 

Test 2. The peak force reached about 1290 kips in Test 1 and 

nearly 900 kips in Test 2. 

Fig. 4: Schematic of Impactor surfaces 

THREE-PHASE FINITE ELEMENT MODEL 

Finite element models were developed to simulate the tests 

described above. In one simplified approach, the gas phase 

was omitted, and the fluid pressure was replaced with a 

prescribed, constant pressure on the inner wall of the tank 

container. This approach can be fairly accurate when the 

structural deformation is small or localized and thus has a 

minimal effect on the fluid pressure. However, in the shell 

impact cases described above, the structural deformation 

spanned a large domain, the FSI effect was sufficiently strong, 

and the simplified approach became inaccurate. In the 

computational framework presented here, all of the solid, liquid 

and gas phases following different sets of governing equations 

were explicitly modeled, and their interactions were accounted 

for via available contact options. 

Fig. 3: Tank and ram cars in a shell impact test 
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 4 

Governing equations

Solid structure 

The tank car structure is made of specialty steel such as 

TC-128B. The behavior of this solid structure phase is 

modeled with elastic-plastic and fracture constitutive relations. 

The elastic behavior is assumed to be linear and isotropic with 

Young’s modulus E and Poisson’s ratio ν. Once the elastic 

limit is reached, a modified Ramberg-Osgood strain hardening 

law [9] is followed 

( )n ε = σ E + σ K (2) 

where ε and σ are true strain and true stress, respectively, and n

and K are material constants determined from basic material 

parameters such as the initial yield strength σy0. 

As the yield stress evolves to its peak level, fracture or 

damage is assumed to initiate at an equivalent plastic strain 

pl

0

pl ε = ε , which can be a function of stress triaxiality, strain 

rate, temperature, etc. This study adopts a fracture initiation 

criterion dependent on the stress triaxiality η, which is defined 

as the ratio of the hydrostatic mean stress (σm) to the von Mises 

equivalent stress (σ ) 

η = σ m σ (3) 

where 

( ) m 1 2 3 3

1

σ = σ +σ +σ (4) 

and 

[ ] ( )( )( )2

3 1

2

2 3

2

1 2 2

1

σ = σ −σ + σ −σ + σ −σ (5) 

A fracture locus can be constructed in the (η, pl

0 ε ) plane 

from a material’s fracture initiation criterion. A three-branch 

fracture locus similar to that calibrated by Lee and Wierzbicki 

[10] for industrial aluminum and steel is adopted and expressed 

as 

( )

( )( ) 













≤

+ − ≤ ≤

+ − < ≤

∞ ≤ −

=

η η η η

η η η η

η η

η

ε

2 0 0

0

2

1 2 1 0

1 pl

0

 

 0

1 3 1 3 0

 1 3

C ,

C C C ,

C ,

,

 (6) 

where C1 is pl

0 ε in pure shear (η=0), and C2 is pl0 ε in uniaxial 

tension where η=η0=1/3. The fracture locus derived from this 

expression is plotted in Fig. 5: Branch I for ductile fracture due 

to the mechanism of void nucleation, growth and coalescence; 

Branch III for shear fracture due to shear bank localization; and 

Branch II for mixed mode fracture. Note that the original 

calibration by Lee and Wierzbicki [10] treated η as the average 

stress triaxiality over a deformation history; in particular, η0 for 

uniaxial tension was assigned values greater than 1/3. 

However, η0=1/3 was adopted in this study because (1) 

previous studies established that 1/3 was a good approximation 

of the stress triaxiality at the center section of a uniaxial tensile 

specimen [11], and (2) the stress triaxiality appeared to remain 

at 1/3 for most of the deformation history obtained for a 

smooth (i.e., unnotched) tensile specimen [12]. 

Fig. 5: Three-branch fracture initiation locus for 

industrial aluminum or steel 

ABAQUS’ “progressive damage and failure” material 

model accommodates the material behavior described above 

[13]. With a predefined fracture initiation criterion 

pl

0 ε = pl0 ε (η), ABAQUS determines that damage initiates if the 

following condition is met 

 ωD= ∫ pl

0

pl

ε

dε

=1 (7) 

where ωD is a state variable that increases monotonically with 

plastic deformation. This takes into account the plastic 

deformation history in determining any fracture initiation. 

