US Department

of Transportation

Federal Railroad

Administration

Engineering Studies on Structural Integrity 

of Railroad Tank Cars Under Accident

Loading Conditions

Office of Research and

Development

Washington, DC 20590

DOT/FRA/ORD-09/18 Final Report

October 2009
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Final Report – August 2008

4. TITLE AND SUBTITLE

Engineering Studies on Structural Integrity of Railroad Tank Cars Under Accident Loading 

Conditions

5. FUNDING NUMBERS

EB034/RR-28

6. AUTHOR(S)

D.Y. Jeong, Y.H. Tang, H. Yu, M.L. Lyons, J.E. Gordon, O. Orringer, and A.B. Perlman

7. PERFORMING ORGANIZATION NAME(S) AND ADDRESS(ES)

U.S. Department of Transportation

Volpe National Transportation Systems Center

Research and Innovative Technology Administration

Cambridge, MA 02142-1093

8. PERFORMING ORGANIZATION 

REPORT NUMBER

9. SPONSORING/MONITORING AGENCY NAME(S) AND ADDRESS(ES)

Federal Railroad Administration

Office of Research and Development

1200 New Jersey Ave., SE

Washington, D.C. 20590

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

DOT/FRA/ORD-09/18

11. SUPPLEMENTARY NOTES

12a. DISTRIBUTION/AVAILABILITY STATEMENT

This document is available on the FRA Web site at http://www.fra.dot.gov/.

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

This report describes research conducted to support the Federal Railroad Administration (FRA) in addressing safety 

recommendations made by the National Transportation Safety Board (NTSB) regarding a train derailment that occurred near 

Minot, North Dakota on January 18, 2002. Engineering studies entailing analysis and testing are described, which include (1) 

analysis of derailment dynamics based on lumped-parameter models, (2) analysis of the structural behavior of tank car 

components (such as the head and shell) based on finite element modeling, (3) tank car steels characterization based on laboratory 

testing of samples obtained from tank cars. Specific details of the research are described. Conclusions based on the research 

findings to date are outlined.

The research began to provide FRA with technical support in responding to recommendations made by the NTSB following the 

Board’s investigation of the Minot accident. Research results are now being applied to support: (1) rulemaking proposed by FRA 

and the Pipeline and Hazardous Materials Safety Administration to ensure the safe transport of hazardous materials by tank cars

and (2) an industry research-and-development effort, called the Next Generation Rail Tank Car Project that was formed to develop 

and implement new improved designs for tank cars carrying hazardous materials. 

14. SUBJECT TERMS

Accidents, closing speed, finite element analysis, derailment dynamics, hazardous materials, impact 

loads

15. NUMBER OF PAGES

90

16. PRICE CODE

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

18. SECURITY CLASSIFICATION

OF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATION

OF ABSTRACT

Unclassified

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ABSTRACT

NSN 7540-01-280-5500 Standard Form 298 (Rev. 2-89)

Prescribed by ANSI Std. 239-18

iii

Preface

The Federal Railroad Administration (FRA), Office of Research and Development,

sponsored the work described in this report. Specifically, this work was conducted and 

managed by the Structures and Dynamics Division of the Volpe National Transportation 

Systems Center (Volpe Center) through a Project Plan Agreement with FRA. Moreover, 

this work is carried out through the Volpe Center’s Tank Car Structural Integrity Project 

in FRA’s Rail Equipment Safety Research Program. Ms. Claire Orth (retired) was the 

Chief of the Equipment and Operating Practices Division. Mr. Francisco González, III is 

the Project Manager for research on railroad tank cars. Mr. Eloy Martinez also provided

technical direction to this project.

Part of the work described in this report, specifically the full-scale tank car shell impact 

tests, was also conducted in support of an industry research-and-development effort 

called the Next Generation Rail Tank Car (NGRTC) Project. Dow Chemical Company, 

Union Pacific Railroad, and Union Tank Car Company are the industry sponsors of this 

collaboration. In January 2007, FRA signed a Memorandum of Cooperation with the 

industry sponsors of the NGRTC Project to share research information. Transport 

Canada and the Department of Homeland Security also participated in this project 

through Memoranda of Cooperation.

Professor Christopher Barkan of the University of Illinois at Urbana-Champaign is 

acknowledged for his assistance in providing access to computers at the National Center 

for Supercomputing Applications.
iv

METRIC/ENGLISH CONVERSION FACTORS

ENGLISH TO METRIC METRIC TO ENGLISH

LENGTH (APPROXIMATE) LENGTH (APPROXIMATE)

1 inch (in) = 2.5 centimeters (cm) 1 millimeter (mm) = 0.04 inch (in)

1 foot (ft) = 30 centimeters (cm) 1 centimeter (cm) = 0.4 inch (in)

1 yard (yd) = 0.9 meter (m) 1 meter (m) = 3.3 feet (ft)

1 mile (mi) = 1.6 kilometers (km) 1 meter (m) = 1.1 yards (yd)

1 kilometer (km) = 0.6 mile (mi)

AREA (APPROXIMATE) AREA (APPROXIMATE)

1 square inch (sq in, in2) = 6.5 square centimeters (cm2) 1 square centimeter (cm2) = 0.16 square inch (sq in, in2)

1 square foot (sq ft, ft2) = 0.09 square meter (m2) 1 square meter (m2) = 1.2 square yards (sq yd, yd2)

1 square yard (sq yd, yd2) = 0.8 square meter (m2) 1 square kilometer (km2) = 0.4 square mile (sq mi, mi2)

1 square mile (sq mi, mi2) = 2.6 square kilometers (km2) 10,000 square meters (m2) = 1 hectare (ha) = 2.5 acres

1 acre = 0.4 hectare (he) = 4,000 square meters (m2)

MASS - WEIGHT (APPROXIMATE) MASS - WEIGHT (APPROXIMATE)

1 ounce (oz) = 28 grams (gm) 1 gram (gm) = 0.036 ounce (oz)

1 pound (lb) = 0.45 kilogram (kg) 1 kilogram (kg) = 2.2 pounds (lb)

1 short ton = 2,000 pounds 

(lb)

= 0.9 tonne (t) 1 tonne (t) =

=

1,000 kilograms (kg)

1.1 short tons

VOLUME (APPROXIMATE) VOLUME (APPROXIMATE)

1 teaspoon (tsp) = 5 milliliters (ml) 1 milliliter (ml) = 0.03 fluid ounce (fl oz)

1 tablespoon (tbsp) = 15 milliliters (ml) 1 liter (l) = 2.1 pints (pt)

