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. 

 1 

Proceedings of the 2007 ASME Rail Transportation Division Fall Technical Conference 

RTDF2007 

September 11-12, 2007 Chicago, Illinois, USA 

 RTDF2007-46010 

ANALYSES OF FULL-SCALE TANK CAR SHELL IMPACT TESTS 

Y.H. Tang 

Volpe National Transportation Systems Center 

Cambridge, Massachusetts, USA 

H. Yu 

Chenga Advanced Solutions & Engineering, LLC 

Cambridge, Massachusetts, USA 

J.E. Gordon 

Volpe National Transportation Systems Center 

Cambridge, Massachusetts, USA 

M. Priante 

Volpe National Transportation Systems Center 

Cambridge, Massachusetts, USA 

D.Y. Jeong 

Volpe National Transportation Systems Center 

Cambridge, Massachusetts, USA 

D.C. Tyrell 

Volpe National Transportation Systems Center 

Cambridge, Massachusetts, USA 

A.B. Perlman 

Volpe National Transportation Systems Center 

Cambridge, Massachusetts, USA 

ABSTRACT 

This paper describes analyses of a railroad tank car 

impacted at its side by a ram car with a rigid punch. This 

generalized collision, referred to as a shell impact, is examined 

using nonlinear finite element analysis (FEA) and threedimensional (3-D) collision dynamics modeling. Moreover, the 

analysis results are compared to full-scale test data to validate 

the models. Commercial software packages are used to carry 

out the nonlinear FEA (ABAQUS and LS-DYNA) and the 3-D 

collision dynamics analysis (ADAMS). Model results from the 

two finite element codes are compared to verify the analysis 

methodology. Results from static, nonlinear FEA are compared 

to closed-form solutions based on rigid-plastic collapse for 

additional verification of the analysis. Results from dynamic, 

nonlinear FEA are compared to data obtained from full-scale 

tests to validate the analysis. The collision dynamics model is 

calibrated using test data. While the nonlinear FEA requires 

high computational times, the collision dynamics model 

calculates gross behavior of the colliding cars in times that are 

several orders of magnitude less than the FEA models. 

INTRODUCTION 

Comprehensive data on tank car accident damage have 

been collected since the late 1960s by the Railroad Tank Car 

Safety Research and Test Project, which is co-sponsored by the 

Railway Supply Institute and the Association of American 

Railroads. An evaluation of the data indicates that releases of 

toxic inhalation hazard (TIH) materials from accident events 

(e.g., collisions and derailments) are commonly caused by 

failures in three general locations: (1) tank car head or end cap, 

(2) tank car shell or side, and (3) fittings [1]. Two recent 

accidents that led to the release of hazardous materials (hazmat) 

occurred from impacts and penetrations to the head [2] and the 

shell [3]. Moreover, the structural integrity of railroad tank cars 

involved in accidents was brought to the forefront of research 

after the National Transportation Safety Board (NTSB) 

published its findings of the train derailment that occurred in 

Minot, North Dakota on January 18, 2002 [4]. As a result of its 

Minot accident investigation, NTSB made several safety 

recommendations to the Federal Railroad Administration 

(FRA) concerning railroad tank cars. In its role to provide 

technical support to FRA, the Volpe National Transportation 

Systems Center (Volpe Center) developed a research program 

to address NTSB concerns. This research program began in 

2004, and entails the development of computational tools and 

validation through testing. 

In 2006, Dow Chemical Company, Union Pacific Railroad, 

and Union Tank Car Company began an industry research and 

development effort called the Next-Generation Rail Tank Car 

(NGRTC) Project to develop improved designs for railroad 
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. 

 2 

tank cars carrying hazmat. Since early in 2007, FRA, 

Transport Canada, and the Volpe Center have been 

collaborating with the industry sponsors of the NGRTC project 

to share research information. 

This paper describes work that is a product of research 

conducted to address the NTSB tank car safety 

recommendations from the Minot accident and work related to 

the NGRTC Project. The research described in this paper will 

also be used to support rulemaking for transporting hazmat by 

railroad tank cars. 

Previous research on the vulnerability of tank cars to 

puncture from impacting objects (such as couplers and wheels 

from adjacent cars, etc.) has focused on head impacts [5-8]. 