ABAQUS directs this implementation to the ductile fracture 

type, but a fracture initiation criterion defined over the stress 

triaxiality range (-∞, +∞) would cover the shear and mixed 

fracture modes as well. 

With the onset of damage, the yield stress softens and the 

elastic modulus degrades until the equivalent plastic strain 

reaches its failure limit pl

f ε . This damage evolution is 

monitored by an overall damage variable D which starts at 0 

when ωD reaches 1 and progresses to 1 at complete failure. 

ABAQUS allows various damage evolution forms and for 

simplicity, this study adopts a linear softening law. To reduce 
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 5 

the mesh dependency inherent in softening responses, 

ABAQUS has introduced the concept of an element 

characteristic length (denoted as Le) in the constitutive relation. 

Accordingly, an equivalent plastic displacement pl u is defined 

and evolves according to the following equation 

pl

e

pl ε & & u = L (8) 

When pl u reaches pl

f u upon complete failure, elements 

representing failed material points may be removed. These 

elastic-plastic-fracture constitutive relations for tank car steels 

were previously employed in modeling the fracture mechanics 

of unnotched Charpy specimens [14-15]. 

The thickness dimension of a tank car is considerably 

smaller that the other dimensions such as tank diameter and 

length. Previous studies established that to capture pure 

elastic-plastic behaviors, a shell element formulation was 

accurate with a typical element size of about two times the tank 

thickness [16]. For the progressive damage and failure 

behavior, the shell element formulation can produce misleading 

results and therefore, a solid element formulation must be 

employed. Multiple layers of solid elements through the 

thickness dimension are needed in this case to accurately 

capture the progressive deterioration process. However, an allsolid-element model of a tank car is expensive; it is also 

unnecessary with the solid-to-shell coupling technique 

available in ABAQUS. That is, the impact zone is modeled 

with multi-layered solid elements, the rest of the domain is 

modeled with shell elements, and the two domains are joined 

via solid-to-shell coupling. Figure 6 illustrates a typical mesh 

involving both shell and solid elements and solid-to-shell 

coupling. 

Liquid phase 

The hydrostatic behavior of the liquid phase is governed 

by equations of state that determine the pressure p (positive in 

compression) as a function of the density ρ and the specific 

energy Em (internal energy per unit mass) 

 p=f(ρ,Em) (9) 

The Mie-Grüneisen equation of state available in 

ABAQUS/Explicit is linear with respect to energy and can be 

written in the following form 

 p=f1(ρ)+f2(ρ)Em (10) 

where f1(ρ) and f2(ρ) are model-dependent functions of density. 

A linear Us–Up Hugoniot form of the Mie-Grüneisen equation 

of state is verified to be an effective method to model the 

behavior of liquids such as water [17]. For this model, the 

initial density ρ0 and wave speed c0 (from which ρ0c0

2

 yields 

the elastic bulk modulus) are required material inputs. 

Fig. 6: Typical finite element mesh involving both 

shell and solid elements in a tank car impact zone 

The deviatoric behavior of the liquid phase is assumed to 

be uncoupled from its volumetric response and governed by 

either a linear isotropic elastic model or a Newtonian viscous 

fluid model. The shear viscosity parameter serves as a penalty 

to suppress the shear modes that can distort a mesh, and it must 

be small for water which is inviscid. 

Gas phase 

The gas phase is assumed to follow the ideal gas equation 

of state 

pV=mRT (11) 

where p is the absolute pressure, V is the volume, m is the 

mass, R is the (specific) gas constant and T is the absolute 

temperature. The gas constant R is a required input for this 

model. The ideal gas assumption is approximately true for the 

conditions considered. If there is no leakage or temperature 

change, the gas pressure is inversely proportional to the volume 

that the gas occupies, which can change with structural 

deformations. It is assumed that the liquid and gas phases are 

in dynamic equilibrium and that temperature is constant 

throughout the process. 

Modeling fluid-structure interaction

In the experimental study described in a previous section, 

only small to moderate fluid sloshing was believed to have 

occurred, and the same was assumed in the modeling approach. 

Under this assumption, mesh distortion due to fluid flow was 

moderate at most, and the Lagrangian framework was applied. 