1 fluid ounce (fl oz) = 30 milliliters (ml) 1 liter (l) = 1.06 quarts (qt)

1 cup (c) = 0.24 liter (l) 1 liter (l) = 0.26 gallon (gal)

1 pint (pt) = 0.47 liter (l)

1 quart (qt) = 0.96 liter (l)

1 gallon (gal) = 3.8 liters (l)

1 cubic foot (cu ft, ft3) = 0.03 cubic meter (m3) 1 cubic meter (m3) = 36 cubic feet (cu ft, ft3)

1 cubic yard (cu yd, yd3) = 0.76 cubic meter (m3) 1 cubic meter (m3) = 1.3 cubic yards (cu yd, yd3)

TEMPERATURE (EXACT) TEMPERATURE (EXACT)

[(x-32)(5/9)] °F = y °C [(9/5) y + 32] °C = x °F

QUICK INCH - CENTIMETER LENGTH CONVERSION

0 1 2 3 4 5

Inches

Centimeters 0 1 2 3 4 5 6 7 8 9 10 11 12 13

QUICK FAHRENHEIT - CELSIUS TEMPERATURE CONVERSIO

 -40° -22° -4° 14° 32° 50° 68° 86° 104° 122° 140° 158° 176° 194° 212°

 

°F

 °C -40° -30° -20° -10° 0° 10° 20° 30° 40° 50° 60° 70° 80° 90° 100°

For more exact and or other conversion factors, see NIST Miscellaneous Publication 286, Units of Weights and 

Measures. Price $2.50 SD Catalog No. C13 10286 Updated 6/17/98
v

Contents

1. INTRODUCTION ...................................................................................................1

2. ANALYSIS OF DERAILMENT DYNAMICS ......................................................5

2.1 Review of Previous Research ......................................................................5

2.2 Purpose-Built and ADAMS Models............................................................6

2.3 Sensitivity Studies........................................................................................7

2.4 Closing Speeds and Impact Forces............................................................13

2.5 Discussion and Summary...........................................................................20

3. STRUCTURAL FINITE ELEMENT ANALYSIS ...............................................23

3.1 Verification ................................................................................................24

3.1.1 Sensitivity Studies..........................................................................25

3.1.2 Static Case Studies.........................................................................37

3.1.3 Dynamic Case Studies ...................................................................39

3.2 Validation...................................................................................................41

3.2.1 Head Impacts .................................................................................42

3.2.2 Shell Impacts..................................................................................48

3.2.3 Unnotched Charpy Tests................................................................54

3.3 Discussion and Summary...........................................................................59

4. TANK CAR STEELS CHARACTERIZATION...................................................65

4.1 Basic Material Characterization.................................................................66

4.2 High-Rate Fracture Toughness..................................................................70

4.3 Pendulum Impact Testing of Bulk Fracture Behavior...............................77

4.4 Discussion and Summary...........................................................................79

5. CONCLUSIONS....................................................................................................81

6. REFERENCES ......................................................................................................83

APPENDICES

A NTSB RECOMMENDATIONS FROM THE MINOT ACCIDENT ...................88

B ESTIMATION OF SAMPLE SIZE AND CONFIDENCE LEVEL.....................89
vi

Figures

1. Number of Accidents per Year with at least One Car Releasing 

Hazmat from FRA RAIRS Database .........................................................................1

2. TIH Tank Cars Releasing Lading in Accidents by Year, 1965-2005 [1]...................2

3. Accident-Caused Releases in TIH Tank Cars, 1965-2005 [1]...................................2

4. Derailment Buckling Patterns ....................................................................................7

5. Relative Effect of Parameters on Number of Derailed Cars using 

Purpose-Built Model ..................................................................................................9

6. Relative Effect of Parameters on Number of Derailed Cars using

ADAMS Model..........................................................................................................9

7. Relative Effect of Parameters on Maximum Closing Speed using 

Purpose-Built Model ................................................................................................10

8. Relative Effect of Parameters on Maximum Closing Speed using 

ADAMS Model........................................................................................................10

9. Relative Effect of Parameters on Peak Coupler Force

Purpose-Built Model ................................................................................................11

10. Relative Effect of Parameters on Peak Coupler Force

ADAMS Model........................................................................................................11

11. Effect of Train Speed on Number of Derailed Cars from Different Models ...........12

12. Effect of Ground Friction on Number of Derailed Cars from Different Models.....13

13. Characteristic Motions as Possible Sources of Impact.............................................13

14. Maximum Closing Speeds Based on Difference in Translational Velocity.............14

15. Maximum Closing Speeds Based on Difference in Angular Velocity.....................15

16. Maximum Coupler Forces for First 40 Cars of 100-Car Train ................................16

17. Closing Speeds for Initial Contact ...........................................................................17

18. Impact Forces for Initial Contact .............................................................................18

19. Gross Motions of Rail Cars and Post-Derailment, Car-to-Car Impacts...................18

20. Closing Speeds for Secondary Contact ....................................................................19

21. Impact Forces for Secondary Contact ......................................................................20

22. Simulated and Generalized Car-to-Car Impact Scenarios........................................21

23. Stills from Surveillance Video of an Actual Train Derailment................................22

24. Schematic of Dynamic Simulations for Sensitivity Studies.....................................27

25. Schematic of Static Analysis for Sensitivity Studies...............................................27

26. Comparison of Force-Indentation Results................................................................30

27. Contours of Equivalent Plastic Strain using Solid Elements ...................................31

28. Contours of Equivalent Plastic Strain using Shell Elements....................................31

29. Comparison between Static and Dynamic Finite Element Analyses.......................32

30. Comparison between Static and Dynamic Finite Element Analyses.......................33
vii

Figures (continued)

31. Contours of Equivalent Plastic Strain from Dynamic Analysis 

using Shell Elements................................................................................................33

32. Comparison Force-Indentation Curves from Static Analysis

using Shell Elements................................................................................................34

33. Comparison Force-Indentation Curves from Dynamic Analysis

using Shell Elements................................................................................................35

34. Force-Indentation Curves from Static and Dynamic Analysis using 

Solid and Shell Elements..........................................................................................35