However, no previous work has been performed to examine 

shell impacts. 

This paper describes nonlinear (i.e., elastic-plastic) finite 

element models to examine the force-indentation behavior of 

tank cars from shell impacts. The models are developed using 

the commercial finite element codes ABAQUS and LS-DYNA. 

The finite element models are verified by comparing results 

from both solvers with each other and with known solutions for 

static loading. The models are then validated with data 

obtained from full-scale tests that were performed at the 

Transportation Technology Center in Pueblo, Colorado. 

Finite element analysis (FEA) can be used to calculate 

deformations, stresses, and strains in specific locations within 

the tank structure. Gross behavior of impacting cars can be 

readily calculated using collision dynamics models. A threedimensional collision dynamics model was developed using the 

force-indentation characteristics from the validated finite 

element models. Moreover, the collision dynamics model was 

developed using a commercial software program for rigid 

multi-body dynamics called Automatic Dynamic Analysis of 

Mechanical Systems (ADAMS). Results from the collision 

dynamics model are presented and compared to the full-scale 

test data. 

The collision dynamics model was used to guide the 

development of the test design and to ensure that the test can be 

conducted safely and effectively. The model can be used to 

extrapolate test results for different impact speeds. 

FINITE ELEMENT MODEL 

Finite element models are developed to examine the 

deformation and failure of the tank due to impact. The 

computational times for these models are extensive because the 

models must include (1) structural dynamics, (2) nonlinear (i.e., 

elastic-plastic) material behavior, (3) fluid-structure interaction, 

and (4) material failure. 

FEA is readily suitable for analysis of structural dynamics 

in terms of how a structure moves with time under prescribed 

loads. 

Elastic-plastic material behavior is modeled using a 

Ramberg-Osgood equation for strain as a function of stress, 

n

E K

σ σ

ε = +       (1) 

where ε is the strain, σ is the stress, and E is the modulus of 

elasticity. In addition, n and K are material constants. Table 1 

lists the values for these constants assumed for TC-128B tank 

car steel in the finite element analyses. These constants were 

derived from the yield and ultimate tensile strengths listed in 

the table, which correspond to the minimum requirements for 

this particular tank car steel. 

Table 1. Constants and Mechanical Properties 

Corresponding to Minimum Requirements for TC-128B 

Tank Car Steel 

Constant or property Value 

Modulus of elasticity, E (ksi) 30,000 

Hardening exponent, n 9.41 

R-O Constant, K (ksi) 96.8 

Yield strength (ksi) 50 

Tensile strength (ksi) 81 

When the tank contains lading, the fluid and the tank 

structure both move and exert forces upon one another during 

the impact event. Different mesh representations are used in 

the finite element models to account for fluid-structure 

interaction. Specifically, Lagrangian and Eulerian mesh 

formulations are used. In a Lagrangian mesh, the nodes follow 

the material as it deforms. An Eulerian mesh is fixed in space, 

and tracks the material passing through. A Lagrangian mesh is 

used to model the tank structure. Both Lagrangian and 

Eulerian mesh formulations are used to model the fluid. 

Prediction of material failure in a crack-free structure 

requires application of a reliable fracture initiation criterion. 

An evaluation of several criteria was recently conducted to 

examine their merits [9]. In the present work, a criterion based 

on stress triaxiality [10] was used to predict failure by puncture 

in the full-scale impact tests. Briefly, stress triaxiality describes 

the portion of the stress tensor that is hydrostatic. The failure 

criterion based on stress triaxiality was calibrated using data 

from pendulum impact tests conducted on un-notched Charpy 

specimens made from TC-128 tank car steel [11]. The analysis 

on the unnotched Charpy tests provides a benchmark for which 

the failure criterion can be applied to the full-scale tests. 

Credibility is built into the models by conducting various 

activities referred to as Verification and Validation (V&V). 

Verification assesses the accuracy of the solutions from the 

computational models by comparing model results with known 

solutions. Validation assesses the accuracy of the computational 

simulation by comparing model results with data. Moreover, 

verification means that the mathematics associated with the 
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. 