In addition to each individual phase, the interactions 

among different phases needed to be addressed. These 
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 6 

Tab. 1: Material and geometry data and initial condition of tank cars in the tests 

Tank 

material 

Inner 

diameter 

(inch) 

Head 

thickness 

(inch.) 

Shell 

thickness 

(inch.) 

Shell 

length 

(inch.) 

Jacket 

material 

Jacket 

thickness 

(inch.) 

Initial fluid 

pressure 

(psi) 

TC-128B 100.75 0.828 0.777 471.47 ASTM 

A1011/A569 0.119 100 

Tab. 2: Model parameters for tank car materials 

Material ρ (lbm-in-3) E (ksi) ν σy0 (ksi) n K (ksi) C1 C2 pl uf (inch)

TC-128B from Test 1 0.2835 29800 0.3 55 10.55 99.15 - - - 

TC-128B from Test 2 0.2835 31650 0.3 55 11.17 96.04 0.31 1.05 0.32 

ASTM A1011/A569 0.2835 29000 0.3 30 9.00 59.85 0.31 0.92 0.25 

interactions were analyzed as inter-phase contacts. The general 

contact option provides a robust solution to modeling solid-toliquid contacts. However, contacts involving the gas phase can 

be more problematic because its mass is extremely small 

compared to those of the other phases. 

The gas-to-liquid interface was usually modeled with no 

separation, no slip contact, equivalent to firmly attaching two 

materials along their interface. Alternatively, such contact can 

be replaced with shared nodes along the interface to achieve the 

same modeling effect while eliminating a potential source of 

numerical instability – contacts between two materials vastly 

mismatched in mass. The choice of either option depended on 

the application and the desired performance. 

To model the gas-to-solid interaction, general contact 

worked well when the structural model included only shell 

elements. However, when solid-to-shell coupling was 

involved, numerous trials led to the conclusion that contact 

between gas and solid phases must also be specifically defined. 

In addition, it was helpful to define smooth contact surfaces for 

the fluids and zero contact thickness for shell elements. 

Frictionless contact was assumed for all fluid-to-fluid and 

fluid-to-structure interfaces. 

VERIFICATION WITH EXPERIMENTAL DATA 

The next step was to simulate the full-scale shell impact 

tests within the multi-phase FEA framework described above 

and verify the computational results with the corresponding 

experimental data. An example problem derived from the shell 

impact simulations was also analyzed with both the multi-phase 

approach and a simplified approach where the gas phase was 

omitted and the fluid pressure was replaced with a constant 

inner wall pressure. A comparison of the results from both 

approaches demonstrated that the multi-phase approach 

accounted for the FSI effect more adequately. The example 

problem, its analysis and the results are presented in the 

Appendix. This section compares FEA results from both the 

multi-phase and simplified approaches with the full-scale shell 

impact test data. 

The material and geometry data of the tank cars involved 

in the tests and the initial fluid pressure are summarized in Tab. 

1. Like its physical counterpart, the tank car model consisted 

of a cylindrical shell with two ellipsoidal heads. The only other 

explicitly modeled structural entity was the jacket with a 

clearance of about four inches from the exterior tank body. All 

the accessories were lumped into point masses. The model 

parameters for the steel materials are summarized in Tab. 2. 

The ram car was modeled as one of the impactor shapes shown 

in Fig. 4 with a lumped mass of 286,000 pounds. As in the 

tests, the tank car model was filled with liquid for 89.4% of its 

volume and gas for 10.6% of its volume. The model 

parameters for liquid and gas phases are shown in Tab. 3. The 

liquid properties were derived from those of the clay slurrywater mixture and liquid chlorine, and the gas properties were 

those of air. 

Tab. 3: Model parameters for liquid and gas phases 

Material ρ0 (lbm-in-3) c0 (in-sec-1) R (in2-sec-2-K-1) 

Liquid 0.0510 34732.95 - 

Gas 0.0003 - 479034.86 

The initial fluid pressure p0 was introduced as an initial 

hydrostatic stress state (σ11=σ22=σ33=-p0, σ12=σ23=σ31=0) for 

the three-dimensional fluid elements. Because initial gaps 

existed in FE models between the inner tank wall and the fluid 

surfaces, the fluids would experience an initial volume 

expansion to close the gaps, which would cause an initial drop 

in the fluid pressure. To mitigate this effect, a fluid pressure 

slightly larger than p0 needed to be assigned for model 

initialization and was denoted as p0

′ . The magnitude of p0′

depends on the model setup and can be determined from 

iterative initialization steps. 