35. Comparison of Force-Indentation Curves for Center Loaded Ellipsoidal Cap........38

36. Comparison of Force-Indentation Curves for Cylindrical Shell ..............................38

37. Comparison between Static and Dynamic FEA for Head Indentation.....................40

38. Comparison between Static and Dynamic FEA for Shell Indentation.....................40

39. Dynamic Lumped-Mass Model for Tank Car Impacts ............................................41

40. Impact Force as a Function of Closing Speed for Head Impacts.............................41

41. Rigid-Deformable Finite Element Model of Tank Container..................................42

42. Comparison between Calculated and Measured Impact Forces...............................47

43. Comparison between Calculated and Measured Residual Dent Depths..................47

44. Comparison between Calculated and Measured Residual Dent Widths..................48

45. Position of Tank Car in Full-Scale Tests .................................................................49

46. Comparison of Force-Time Histories for Test 0 ......................................................50

47. Comparison of Force-Time Histories for Test 1 ......................................................51

48. Comparison of Force-Indentation Curves for Test 1 ...............................................52

49. Comparison of Force-Time Histories for Test 2 ......................................................53

50. Schematic of Failure Initiation Envelope based on Stress Triaxiality .....................55

51. Schematic of Linear Strain Softening ......................................................................56

52. Comparison of BFCM data for Normalized TC-128B with FEA

assuming Bao-Wierzbicki Criterion.........................................................................56

53. Comparison of Different Failure Criteria with BFCM Test Data 

for TC-128B Tank Car Steel ....................................................................................57

54. Comparison of Measured and Calculated Fracture Energies for

Different Steels (Blunt Striker) ................................................................................58

55. Percent Variation in Impact Energy with Parameter Changes.................................59

56. Force-Indentation Characteristic for Shell Impact ...................................................60

57. Typical FEA Mesh for Full-Scale Shell Impact Simulations...................................61

58. Generalized Impact Scenarios Examined by FEA ...................................................62

59. Distribution of Steels in Pre-1989 Pressure Tank Car Fleet ....................................66

60. Cumulative Distribution of Pressure Tank Car Fleet and Tank Cars

used for Testing........................................................................................................67

61. CVN Data for Cars Involved in Three Different Accidents.....................................69

62. Fracture Toughness Master Curve Applied to Shell Data from Retired Cars..........73
viii

Figures (continued)

63. Fracture Toughness Master Curve Applied to Shell Data from Minot Cars............74

64. High-Rate Fracture Toughness as a Function of CVN Energy at 0oF......................76

65. High-Rate Fracture Toughness as a Function of CVN Energy at –50oF..................77

66. Oversized, Nonstandard Pendulum Impactor...........................................................77

67. BFCM Test Specimen ..............................................................................................78

68. Impact Tups Used in BFCM Tests...........................................................................78

69. Fracture Energies for TC-128B Measured in BFCM Tests .....................................79
ix

Tables

1. Baseline Parameters for Sensitivity Studies on Derailment Dynamics Models.........7

2. Mechanical Properties and Constants Assumed for Tank Car Steels ......................24

3. Parameters for Simulated Head Impact Sensitivity Studies.....................................26

4. Results from Sensitivity Analyses using ABAQUS ................................................28

5. Results from Sensitivity Analyses using LS-DYNA ...............................................29

6. Details of Simulated Tank Car Head Impact Tests..................................................42

7. Material Properties Assumed for Tank Car Head ....................................................43

8. Comparison between FEA and RPI-AAR Head Impact Tests with

100% Outage ............................................................................................................43

9. Effect of Modeling Assumptions on Results at Impact Speed of 6 mph .................44

10. Effect of Modeling Assumptions on Results at Impact Speed of 11.5 mph ............45

11. Comparison between FEA and RPI-AAR Head Impact Tests with

2% Outage ................................................................................................................46

12. Summary of Full-Scale Shell Impact Test ...............................................................49

13. Indenter Face Dimensions........................................................................................49

14. Comparison of Maximum Forces in Assurance Test...............................................51

15. Comparison between Test 1 and FEA......................................................................52

16. Tank Car Configurations Examined by FEA ...........................................................63

17. Estimated Range of Puncture Velocity and Associated Kinetic Energy for 

Generalized Head Impact Scenario .........................................................................63

18. Estimated Range of Puncture Velocity and Associated Kinetic Energy for 

Generalized Shell Impact Scenario .........................................................................64

19. Summary of Tensile Test Measurements for TC-128B ...........................................68

20. Tensile Property Specifications for TC-128B..........................................................68

21. Summary of CVN Impact Energies (ft-lb) at Three Temperatures..........................68

22. Summary of High-Rate Fracture Toughness Data for Retired Cars ........................72

23. Summary of High-Rate Fracture Toughness Data from Minot Cars.......................72

24. Estimated Reference Temperatures..........................................................................75

25. Estimated Tolerance Limits for High-Rate Fracture Toughness (in ksi-√in) ..........75
x

Executive Summary

On behalf of the Federal Railroad Administration (FRA), the Volpe National 

Transportation Systems Center (Volpe Center) conducts and manages research on 

structural integrity of railroad tank cars under accident loading conditions. The research 

began to provide the FRA with technical support in responding to recommendations 

made by the National Transportation Safety Board (NTSB) following the Board’s 

investigation of a derailment that occurred near Minot, North Dakota, on January 18, 

2002. Research results are now being applied to support: (1) rulemaking proposed by 

FRA and the Pipeline and Hazardous Materials Safety Administration to ensure the safe 

transport of hazardous materials (hazmat) by tank cars and (2) a research-anddevelopment effort, called the Next Generation Rail Tank Car (NGRTC) Project, that was 

formed to develop and implement new improved designs for tank cars carrying hazmat.

The Volpe Center developed a multiphase approach to assess the risks associated with 

accidents in which railroad tank cars carrying hazardous materials might be involved. 

Engineering studies entailing analysis and testing are being conducted:

1) Derailment Dynamics–Physics-based computer simulation models are developed to 

examine the gross motions of rail cars in a generalized derailment. Moreover, the 

derailment dynamics model is used to estimate closing speeds that occur when 

derailed cars separate from the train and collide with one another.

2) Structural Finite Element Analysis–Dynamic, nonlinear (i.e., elastic-plastic material 

behavior with large deformations) finite element analysis models are developed to 

estimate the structural response of the tank car shell and end cap to an assumed 

scenario (i.e., penetrator shape, initial closing speed, and effective collision mass). 

The structural finite element analyses are carried out using commercial finite element 

software.

3) Tank Car Steels Characterization–A laboratory testing program was conducted to 

examine the mechanical properties of different steels obtained from either retired 

railroad tank cars or those involved in accidents. The tests were carried out by 

Southwest Research Institute under a task order contract with the Volpe Center.