 3 

model are being calculated correctly, and validation means that 

the physics are being modeled properly. 

Verification 

Closed-form solutions are available in the open literature 

for large plastic deformations of cylindrical tubes subjected to 

various static loading conditions, including lateral loads [12-

13]. The closed-form solutions assume rigid-plastic material 

behavior, which confines the deformation within a narrow 

region. Moreover, the deformation behaves as a mechanism or 

a system of rigid bars linked by hinges such that the motion of 

the system takes place through rotations at the hinges. In 

addition, the closed-form solutions are strongly sensitive to the 

assumed boundary conditions. 

Figure 1 compares the closed-form force-indentation curve 

for the plastic deformation of a cylindrical tube under lateral 

loading to that from a static, elastic-plastic FEA using 

ABAQUS. The cylinder is assumed to rest on a rigid surface 

on the opposite side from the applied lateral load, and is free to 

slide and rotate at its ends. Moreover, the comparison between 

the FEA result and the closed-form solution shows reasonable 

agreement. The effects of internal pressure and fluid lading are 

not included. 

Indentation (inches)

0 5 10 15 20

Force (kips)

0

100

200

300

400

500

Closed-form solution

Finite element analysis

Figure 1. Static Force-Indentation Curves from ClosedForm Solution and FEA 

Figure 2 compares static results from ABAQUS with 

dynamic results at two different impact speeds (16 and 20 mph) 

from LS-DYNA. The figure demonstrates that the analyses 

are producing similar results. Moreover, the comparisons 

provide further verification of the modeling development. 

Indentation (inches)

0 5 10 15 20

Force (kips)

0

100

200

300

400

500

Static

Dynamic (16 mph)

Dynamic (20 mph)

Figure 2. Force-Indentation Curves from Static and 

Dynamic Elastic-Plastic FEA 

Validation 

Three full-scale tank car shell impact tests were performed 

to validate the finite element models. In these tests, the tank 

car was positioned next to a concrete wall, as shown in Figure 

3. 

Figure 3. Position of Tank Car in Full-Scale Tests 

The tank car contains water mixed with clay slurry to 

produce the density approximately equal to that of liquid 

chlorine. The outage in the tests is 10.6 percent with an 

internal pressure of 100 psi. A ram car weighing 286,000 lb 

with a rigid impactor was used to strike the side of tank car at 

its center on the beltline. The couplers at each end of the tank 

car were removed, and replaced with outriggers to support the 

tank car as it rebounded off the wall after impact. The 
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. 

 4 

outriggers were L-shaped beams installed in the draft pockets, 

which were supported by wood blocks. These outriggers were 

used in the first two tests. A new design, referred to as skids, 

was used in the third test to reduce the gross motion of the tank 

car during impact. 

Table 2 briefly summarizes the three full-scale shell impact 

tests in terms of impact speeds and outcomes. The first test, 

called the Assurance Test (also referred to as Test 0), was 

conducted to understand the test environment and the gross 

motions of the cars during the impact test. Moreover, the cars 

in Test 0 were equipped with limited instrumentation. The cars 

in subsequent tests were heavily instrumented to provide 

redundant measurements for forces and displacements. In 

addition, different impactor sizes were used in the tests, which 

are denoted in the table. The impactor shape was a rectangular 

cross-section with rounded edges. Different impactor sizes 

were used in the full-scale tests. The dimensions for each 

impactor face are listed in Table 3. Test 2 was originally 

intended to be run at 14 mph, so that only one variable 

(impactor size) would be varied. However, a slightly higher 

impact speed of 15 mph was targeted in Test 2. 

Table 2. Full-Scale Tank Car Shell Impact Tests 

Impact 

Speed 

(mph) 

Impactor Outcome 

Test 0 10 1 Tank integrity maintained, 

4-inch residual dent depth 

Test 1 14 1 Tank integrity maintained, 

9-inch residual dent depth 

Test 2 15 2 Tank punctured 

Table 3. Dimensions of Impactor Faces 

Impactor Width 

(inches) 

Height 

(inches) 

Edge Radii 

(inch) 

1 17 23 1 

2 6 6 1⁄2 

The finite element models to simulate the full-scale tests 

do not include tank car components such as the manway, body 

bolsters, and draft sills. In addition, the presence of the thermal 

protection is ignored for all tests and the presence of the steel 

jacket is ignored for both Test 0 and Test 1. 