Elastic-plastic and FSI analysis

To simulate shell impact Test 1, only shell elements and 

elastic-plastic material models were employed, because the 

deformation was not too severe and the structural integrity was 

maintained as a result of the impact. Modeling FSI was 

straightforward with one general contact definition. The 

calculated mass of the tank car assembly was 268,656 pounds, 
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 7 

0

200

400

600

800

1000

1200

1400

0 0.1 0.2 0.3 0.4

F (kips)

Time (sec)

(a)

0

5

10

15

20

25

30

35

0 0.1 0.2 0.3 0.4

Test

Multi-phase FEA

Simplified FEA

d (inch.)

Time (sec)

(b)

0

200

400

600

800

1000

1200

1400

0 5 10 15 20 25 30 35

F (kips)

d (inch.)

(c)

0

5

10

15

20

25

0 0.1 0.2 0.3 0.4

W (x106 lbf-inch.)

Time (sec)

(d)

Fig. 8: Test vs. multi-phased and simplified FEA results for shell impact Test 1: (a) impact force F, (b) impactor 

displacement d, (c) F-d cross plot, and (d) work W done by impact force 

within 2.2% of the nominal 263,000 pounds. The problem 

domain, boundary conditions and loading were assumed to be 

symmetric about the center transverse section, so the halfsymmetric model illustrated in Fig. 7 was developed. In 

addition to the tank car and its fluid contents, Fig. 7 shows a 

rigid wall (fixed in space) and a rigid lower support which was 

attached to the tank car assembly and prevented it from moving 

downward by means of contract with a fixed rigid floor not 

shown in the picture. Initially, the impact mass moved at a 

speed of 14 mph toward the stationary tank assembly. The 

fluid pressure p0

′ for model initialization was 101 psi in this 

case. 

The following analysis results from both the multi-phase 

and simplified approaches were compared with the 

experimental data: time histories of the impact force (F, Fig. 

8a) and impactor displacement (d, Fig. 8b) along the impact 

direction; F-d cross plot (Fig. 8c); and time history of the work 

done by the impact force, or integration of the F-d curve (W, 

Fig. 8d). The multi-phase FEA results show good correlations 

with the experimental data. The simplified FEA appeared to 

underestimate the peak forces and overestimate the rebounding 

impactor displacements. 

Fig. 7: Half symmetric model for shell impact Test 1 

Some key deformation/contact states observed from the 

simulation were (all times were approximate): the impactor 

initially contacted the jacket at 0.014 seconds; the jacket 

overcame the four inch clearance and contacted the exterior 

tank surface, and the force reached its first peak at 0.124 

seconds; the tank surface on the back side contacted the rigid 

wall at 0.172 seconds, and the force started to climb again; the 
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 8 

maximum tank indentation was reached at approximately the 

same time as the second peak force at 0.246 seconds, and the 

impact mass lost its forward momentum and started to rebound 

from the tank assembly, which in turn rebounded from the rigid 

wall; at 0.44 seconds, the rebound process was completed and 

the solid entities were separated from each other. 

Fracture and FSI analysis

With a smaller impactor (Impactor II in Fig. 4) and a 

greater initial impact velocity (15.1 mph), the tank car was 

punctured in shell impact Test 2. The progressive damage and 

failure material model was applied to the solid elements in the 

tank car’s impact zone. The tank car assembly weighed 

264,756 pounds in the model (the weight difference from that 

in Test 1 simulation was attributed mainly to differences in the 

fluid mesh). In addition to the general contact definition, 

contact interaction was specifically defined for the solid-to-gas 

interaction. The initialization fluid pressure p0

′ was 110 psi 

for this model, again attributable to the fluid mesh. Figure 9 

shows the final damage profile from Test 2 and the model 

predicted damage at 0.104 seconds. Note that the elastic 

deformations of the model specimen in Fig. 9 were not 

recovered, and as a result, the cutout model specimen had a 

concave shape instead of the convex shape observed in the test 

specimen. The simulation was discontinued beyond the point 

of puncture, because the failed structure could no longer 

contain the fluids. 