This report describes the engineering studies to examine the structural integrity of 

railroad tank cars under extreme loading conditions that may be experienced in accidents. 

Specific details of the research are described.

Major conclusions based on the results to date are summarized as follows for each of 

phase of research.

Derailment Dynamics

Sensitivity studies using the lumped-parameter models developed for derailment 

dynamics indicate that train speed and friction have the most significant effect on the 

derailment outcome in terms of either the number of derailed cars, maximum closing 

speed, or peak coupler force.
xi

For flat terrain and train speeds not exceeding roughly 40 mph, the maximum closing 

speeds between cars engaging in post-derailment collisions appear to average about onehalf the initial train speed.

Structural Response

The nonlinear finite element analysis (FEA) models developed to examine forceindentation behavior for head and shell deformations were verified through various 

comparisons.

Dynamic, nonlinear FEA for shell impacts with fluid-structure interaction were validated 

with data obtained from full-scale tank car tests.

Based on comparisons between FEA and full-scale shell impact test data, peak impact 

forces and maximum indentations depend on impact speed. In addition, indenter size 

appears to have a relatively weak effect on the force-indentation characteristic, but a 

strong effect on puncture.

Finite element procedures will remain useful for predicting structural response of any 

new car designs that might differ from current practice. Research employing these 

procedures is ongoing to develop alternative or improved designs for tank cars carrying 

hazardous materials

Tank Car Steels Characterization

No clear trends were observed between chemical composition, tensile properties, Charpy 

impact energies, or fracture toughness values and tank car build date.

The extent of scatter observed in the measurements of fracture toughness was quite large, 

which obscures making definitive conclusions regarding toughness variation with age.

The large scatter makes it unlikely that a practical specification of minimum fracture 

toughness can be devised to guarantee the prevention of unstable fracture in railroad tank 

cars subject to derailment forces. A specification of average fracture toughness is 

possible and could serve to decrease the population of cars at risk of fracture.
1

1. Introduction

The safe transport of hazardous materials (hazmat) by railroad tank cars is a key concern 

of the Federal Railroad Administration (FRA). Moreover, the objective of FRAsponsored research is to maintain tank integrity over a broad range of loading conditions 

that vary from the normal operating environment to rare events such as accidents.

Data from FRA’s Railroad Accident/Incident Reporting System (RAIRS) indicates that 

the number of accidents per year with at least one car releasing hazmat has decreased 

significantly since the late 1970s (Figure 1). The decrease is attributed to improvements 

in tank car designs and to Federal regulations that instituted requirements for head shield, 

thermal protection, and double shelf couplers—each of which reduces the likelihood of 

rupturing a tank car during an accident.

Year

1975 1980 1985 1990 1995 2000 2005

Number of accidents

10

20

30

40

50

60

70

80

90

100

Figure 1. Number of Accidents per Year with at least One Car Releasing Hazmat 

from FRA RAIRS Database

Data on damage to tank cars involved in accidents is also maintained by the Railroad 

Tank Car Safety Research and Test Project, sponsored by the Railway Supply Institute 

(RSI) and the Association of American Railroads (AAR). Figure 2 shows a similar trend 

in the number of accident-caused releases from tank cars carrying specific lading called

toxic inhalation hazardous (TIH) materials [1]. Between 1965 and 2005, a total of 252 

tank cars released TIH in 176 accidents. Figure 3 shows the causes of lading loss and the 

number of gallons lost associated with these releases. For example, roughly less than half 

of the releases are caused by failures in the head and the shell of the tank car, but head 

and shell failures resulted in over 85 percent of the gallons lost. Failures to valves and 

fittings account for about one-third of the number of accident-caused releases, but less 

than 5 percent of the total gallons of lost lading.
2

Year

19651966196719681969197019711972197319741975197619771978197919801981198219831984198519861987198819891990199119921993199419951996199719981999200020012002200320042005

Releases

0

5

10

15

20

25

43 125 50 12 22

1960s 1970s 1980s 1990s 2000s

11 from Minot

Figure 2. TIH Tank Cars Releasing Lading in Accidents by Year, 1965-2005 [1]

Figure 3. Accident-Caused Releases in TIH Tank Cars, 1965-2005 [1]
3

Significant accidents involving the release of hazmat are investigated by the National 

Transportation Safety Board (NTSB). Based on findings from their accident 

investigations, the NTSB issues recommendations that are intended to prevent similar 

accidents from occurring.

Three recent accidents have focused attention on the structural integrity of railroad tank 

cars under accident loading conditions:

• On January 18, 2002, a freight train traveling about 41 miles per hour (mph) derailed 

near Minot, North Dakota. Five tank cars carrying anhydrous ammonia 

catastrophically ruptured, which resulted in one fatality, evacuation of the nearby 

town, property damage exceeding $2 million, and over $8 million on environmental 

remediation [2]. Figure 2 shows that 11 tank cars in this accident released lading, 

which account for all but one of the total TIH releases for the entire year of 2002 and 

for half of the total TIH releases between 2000 and 2005 (inclusive).

• On June 28, 2004, a freight train traveling about 45 mph struck the side of a car in 

another freight train that was entering a siding while traveling about 20 mph in the 

opposite direction. The collision occurred near Macdona, Texas and resulted in 39 

derailed cars, breach of a tank car containing chlorine, three fatalities, and total (i.e., 

property and environment) damages exceeding $7 million [3].

• On January 6, 2005, a freight train traveling about 47 mph through Graniteville, 

South Carolina encountered an improperly lined switch that diverted the train from 

the mainline onto a side track where it collided with an unoccupied, parked train. 

Among the derailed freight cars were three tank cars, one of which was breached, 

releasing chlorine. This accident resulted in nine fatalities; evacuation of about 5,400 

people; and total damages exceeding $6.9 million [4].

Sponsored by the FRA Office of Research and Development, the Volpe National 

Transportation Systems Center (Volpe Center) conducts and manages research to 

examine the structural integrity of railroad tank cars. Before the Minot derailment, FRAsponsored research focused on maintaining tank integrity under normal operating 

conditions (e.g., metal fatigue and crack propagation). After Minot, research began to 

support FRA in responding to recommendations made by the NTSB following the 

Board’s investigation of the accident. The NTSB safety recommendations from the 

Minot derailment are listed in Appendix A.