Assurance Test

In all of the tests, the ram car was instrumented with 

accelerometers. The accelerometer data were filtered, and 

processed to provide forces. Figure 4 compares the force-time 

history as measured in Test 0 with those calculated from the 

finite element models. Results from different fluid formulations 

to account for fluid-structure interaction are shown in the 

figure. These results suggest that the Eulerian fluid 

formulation provides the most accurate results in terms of 

capturing the overall character of the force-time history. 

Moreover, these results suggest that the movement or sloshing 

of the fluid during the impact event plays a significant role in 

the force-time behavior. 

Time (seconds)

0.0 0.1 0.2 0.3 0.4 0.5

Force (kips)

0

200

400

600

800

1000

1200

Processed Test Data

LS-DYNA, Eulerian

ABAQUS, Lagrangian

Figure 4. Comparison of Force-Time Histories for Test 0 

Table 4 compares the maximum impact force measured in 

Test 0 with results from the FEA with different fluid 

formulations. The maximum impact force calculated using LSDYNA with the Eulerian fluid formulation is within 5 percent 

of the test data, which is excellent agreement. 

Table 4. Comparison between Test 0 and FEA 

 Maximum 

Force (kips) 

Assurance Test 837 

LS-DYNA, Eulerian 877 

ABAQUS, Lagrangian 707 

Full-Scale Shell Impact Test 1

The accelerometer measurements in Shell Impact Test 1 

were filtered and processed in the same manner as in the 

Assurance Test. Figure 5 compares the force-time histories 

from the data and the FEA using LS-DYNA with the Eulerian 

fluid representation, which again shows excellent agreement. 
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. 

 5 

Time (seconds)

0.0 0.1 0.2 0.3 0.4 0.5

Force (kips)

0

200

400

600

800

1000

1200

1400

1600

Processed Test Data

LS-DYNA, Eulerian

Figure 5. Comparison of Force-Time Histories for Test 1 

Table 5 compares the maximum impact forces and 

maximum indentations from Test 1 and the FEA results using 

LS-DYNA with the Eulerian fluid formulation. The maximum 

impact forces are within 10 percent. Figure 6 is a still 

photograph taken during the test with the FEA simulation 

overlayed. The figure indicates that the analysis provides a 

reasonable simulation for the overall deformation of the tank in 

the test. 

The maximum indentation of 26 inches was measured in 

the test with string potentiometers, compared to the FEA 

prediction of 30 inches. The FEA prediction was a calculation 

performed prior to the test assuming the minimum requirements 

for mechanical properties of TC-128B tank car steel. After Test 

1 was conducted, tensile tests were performed to determine the 

actual mechanical properties, which were roughly 10 percent 

greater than the minimum requirements for both yield and 

ultimate tensile strengths. The FEA calculations were 

conducted with the actual properties, which resulted in slightly 

better agreement for both maximum impact force and 

maximum indentation (Table 5). 

 

Table 5. Comparison between Test 1 and FEA 

 Maximum 

Force (kips) 

Maximum 

Dent (inches) 

Test 1 Data 1290 26 

LS-DYNA, Eulerian (1) 1223 29 

LS-DYNA, Eulerian (2) 1170 30 

NOTES: 

(1)Based on material properties measured from Test 1 tank car 

(2)Based on minimum requirements for mechanical properties 

Figure 6. Overlay of Deformed Shape from FEA 

Simulation on Still Frame from High-Speed Movie 

A key output from the FEA is the force-indentation 

characteristic. Figure 7 compares the curves from the test data 

and the FEA results. The curve from the test data is a crossplot of indentation-time history from the string potentiometers 

and force-time history from the processed accelerometer data. 

The force-indentation curve from the FEA shows qualitative 

agreement with the test. Both curves show the drop in force 

due to the movement of the fluid during the impact event. In 

addition, both curves show nonlinear, dynamic recovery of the 

indentation. That is, the test data shows that the maximum 

indentation 26 inches, but the permanent or residual dent depth 

is about 9 inches. The maximum indentation and residual dent 

calculated by the FEA assumed the minimum required 

mechanical properties for TC-128B tank car steel. 