Figures 10(a-d) show the predicted impact force F, 

impactor displacement d, F-d cross plot and work W done by 

the impact force in comparison with the corresponding test 

data. Again good correlations with the experimental data were 

observed with the multi-phase approach. The sudden drop in 

force near 0.1 seconds indicates the breach of the tank car. The 

multi-phase FEA predicted well both the timing of this event 

and the maximum force level, whereas the simplified approach 

under-predicted the peak force and the impactor displacement 

at puncture. 

Fig. 9: Damage profile from shell impact Test 2 and 

model predicted damage at 0.104 seconds 

0

200

400

600

800

0 0.02 0.04 0.06 0.08 0.1

F (kips)

Time (sec)

(a)

0

5

10

15

20

25

30

0 0.02 0.04 0.06 0.08 0.1

Test

Multi-phase FEA

Simplified FEA

d (inch.)

Time (sec)

(b)

0

200

400

600

800

0 5 10 15 20 25

F (kips)

d (inch.)

(c)

0

2

4

6

8

10

12

0 0.02 0.04 0.06 0.08 0.1

W (x106 lbf-inch.)

Time (sec)

(d)

Fig. 10: Test vs. multi-phased and simplified FEA results for shell impact Test 2: (a) impact force F, (b) impactor 

displacement d, (c) F-d cross plot, and (d) work W done by impact force 
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 9 

AVERAGE GAS PRESSURE 

From the multi-phase simulations, the pressure time 

history averaged over all gas elements, denoted as pgas, can be 

obtained from ABAQUS. Figure 11 shows the time history of 

pgas obtained from the simulations of both Tests 1 and 2. The 

corresponding test data were unavailable. The gas pressure 

reached a maximum of 135 psi at about 0.216 seconds in the 

simulation of Test 1, and it reached a maximum of 110 psi right 

before the tank car punctured in the simulation of Test 2. The 

maximum air pressure level was higher in Test 1 than in Test 2 

because (1) the impact event was more prolonged in Test 1 

resulting in more tank deformation and (2) the larger impactor 

affected broader areas on the tank car and introduced more 

significant volumetric changes to the fluids. Based on these 

pressure levels, it appeared that FSI played a stronger role in 

Test 1 than in Test 2. 

100

105

110

115

120

125

130

135

140

0 0.1 0.2 0.3 0.4

Test 1 simulation

Test 2 simulation

pgas (psi)

Time (sec)

Fig. 11: Average gas pressure pgas obtained from 

multi-phase simulations of Tests 1 and 2 

PUNCTURE ANALYSIS 

The puncture energy (Ep) of a tank car can be defined as 

the minimum impact energy to cause the loss of structural 

integrity with given tank car configuration, ram car mass, 

impactor geometry and size, etc. In the simulations, a tank car 

was deemed to lose its structural integrity when complete, 

through-the-thickness element failure occurred at any location 

in the impact zone. The test, simplified FEA and multi-phase 

FEA showed that the tank car was punctured with an initial 

impact velocity v0=15.1 mph under the Test 2 configurations. 

Further, v0 was decreased in simulations until the model no 

longer predicted tank car puncture for a given v0. Because it 

was not possible to change v0 continuously, integer v0 values 

were used with decrements of 1 mph. The lowest integer v0

that did cause puncture was approximated as the minimum 

puncture velocity of a tank car and denoted as vp. The puncture 

energy Ep was estimated as the work done by the impact force 

up to the point of loss of structural integrity with an initial 

impact velocity v0=vp. 

Following the method outlined above, the simplified 

approach predicted vp=11 mph and Ep=1.158 million lbf-ft, 

whereas the multi-phase approach predicted vp=10 mph and 

Ep=0.967 million lbf-ft, for the tank car subjected to the 

configurations of Test 2. Figure 12 shows the F-d and W-d

relations obtained from both the simplified and multi-phase 

FEA with v0=vp. All curves are shown to the point of loss of 

structural integrity. Compared to the multi-phase approach, the 

simplified approach overestimated the puncture energy by 

nearly 20%. 

0

200

400

600

800

1000

0 5 10 15 20 25 30

F (kips)

d (inch.)

(a)

0

2

4

6

8

10

12

14

0 5 10 15 20 25 30

Simplified FEA (11 mph)

Multi-phase FEA (10 mph)

W (x106 lbf-inch.)

d (inch.)