Research results are now being applied to support: (1) rulemaking proposed by the FRA 

and the Pipeline and Hazardous Materials Safety Administration, and (2) an industrysponsored research-and-development effort called the Next Generation Rail Tank Car 

(NGRTC) Project [5]. Dow Chemical Company, Union Pacific Railroad, and Union 

Tank Car Company are the industry sponsors of this project. The NGRTC Project began 

in 2006 with the objective to develop and implement new improved designs for railroad 

tank cars carrying hazardous materials. In January 2007, FRA signed a Memorandum of 

Cooperation with the industry sponsors of the NGRTC Project to share research 

information. Transport Canada and the U.S. Department of Homeland Security also 

participate in this project through the Memorandum of Cooperation.
4

The Volpe Center developed a multiphase approach to assess the risks associated with 

accidents in which railroad tank cars carrying hazardous materials might be involved. 

Engineering studies entailing analysis and testing are being conducted:

1) Derailment Dynamics–Physics-based computer simulation models are developed 

to examine the gross motions of rail cars in a generalized derailment. Moreover, 

the derailment dynamics model is used to estimate closing speeds that occur when 

derailed cars separate from the train and collide with one another.

2) Structural Finite Element Analysis–Dynamics, nonlinear (i.e., elastic-plastic

material behavior with large deformations) finite element analysis models are 

developed to estimate the structural response of the tank car shell and end cap to 

an assumed scenario (i.e., penetrator shape, initial closing speed, and effective 

collision mass). The structural finite element analyses are carried out using 

commercial finite element software (e.g., ABAQUS and LS-DYNA).

3) Tank Car Steels Characterization–A laboratory testing program was conducted to 

examine mechanical behavior of different steels obtained from either retired 

railroad tank cars or those involved in accidents (e.g., Minot). The testing 

program was carried out by Southwest Research Institute under a task order 

contract with the Volpe Center.

This report describes these engineering studies to examine the structural integrity of 

railroad tank cars under extreme loading conditions that may be experienced in accidents. 

Specific details of the research are described. Conclusions based on the research findings 

are presented.
5

2. Analys is of Derailment Dynamics

Physics-based models are developed to calculate the gross motions of rail cars during a 

train derailment. The inputs to the analysis include train make-up and initial train speed. 

The objective of this modeling phase is to estimate the ranges of closing speeds and 

incidence angles between cars impending to collide with a loaded tank car. Moreover, 

the results from the models developed in this phase will be used as initial conditions to 

more detailed structural finite element models.

In this phase of the modeling research, the verification and validation activities are: 

deriving the equations of motion for rail cars in a derailment, comparing results from 

alternative methods that implement the numerical solution to the derived equations of 

motion, and comparing the present modeling results to those developed from previous 

work.

2.1 Review of Previous Research

Previous research on modeling of rail accidents can be roughly divided into two 

categories: (1) investigations of vehicle-track interaction and (2) studies of the actions 

between cars. The objective of research in the first category is to understand the 

mechanisms of derailment (e.g., wheel climb, excessive lateral-to-vertical wheel load 

ratio, etc.) The results from vehicle-track interaction models are not directly applicable 

to the present work, but they can provide some useful information regarding modeling 

techniques. Past research in the second category is directly applicable to the present 

work, and has been conducted through two approaches: (a) development of special 

purpose models and (b) development of models using commercial general purpose 

software for multibody dynamics.

A special purpose model was developed in the 1970s to examine the gross motions of rail 

cars in a train derailment [6]. Each car in this planar (i.e., two-dimensional) analysis was 

assumed to behave as a rigid body of finite length but zero width. A major limitation of 

this model was that the cars were assumed to remain coupled during the derailment. 

Another special purpose model was later developed under the sponsorship of Transport 

Canada (TC) that allowed the cars to decouple, but the criterion for decoupling was 

incomplete [7] and [8]. The Transport Canada model included provisions for: tangent or 

curved track, initial derailment at either the lead or trailing truck of the first car off the 

track, and potential for tank car rollover based on a vertical-to-horizontal force ratio 

criterion. More recently, a planar model was developed at Queen’s University [9], in 

which the differential equations of motion were derived from Lagrange’s equations and 

were solved numerically using a special-purpose computer program written in 

FORTRAN.

Commercial general purpose software for multibody dynamics has been used to develop 

a three-dimensional model to examine train crashes [10]. Specifically, a software 

package called DADS (Dynamic Analysis Design Simulation) was used to calculate the 

gross motions for a 20-car train.
6

None of the previous models made any provisions to calculate relative closing speed, 

which is a key variable in assessing collision damage.

2.2 Purpose-Built Model and ADAMS Model

A planar (i.e., two-dimensional) purpose-built model to calculate the gross motions of rail 

cars during a derailment scenario is developed in the present work. The differential 

equations of motion are derived via Newton’s laws of physics. Car motions are defined 

with respect to a fixed (i.e., non-rotating) and right-handed reference frame. The 

mathematical formulation is presented in reference 11. The equations of motion are 

solved numerically via a FORTRAN computer code.

Analysis of derailment dynamics is also carried out using a commercially available 

general purpose software program for rigid-body dynamics called ADAMS (Automatic 

Dynamic Analysis of Mechanical Systems) [12].

1

Couplers are characterized by a length, a dead band, stiffness, and maximum swing 

angle. The coupler length defines the neutral distance between cars. The coupler dead 

band is the distance the coupler length can displace before a restoring force is applied. 

 ADAMS allows the user to create 

objects, forces, and constraints within the modeling environment, and solves for the 

resulting motions without the user explicitly deriving the equations of motion. Another 

advantage of using ADAMS is the graphical interface and post-processing tools that 

readily display output information

Rail cars are constructed in ADAMS as a cylindrical part with an arbitrary radius of 9 

feet (ft). The length of the cylinder depends on whether it represents a tank or a 

locomotive. The locomotive is approximately 60 ft, and tank cars are slightly longer at 

about 65 ft. A planar constraint, connecting the car center of mass to the ground, is used 

to limit the car’s motion to the x-z plane. A planar constraint is only required on one in a 

train consist as constraints in the couplers limit the motion of subsequent cars.

In both the purpose-built and ADAMS models, the entire train consist is given an initial 

velocity in the longitudinal direction and the derailment is modeled with an initial angular 

velocity and an associated lateral velocity applied on the lead car. The car’s motion is 

resisted by a frictional force applied at the car’s trucks, which increases as the truck 

passes the point of derailment.

Both models include two types of friction: (1) on-track coefficient of friction is an 

approximation of the maximum frictional force associated with emergency braking and 

(2) off-track coefficient of friction is an estimate of the complicated resistive forces 

present when the cars derail.