Indentation (inches)

0 5 10 15 20 25 30 35

Force (kips)

0

200

400

600

800

1000

1200

1400

1600

Processed Test Data

LS-DYNA, Eulerian

Figure 7. Comparison of Force-Indentation Curves for 

Test 1 
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. 

 6 

Full-Scale Shell Impact Test 2

 The second full-scale shell impact test used an impactor 

with a smaller cross-sectional area than the previous tests 

(recall Table 3) to increase the likelihood of rupturing the tank 

during the test. Moreover, the impacting car in this test struck 

the side of the tank car at 15 mph, and created a puncture. 

Analyses of Test 0 and Test 1 demonstrated that the FEA 

with the Eulerian fluid formulation provides results that more 

closely resemble the test data. However, the present 

capabilities of the software are such that material failure was 

incorporated into the FEA with the Lagrangian fluid 

formulation only. Moreover, material failure is assumed to 

initiate when the effective strain reaches a certain value for a 

given state of stress in terms of stress triaxiality [11]. 

The fracture of unnotched Charpy specimens was 

examined and was shown to provide a benchmark in applying 

the failure criterion. The failure criterion based on stress 

triaxiality was then applied to examine the puncture resistance 

of the tank car in Test 2. 

The accelerometer measurements in Shell Impact Test 2 

were filtered and processed in the same manner as the previous 

tests. Figure 8 compares the force-time histories from Test 2 

with finite element analyses with and without applying the 

failure criterion. The figure shows that the processed force 

data quickly drops off at about 90 milliseconds, indicating the 

time at which failure of the tank initiated and eventually led to 

puncture. The data also indicates that the impact force at the 

time of failure was 910 kips. The force-time history curves 

from the FEA with and without the failure criterion are nearly 

identical up to 90 milliseconds. The force drop-off calculated 

by the FEA with the failure criterion occurs slightly earlier than 

the test. In addition, the maximum force calculated by the FEA 

with the failure criterion is lower than the peak impact force 

measured in Test 2. These differences are attributed to the new 

skid design for Test 2 in which the tank car is positioned next to 

the wall. That is, the skid design may provide more structural 

stiffening to the tank than the previous outrigger design used in 

the previous tests. The overall character of the calculated 

force-time history resembles the test data reasonably well. 

FEA of Test 2 assumed material properties measured from 

the tank car used in Test 1, which are roughly about 10 percent 

greater than the minimum requirements for both yield strength 

and ultimate tensile strength. 

Time (seconds)

0.00 0.05 0.10 0.15

Force (kips)

0

200

400

600

800

1000

1200

1400

Processed Test Data

LS-DYNA, Eulerian without Failure

ABAQUS, Lagrangian with Failure

Figure 8. Comparison of Force-Time Histories for Test 2 

COLLISION DYNAMICS MODEL 

The collision dynamics model consists of a system of 

springs and lumped masses, and is implemented using 

ADAMS, a commercial software program. The model is 

developed to ensure that the test can be conducted safely and 

effectively. Moreover, the model can be used to extrapolate 

test results. The key inputs to this model are the ram car weight 

(286 kips), the tank car weight (241 kips), and the forcedisplacement characteristics for the tank structure and 

suspension elements. The outputs from the model are gross 

motions of the ram and tank cars such as linear and angular 

displacement, velocity and acceleration (equivalent to force). 

Figure 9 shows a schematic of the masses representing the 

tank car fluid and shell. Not shown are masses and suspension 

for the trucks on the tank and ram cars. The entire tank is 

represented by three masses; one for the fluid and two for the 

tank structure, each representing half of the tank’s mass. An 

elastic spring connects the two masses representing the tank. 

Elastic springs also connect the fluid to the tank. The value of 

these spring constants is chosen to represent the frequency of 

the fluid movement relative to the tank. 

Ram Car

m1⁄2 tank m1⁄2 tank

mfluid

Wall

Figure 9. Tank and Fluid Masses Connected by Springs 
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. 