(b)

Fig. 12: (a) F-d and (b) W-d relations obtained from 

simplified and multi-phase FEA with the predicted 

minimum puncture velocities as the initial impact 

velocities under Test 2 configurations 

CONCLUSIONS AND DISCUSSIONS 

A computational method within the Lagrangian framework 

of ABAQUS/Explicit was developed and applied in simulating 

two shell impact tests on full-scale tank cars. The simulations 

predicted force, displacement and work time histories in good 

agreement with those recorded in the tests. It was 

demonstrated that the presented multi-phase modeling 

approach was effective and accurate in depicting the elasticplastic-fracture material behavior and fluid-structure interaction 

mechanisms involved in an impacted tank car. 

Although the computational method was verified with 

shell impact scenarios, it can be similarly applied to head 

impact scenarios as long as fluid flow does not cause excessive 

mesh distortion. In addition, the computational approach can 
This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited. 

 10 

help to evaluate the benefits of improved protective strategies 

for tank cars. 

Potential future work includes incorporating the 

temperature and strain rate dependencies in the elastic-plasticfracture constitutive relations of the solid phase. Further, the 

current method needs to be extended to solve problems 

involving more significant fluid sloshing. 

ACKNOWLEDGMENTS 

The Federal Railroad Administration’s Office of Research 

and Development sponsored the research presented in this 

paper. Mr. Francisco Gonzalez is the FRA project manager for 

research on railroad tank cars. Mr. Eloy Martinez also provides 

technical direction to the project. The full-scale shell impact 

tests described in this paper were funded and conducted by the 

Next Generation Rail Tank Car Project which was sponsored 

by Dow Chemical Company, Union Pacific Railroad, and 

Union Tank Car Company. FRA participated in this project 

through a Memorandum of Cooperation. HY was employed 

with Chenega Advanced Solutions and Engineering, LLC 

during part of this research. 

REFERENCES 

[1] National Transportation Safety Board (NTSB), 

“Derailment of Canadian Pacific Railway Freight Train 

292-16 and Subsequent Release of Anhydrous Ammonia 

Near Minot, North Dakota January 18, 2002,” Railroad 

Accident Report NTSB/RAR-04/01, March 2004. 

[2] National Transportation Safety Board (NTSB), “Collision 

of Norfolk Southern Freight Train 192 With Standing 

Norfolk Southern Local Train P22 With Subsequent 

Hazardous Materials Release at Graniteville, South 

Carolina January 6, 2005,” Railroad Accident Report 

NTSB/RAR-05/04, November 2005. 

[3] National Transportation Safety Board (NTSB), “Collision 

of Union Pacific Railroad Train MHOTU-23 With BNSF 

Railway Company Train MEAP-TUL-126-D With 

Subsequent Derailment and Hazardous Materials Release, 

Macdona, Texas, June 28, 2004,” Railroad Accident 

Report NTSB/RAR-06/03, July 2006. 

[4] Tyrell, D.C., Jeong, D.Y., Jacobsen, K., Martinez, E., 

“Improved Tank Car Safety Research,” Proceedings of the 

2007 ASME Rail Transportation Division Fall Technical 

Conference, RTDF2007-46013, September 2007. 

[5] Phillips, E.A., and L. Olsen, “Final Phase 05 Report on 

Tank Car Head Study,” RPI-AAR Tank Car Safety 

Research and Test Project, Report RA-05-1-17, 1972. 

[6] Coltman, M., and M. Hazel, “Chlorine Tank Car Puncture 

Resistance Evaluation,” Final Report, DOT/FRA/ORD92/11, 1992. 

[7] Larson, W.G., “Aluminum/Cold Temperature Tank Car 

Puncture Resistance Tests: Data Report,” Final Report, 

DOT/FRA/ORD-92/29, 1992. 

[8] Tang, Y.H., Yu, H., Gordon, J.E., Priante, M., Jeong, D.Y., 

Tyrell, D.C., Perlman, A.B., "Analysis of Full-Scale Tank 

Car Shell Impact Tests," Proceedings of the 2007 ASME 

Rail Transportation Division Fall Technical Conference, 

RTDF2007-46010, September 2007. 

[9] Ramberg, W., and W.R. Osgood, “Description of StressStrain Curves by Three Parameters,” National Advisory 

Committee for Aeronautics, Technical Note No. 902, 1943. 