 1 Gross motions of cars in a derailment can also be modeled using LS-DYNA, a commercial finite element 

code for dynamic nonlinear analysis. The application of LS-DYNA for dynamic structural analysis is 

described in the next section of this report.
7

The restoring force is proportional to the coupler stiffness. The maximum swing angle is 

the angle at which the restoring moment begins to be applied.

In general, the motion of the train consist in a derailment begins with an initial rotation 

imparted to the lead car and with all cars traveling at a given initial speed. The lead car 

swings out in the direction of the initial rotation, with higher off-track frictional forces 

applied at the truck opposing the direction of motion. As the cars derail, the coupler 

forces between cars create a moment couple. The many highly coupled interactions 

cause an irregular buckling pattern, which generally occurs in two forms, either as an 

alternating pile-up as shown in Figure 4(a) or as a curved string of displaced cars as 

shown in Figure 4(b). The direction of travel is left to right in these figures.

(a) Alternating-Direction Buckling Pattern (b) Curved String of Displaced Cars

Figure 4. Derailment Buckling Patterns

2.3 Sensitivity Studies

Sensitivity studies were conducted using the purpose-built (i.e., FORTRAN) model for 

derailment dynamics [11]. Baseline parameters were developed and varied one factor at 

a time to examine their relative effect on the following metrics: (1) the number of 

derailed cars in the simulation, (2) maximum closing speeds, and (3) peak coupler forces. 

The baseline parameters for the sensitivity studies are listed in Table 1.

Table 1: Baseline Parameters for Sensitivity Studies on Derailment Dynamics 

Models

Parameter Value

Number of cars in train make-up (train length) 60 cars

Car weight 150,000 lb

Initial longitudinal train speed 37 mph

Initial angular velocity 0.2 radians per second

On-track (rail) coefficient of friction 0.15

Off-track (ground) coefficient of friction 0.50
8

Each parameter was varied from its baseline value by ±20 percent and ±50 percent while 

the remaining inputs including car length and width and coupler characteristics were set 

equal to their respective baseline values.

Figure 5 shows the relative effect of changing each parameter on the number of derailed 

cars calculated using the purpose-built model. The baseline case results in 13 cars 

derailing from the 60-car train. Clearly train speed has the greatest effect on the number 

of derailed cars. Increasing the initial train speed by 50 percent over the baseline 

increases the number of derailed cars from 13 to 24. Decreasing the initial train speed by 

50 percent below the baseline decreases the number of derailed cars from 13 to 6. 

Friction also has a significant effect on the number of derailed cars. The relative 

difference between the ground and rail friction coefficients is proportional to the force 

required to decelerate the train consist. Greater differences in friction coefficients lead to 

larger braking forces. Moreover, friction forces have an inverse relationship compared to 

the other inputs. That is, increasing friction decreases the derailment severity in terms of 

the number of derailed cars, while increasing the value of the other parameters increases 

the number of derailed cars.

Figure 6 shows similar results for the number of derailed cars calculated using the 

ADAMS model. The ADAMS model also calculates 13 derailed cars for the baseline 

case, but shows slightly more derailed cars as the train speed increases. The ADAMS 

results also show a slightly greater effect of friction on the number of derailed cars than 

the purpose-built model.

Figure 7 shows the relative effect of changing each parameter on the maximum closing 

speed calculated using the purpose-built model. The baseline case results in a maximum 

closing speed of 19 mph. Train speed has the most significant effect on maximum 

closing speed. Increasing the initial train speed by 50 percent over the baseline increases 

the maximum closing speed by almost 60 percent. Decreasing the initial train speed by 

50 percent below the baseline decreases the maximum closing speed by about 30 percent. 

Ground friction has a moderate effect on closing speed. Increasing ground friction by 50

percent increases the maximum closing speed by more than 20 percent. Changing the 

other input parameters varies the maximum closing speed by, at most, ±15 percent.

Figure 8 shows the variations in maximum closing speeds calculated using the ADAMS 

model, which are similar to those using the purpose-built model.

Figure 9 shows the relative effect of changing each parameter on the peak coupler force 

calculated using the purpose-built model. The peak coupler force corresponding to the 

baseline case is 1,821 kips. Increasing the initial train speed by 50 percent increases the 

peak coupler force by almost twice.

Figure 10 shows the results from the ADAMS model. The baseline case corresponds to a 

peak coupler force of 1,858 kips, which is slightly higher than the baseline calculated by 

the purpose-built model. Again, the variations in peak coupler forces calculated using the 

ADAMS model are similar to those calculated using the purpose-built model.
9

Variation from Baseline (%)

-60 -40 -20 0 20 40 60

Normalized Number of Derailed Cars

(Variation/Baseline)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

Number of Derailed Cars

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

Train Speed

Angular Velocity

Train Length

Car Mass

Ground Friction

Rail Friction

Figure 5. Relative Effect of Parameters on Number of Derailed Cars using PurposeBuilt Model

Variation from Baseline (%)

-60 -40 -20 0 20 40 60

Normalized Number of Derailed Cars

(Variation/Baseline)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

2.2

2.4

Number of Derailed Cars

0

2

4

6

8

10

12

14

16

18

20

22

24

26

28

30

Train Speed

Angular Velocity

Train Length

Car Mass

Ground Friction

Rail Friction

Figure 6. Relative Effect of Parameters on Number of Derailed Cars using ADAMS 

Model
10

Variation from Baseline (%)

-60 -40 -20 0 20 40 60

Normalized Closing Speed (Variation/Baseline)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Maximum Closing Speed (mph)

0

5

10

15

20

25

30

35

Train Speed

Angular Velocity

Train Length

Car Mass

Ground Friction

Rail Friction

Figure 7. Relative Effect of Parameters on Maximum Closing Speed using PurposeBuilt Model

Variation from Baseline (%)

-60 -40 -20 0 20 40 60

Normalized Closing Speed (Variation/Baseline)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Maximum Closing Speed (mph)

0

5

10

15

20

25

30

Train Speed 35

Angular Velocity

Train Length

Car Mass

Ground Friction

Rail Friction

Figure 8. Relative Effect of Parameters on Maximum Closing Speed using ADAMS

Model
11

Variation from Baseline (%)

-60 -40 -20 0 20 40 60

Normalized Peak Coupler Force (Variation/Baseline)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Peak Coupler Force (kips)

0

1000

2000

3000

Train Speed

Angular Velocity

Train Length

Car Mass

Ground Friction

Rail Friction

Figure 9. Relative Effect of Parameters on Peak Coupler Force using Purpose-Built 

Model

Variation from Baseline (%)

-60 -40 -20 0 20 40 60

Normalized Peak Coupler Force (Variation/Baseline)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

1.8

2.0

Peak Coupler Force (kips)

0

1000

2000

3000

Train Speed

Angular Velocity

Train Length

Car Mass

Ground Friction

Rail Friction

Figure 10. Relative Effect of Parameters on Peak Coupler Force using ADAMS 

Model
12

The sensitivity analyses using both the purpose-built and ADAMS models indicate that 

train speed and friction have the most significant effect on derailment severity in terms of 

either number of derailed cars, maximum closing speed, or peak coupler force. The 

results from the sensitivity studies are compared to those from previous work to validate 

the derailment dynamics models. For example, Figure 11 shows the effect of train speed 

on the number of derailed cars as calculated by three different models: the purpose-built 

model, the ADAMS model, and the Queen’s University (QU) special purpose model [9]. 