 7 

Figure 10 shows the force-displacement characteristic 

derived using processed accelerometer data from the ram car in 

Test 1. 

Ram Displacement (inches)

0 5 10 15 20 25 30 35 40

Ram Force (kips)

0

200

400

600

800

1000

1200

1400

Processed Test Data

ADAMS Input

Figure 10. Force-Displacement for Ram Car Impacting 

Tank 

Still photographs from the high-speed cameras of Test 1 

are shown in Figure 11. The three stills show the time at which 

1) the indenter of the ram car makes contact with the tank car, 

2) the maximum penetration the indenter into the tank, 3) and 

the final dent size when the indenter is no longer contacting the 

tank car. The roll of the tank car can be observed in these stills. 

In the first image, the tank car is positioned upright on its 

trucks. In the second image the tank car is fully supported by 

the wall and reaches a maximum roll in the clockwise direction 

of approximately 6 degrees. In the final image, the tank car has 

returned to its original position. 

Similarly Figure 12 shows a sequence of still photographs 

from Test 2. The three stills correspond to 1) triggering the 

instrumentation to start recording, 2) initial contact of the ram 

car with the tank car, and 3) the initiation of the puncture of the 

tank. Moreover the roll of the tank car in Test 2 was less than 

that in the previous tests. 

Figure 13 compares displacements calculated using the 

collision dynamics model with data processed from 

accelerometers on the vehicles in Test 1. The ram car moves 

approximately 34 inches into the tank car, reaching its peak 

displacement at 0.25 seconds after initial contact. The tank car 

CG (center of gravity) moves approximately 7.5 inches towards 

the wall. 

Figure 11. Stills from Test 1 

 

Figure 12. Stills from Test 2 
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. 

 8 

Time (seconds)

0.0 0.1 0.2 0.3 0.4 0.5

Displacement (inches) -10

0

10

20

30

40

50

Test Data: Ram Car

Test Data: Tank Car

Model: Ram Car

Model: Tank Car

Figure 13. Comparison of Displacement-Time Histories for 

Test 1 

Figure 14 compares the velocity-time histories of the tank 

car and the ram car for the accelerometer data from Test 1 and 

the collision dynamics model. The ram car decelerates from 14 

mph until it has zero velocity at 0.24 seconds. The model 

follows the test data quite closely. The tank car velocity 

increases as it moves towards the wall and then decreases as it 

rebounds from the wall. 

Time (seconds)

0.0 0.1 0.2 0.3 0.4 0.5

Velocity (mph) -10

-5

0

5

10

15

20

Test Data: Ram Car

Test Data: Tank Car

Model: Ram Car

Model: Tank Car

Figure 14. Comparison of Velocity-Time Histories for Test 

1 

During the conduct of the full-scale tests, the ram car was 

observed to pitch, and the tank car was observed to roll toward 

the wall. Figure 15 shows a schematic of these gross motions. 

The pitching motion occurs because the center of gravity of the 

ram car is lower than the point of impact with the tank car. The 

rolling motion occurs because the structural response of the 

inner tank, which contains the fluid, does not engage until the 

combination of thermal insulation materials and steel jacket are 

crushed against the wall. The layered combination adds 

roughly 4 inches to the radius of the overall tank, and offers 

effectively no structural resistance. 

Figure 15. Pitch of Ram Car and Roll of Tank Car 

The collision dynamics model was used to calculate the 

gross motions of the ram and tank cars in the full-scale shell 

impact tests. Table 6 shows a comparison of the pitch and roll 

for the first two tests and the model. The tank car roll is 

calculated using data from accelerometers located on the manway and belly of the tank car. 

Table 6. Gross Car Motions in Full-Scale Shell Impact 

Tests 

Maximum Pitch 

Ram Car 

Maximum Roll 

Tank Car 

Test Model Test Model 

Test 0 0.25o 0.4o 4.5o 5.7o 

Test 1 1o 0.53o 5.75o 5o 

The dynamic nonlinear (i.e., elastic-plastic) finite element 

models with fluid-structure interaction are computationally 

intensive and require high computational times to execute. The 

calibrated collision dynamics model requires minimal 

computational times that are several orders of magnitude less 

than the FEA models. Moreover, the collision dynamics model 

can be readily applied to extrapolate results for different impact 

velocities. 