[10] Lee, Y.-W., and T. Wierzbicki, “Quick Fracture Calibration 

for Industrial Use,” Impact & Crashworthiness Laboratory, 

Massachusetts Institute of Technology, Report No: 115, 

August 2004. 

[11] Earl, J.C., and Brown, D.K., “Distribution of Stress and 

Plastic Strain in Circumferentially Notched Tension 

Specimens,” Engineering Fracture Mechanics, 8:599–611, 

1976. 

[12] Bao, Y., and Wierzbicki, T., “On Fracture Locus in the 

Equivalent Strain and Stress Triaxiality Space,” 

International Journal of Mechanical Sciences, 46:81-98, 

2004. 

[13] ABAQUS Analysis User’s Manual, Version 6.8. 

[14] Yu, H., Jeong, D.Y., Gordon, J.E., Tang, Y.H., “Analysis of 

Impact Energy to Fracture Unnotched Charpy Specimens 

Made from Railroad Tank Car Steel,” Proceedings of the 

2007 ASME Rail Transportation Division Fall Technical 

Conference, RTDF2007-46038, September 2007. 

[15] Jeong, D.Y., Yu, H., Gordon, J.E., Tang, Y.H., “Finite 

Element Analysis of Unnotched Charpy Impact Tests,” 

Materials Science & Technology Conference and 

Exhibition, 2008. 

[16] Yu, H., Tang, Y.H., and Jeong, D.Y., “Elastic-PlasticFailure Finite Element Analyses of Railroad Tank Car 

Heads in Impact,” Proceedings 2007 ABAQUS Users’ 

Conference, Paris, France, May 2007. 

[17] ABAQUS Benchmarks Manual, Version 6.8.
This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for public release; distribution is unlimited. 

 11 

APPENDIX 

EXAMPLE PROBLEM 

An example problem was developed to test the application 

of the multi-phase approach and its effectiveness in modeling 

the FSI effects. The example problem consisted of a one-inch 

slice of the tank car cross-section (Fig. A1) and was derived 

from the full-scale tank car model for shell impact Test 2. A 

lateral pressure load was applied on one side of the tank car 

slice which was fixed locally on the other side to prevent rigid 

body motions. The resultant load of the prescribed lateral 

pressure was denoted as F, and its time history is plotted in Fig. 

A2. With two distinctive peaks, the shape of the load curve 

resembled those observed in the shell impact tests. All relevant 

model parameters were the same as those of the full-scale tank 

model for Test 2. 

Fig. A1: (a) Multi-phase and (b) simplified FEA models 

for the example problem 

Both the multi-phase and simplified FEA were conducted 

for the example problem. The multi-phase approach modeled 

both the liquid and gas phases explicitly and assigned both 

fluid phases an initial pressure of 100 psi, shown in Fig. A1(a). 

The simplified approach ignored the gas phase and replaced the 

fluid pressure with a constant 100 psi imposed on the inner 

wall of the tank car slice, shown in Fig. A1(b). 

The deformation histories obtained from both analyses 

indicated that (1) the gas phase in the multi-phase model was 

significantly compressed, and the average gas pressure pgas

reached over 350 psi during its time history shown in Fig. A3; 

(2) the simplified approach predicted unrealistic separations of 

the solid and fluid surfaces along their interfaces; and (3) 

compared to the multi-phase FEA, the simplified FEA overpredicted the tank car deformations. The third observation was 

verified by the F-d curves plotted in Fig. A4, where d was the 

averaged nodal displacement over the effective load area. The 

discrepancies between the two model predictions demonstrated 

that only the multi-phase method fully captured the FSI effects. 

0

20

40

60

80

100

120

140

0 0.05 0.1 0.15 0.2

F (kips)

Time (sec)

Fig. A2: Time history of the resultant lateral pressure 

load on one side of the tank car slice 

100

150

200

250

300

350

0 0.05 0.1 0.15 0.2

pgas (psi)

Time (sec)

Fig. A3: Time history of the average gas pressure 

obtained from the multi-phase FEA 

0

20

40

60

80

100

120

140

160

0 5 10 15 20 25 30 35

Multi-phase FEA

Simplified FEA

F (kips)

d (inch.)

Fig. A4: Comparison of F-d curves obtained from 

multi-phase and simplified FEA