Although the baseline parameters are somewhat different in the parametric studies for 

each derailment dynamics model, the relative effect of train speed of the number of 

derailed cars is consistent.

Variation in Train Speed from Baseline (%)

-60 -40 -20 0 20 40 60

Normalized Number of Derailed Cars

(Variation/Baseline)

0.0

0.5

1.0

1.5

2.0

2.5

Purpose-Built Model

ADAMS Model

QU Model

Figure 11. Effect of Train Speed on Number of Derailed Cars from Different 

Models

Figure 12 shows the effect of ground friction on the number of derailed cars, as

calculated from the different models. The results from the purpose-built and ADAMS 

models are comparable. All three models show that ground friction has a strong effect on 

the number of derailed cars. Moreover the number of derailed cars increases as the offtrack or ground coefficient of friction is increased.

In the development of the special purpose model by Queen’s University, results from the 

derailment dynamics were compared to a derailment that occurred in Mississauga, 

Ontario, Canada on November 10, 1979 [13]. The Queen’s model reproduced the 

number of derailed cars in that derailment (24 cars).
13

Variation in Ground Friction from Baseline (%)

-60 -40 -20 0 20 40 60

Normalized Number of Derailed Cars

(Variation/Baseline)

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Purpose-Built Model

ADAMS Model

QU Model

Figure 12. Effect of Ground Friction on Number of Derailed Cars from Different 

Models

2.4 Closing Speeds and Impact Forces

In this section, the closing speeds of adjacent cars calculated by the ADAMS model are 

examined. Moreover, the kinematics from a 100-car train identified two characteristic 

motions as possible sources of impact, which are shown in Figure 13. The first mode 

occurs from the relative difference in the absolute translational velocities of adjacent cars. 

The second mode of possible collision occurs as the cars buckle.

(a) Difference in Translational Velocities (b) Difference in Angular Velocities

Figure 13. Characteristic Motions as Possible Sources of Impact

In the first characteristic motion, differences in the on- and off-track coefficients of 

friction and coupler interactions cause the velocities of the cars to fluctuate. When the 
14

lead car is slower than the trailing car at a given time, the distance between cars decreases 

until the coupler resists the motion.

The trailing car’s translational velocity is subtracted from the leading car’s to obtain the 

first car’s velocity relative to the second. The relative velocity is considered positive if

the lead car is moving faster than the trailing car and negative if the trailing car is moving 

faster. Therefore, negative relative velocity represents the closing speed between the two 

cars. The maximum closing speeds for the first 40 cars in the analysis of a 100-car train 

are shown in Figure 14. Maximum closing speeds may occur at any given distance 

between adjacent cars, but closer inspection of the kinematics indicates that they 

generally occur when the coupler is at its minimum length.

Car Number

0 10 20 30 40

Maximum Closing Speed (mph)

0

5

10

15

20

Figure 14. Maximum Closing Speeds Based on Difference in Translational Velocity

The closing speeds tend to increase from the front of the train (where the derailment is 

initiated) to the middle of the derailed cars. The maximum closing speed is slightly more 

than 11 mph on the 14th car. The values then drop off to the end of the derailed cars. 

The largest closing speeds of the non-derailed cars fluctuate and are bounded between 3 

and 6 mph, which are significantly lower than those of the derailed cars. The times at 

which the maximum closing speeds occur vary greatly with no trend, but all occur 

between 5 and 10 seconds into the simulation.

In the second characteristic mode of possible collision, the cars derail in an alternating 

direction and tend to collapse on each other. The closing speed is determined by first 

taking the magnitude of the difference of the adjacent cars’ angular velocities (the sign of 

the relative velocity is ignored since cars can collapse in either the positive or negative 
15

angular direction). Then, the relative angular velocity is multiplied by half the car length 

to calculate the speed at the ends of the cars, which is the location where the closing 

speed is the highest. At the time of the maximum closing speed, the cars are not 

necessarily in an alternating buckling pattern. But closer inspection of the kinematics 

indicates that the maxima generally occur as the cars reach their maximum buckling. The 

cars also rotate about their center of gravity, meaning that adjacent cars would not impact 

by pure rotation. Some translational displacement is also required to bring the cars into 

contact.

Determining how fast cars may collapse on each other provides an estimate of the 

maximum closing speeds. Figure 15 shows the results of this calculation for the first 40 

cars. As with the closing speeds found from the relative translational speed of the cars, 

the buckling action of the cars produces higher closing speeds at the front of the train. 

These closing speeds are generally larger than those produced from the difference in 

translational velocity, with a maximum of 19.6 mph. The closing speeds begin to drop 

off for the non-derailed cars and do not vary greatly, averaging about 3.5 mph for the 16 

non-derailed cars shown in Figure 15.

Car Number

0 10 20 30 40

Maximum Closing Speed (mph)

0

5

10

15

20

Figure 15. Maximum Closing Speeds Based on Difference in Angular Velocity

The closing speeds shown in the two previous figures ignore any effect that breaking of 

the couplers may have on the rotation. Moreover, additional criteria or analyses are 

needed to calculate impact forces.

For example, impact forces may be represented by the coupler forces. Although the 

coupler generally prevents adjacent cars from impacting, the coupler forces would likely 
16

result in an impact event for relatively large forces. Figure 16 shows the maximum 

coupler forces calculated from the 100-car train ADAMS model. These results, however, 

only provide an approximation of the impact forces that may be expected because 

breaking of the coupler was not included in this analysis. Also, the force levels are only 

valid relative to the other impact forces. Moreover, these results indicate locations of the 

highest values. The actual quantities would vary depending on factors such as the 

coupler stiffness. The maximum coupler forces generally correspond with the maximum 

closing speed with the values increasing from the first car to the 13th car at 7.9 million 

pounds of force. The maximum coupler forces then begin to decrease to the end of the 

derailed cars. Large forces can be seen throughout the remaining consist and vary 

between about 2 million and 5 million pounds of force.