CONCLUDING REMARKS 

Elastic-plastic finite element models have been developed 

to examine the force-indentation behavior of railroad tank cars 

under shell impact loading conditions. Prior to this work, this 

type of impact loading condition was not examined. The 

models were verified by comparing static analysis results to 

closed-form solutions, which show reasonable agreement. The 

models were validated by comparing dynamic analysis results 
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. 

 9 

with full-scale impact test data, which showed excellent 

agreement. Moreover, the verified and validated models can be 

used to extrapolate structural behavior for different impact 

scenarios and to develop improved designs to maintain tank 

integrity under more severe loading conditions than current 

equipment. 

The finite element analyses described in this paper require 

high computational times due to the complexities in accounting 

for fluid-structure interaction and material failure as well as 

dynamic impact loading and nonlinear (i.e., elastic-plastic) 

material behavior. 

Three-dimensional collision dynamics modeling of the 

full-scale tests has also been conducted. The model results 

provide reasonable estimates for gross motions of the cars in 

the full-scale tests. Moreover, the collision dynamics model 

can be readily applied to extrapolate test results for varying 

impact speeds. 

ACKNOWLEDGMENTS 

The work described in this paper was sponsored by the 

Federal Railroad Administration, Office of Research & 

Development. Ms. Claire Orth is the Chief of the Equipment 

and Operating Practices Division. Mr. Francisco Gonzalez is 

the FRA project manager for research on railroad tank cars. 

Mr. Eloy Martinez is the FRA project manager for the work 

with the NGRTC Project. Discussions with Dr. Oscar Orringer 

are gratefully appreciated and acknowledged. Finally, the 

authors would like to acknowledge Professor Christopher 

Barkan of the University of Illinois at Urbana-Champaign for 

his assistance in providing the Volpe Center with access to 

computers at the National Center for Supercomputing 

Applications. 

REFERENCES 

[1] Treichel, T., 2006: “List of Accident-Caused Releases of 

Toxic Inhalation Hazard (TIH) Materials from Tank Cars, 

1965-2005,” RSI-AAR Railroad Tank Car Safety Research 

and Test Project, RA 06-05. 

[2] National Transportation Safety Board, 2006: “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. 

[3] National Transportation Safety Board, 2005: “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. 

[4] National Transportation Safety Board, 2004: “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. 

[5] Phillips, E.A., Olsen, L., 1972: “Final Phase 05 Report on 

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

Research and Test Project, RA-05-17. 

[6] Shang, J.C. Everett, J.E., 1972: “Impact Vulnerability of 

Tank Car Heads,” Shock and Vibration Bulletin 42, 197-

210. 

[7] Coltman, M., Hazel, M., 1992: “Chlorine Tank Car 

Puncture Resistance Evaluation,” Volpe National 

Transportation Systems Center, Report DOT/FRA/ORD92/11. 

[8] Jeong, D.Y., Tang, Y.H., Yu, H., Perlman, A.B., 2006: 

“Engineering Analyses for Railroad Tank Car Head 

Puncture,” Proceedings of IMECE2006, 2006 ASME 

International Mechanical Engineering Congress and 

Exposition, IMECE2006-13212. 

[9] Wierzbicki, T., Bao, Y.B., Young-Woong, L., Yuanli, B., 

2005: “Calibration and evaluation of seven fracture 

models,” International Journal of Mechanical Sciences 27,

719-743. 

[10] Bao, Y., Wierzbicki, T., 2004: “On fracture locus in the 

equivalent strain and stress triaxiality space,” International 

Journal of Mechanical Sciences 46, 81-98. 

[11] Yu, H., Jeong, D.Y., Gordon, J.E., Tang, Y.H., 2007: 

“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, RDTF2007-46038. 

[12] Wierzbicki, T., Suh, M.S., 1988: “Indentation of Tubes 

under Combined Loading,” International Journal of 

Mechanical Sciences 30, 229-248. 

[13] Liu, J.H., Francis, A, 2004: “Theoretical analysis of local 

indentation on pressurized pipes,” International Journal of 

Pressure Vessels and Piping 81, 931-939.