Car Number

0 10 20 30 40

Maximum Coupler Force (lbs)

0

1e+6

2e+6

3e+6

4e+6

5e+6

6e+6

7e+6

8e+6

9e+6

Figure 16. Maximum Coupler Forces for First 40 Cars of 100-Car Train

Another ADAMS model is used to examine interactions between decoupled cars. A train 

consist of 30 cars with a 70-car equivalent lumped mass on the 30th car is carried out 

which allows coupler breaks and contact forces to occur for the first 10 cars in the train 

consist. The contact between cars is categorized as either initial or secondary contact. 

Initial contacts occur just after the cars decouple. Secondary contact includes all impacts 

that occur after the cars have been decoupled.

As the first car in the train consist rotates and passes the point of derailment, it begins to 

slow. Its rear coupler eventually reaches the maximum displacement and breaks. The car 

continues to slow until the second car impacts it in the rear. This sequence of events sets

off a chain reaction of decoupling and impact, which propagates down the train consist.
17

Figure 17 shows the closing speeds associated with initial impacts. The closing speeds

are relatively low for the lead cars since the difference in speed for the first and second 

car is only a result of off-track friction applied to the first car. The values then sharply 

rise as the contact force of the first car striking the second creates a much larger 

difference in speed between the second and third cars in the consist. The effect of slowing 

cars propagates back and the closing speeds continue to increase. The maximum closing 

speed of about 18 mph occurs between the last two cars with contact forces applied.

Contact Number

0 1 2 3 4 5 6 7 8 9 10

Closing Speed at Contact (mph)

0

2

4

6

8

10

12

14

16

18

20

Figure 17. Closing Speeds for Initial Contact

The corresponding impact forces for initial contact follow a similar general trend, as 

shown in Figure 18. These impact forces are estimated values based upon assumed 

values for spring stiffness of the contact force, and are only valid relative to other forces. 

Moreover, theses results suggest that the maximum closing speeds and maximum impact 

forces for initial contact are somewhat correlated.

Secondary impacts are less orderly than the initial contact. Small differences in the 

timing of the decoupling, the lead car’s initial rotation, and the fact that the 11th car 

cannot decouple, cause the cars to have a non-uniform motion. The action of the 

secondary contact on gross motions of rail cars in this generalized derailment scenario is 

shown in Figure 19. In total, there are eight secondary impacts of significance. The cars 

remain in order corresponding to their original position in the train consist. The time at 

which the secondary impacts occur is also shown in the figure. Also, the figure calls out 

the car-to-car interactions for each contact event. For example, the secondary impact at 

6.79 seconds corresponds to the cars 3 and 4 contacting each other.
18

Contact Number

0 1 2 3 4 5 6 7 8 9 10

Impact Force (lbs)

0.0

2.0e+5

4.0e+5

6.0e+5

8.0e+5

1.0e+6

1.2e+6

1.4e+6

1.6e+6

Figure 18. Impact Forces for Initial Contact

1

2

3

4

5

6

7

8

@t=6.79 sec

@t=7.25 sec

@t=7.70 sec

@t=8.14 sec

@t=8.42 sec

@t=8.93 sec

@t=9.02 sec

@t=10.11 sec

Figure 19. Gross Motions of Rail Cars and Post-Derailment, Car-to-Car Impacts
19

Figure 20 shows the closing speeds corresponding to the secondary or post-derailment, 

car-to-car impacts. The closing speeds at impact vary between a minimum of 9 mph and 

a maximum of 51 mph. Although initial contact involved relatively little difference in 

angular velocity, it appears that secondary contact is generally associated with larger 

differences in angular velocity, which results in larger closing speeds.

Contact Number

0 1 2 3 4 5 6 7 8 9

Closing Speed at Contact (mph)

0

10

20

30

40

50

60

Figure 20. Closing Speeds for Secondary Contact

The impact forces from secondary contact also exhibit a large variance, as shown in

Figure 21. Unlike the initial impact forces, the secondary interactions do not indicate a 

correlation between the closing speeds and impact forces. Also, the majority of forces 

are significantly lower than initial impacts, with a maximum secondary impact force of 

1.6 million pounds. The lack of correlation between closing speeds and impact forces 

demonstrates the chaotic nature of post-derailment, car-to-car impacts.

The results presented in this section for impact forces are estimations based upon the 

analysis of derailment dynamics. The calculation of impact forces is further refined by 

analyzing the structural response of tank car components to various collision scenarios 

through finite element analysis, which is described in the next section of this report.
20

Contact Number

0 1 2 3 4 5 6 7 8 9

Impact Force (lbs)

0.0

2.0e+5

4.0e+5

6.0e+5

8.0e+5

1.0e+6

1.2e+6

1.4e+6

1.6e+6

1.8e+6

Figure 21. Impact Forces for Secondary Contact

2.5 Discussion and Summary

Lumped-parameter models were developed to examine the gross motions of rail cars in 

generalized train derailments. Two different models were developed for this purpose, a 

purpose-built FORTAN model and a model developed using commercial software called 

ADAMS, which produced similar results for the same inputs. The similarity of results 

from the two models suggests that the dynamics are being correctly calculated for the 

assumed scenarios. 

However, the assumptions at best provide only a simplified representation of actual 

conditions. For example, the actual terrain at a derailment site is unlikely to be perfectly 

level; also, the effective friction between derailed rail cars and the ground is likely to 

vary. Thus, the models provide a general representation but do not reproduce specific 

derailment events.

Nevertheless, the general results can provide some useful insights. For example, the 

closing velocities between cars engaging in post-derailment collisions appear to average 

about half the initial speed of the train.

Another general result is that train speed appears to be the most important variable. 

When the assumed train speed is increased by a factor of 3 (18 to 54 mph) in a series of 

cases, the derailment dynamics models calculate following outcomes: (1) the number of 

derailed cars increased by a factor of 4, (2) maximum closing speed for car-to-car 
21

collisions increases by a factor of 2.5, and (3) peak collision force increases by a factor of 

6.

The derailment dynamics models are used to examine post-derailment, car-to-car 

impacts. That is, rail cars collide with other cars as they come off the tracks in the 

simulated derailment. Moreover, the simulations produce car-to-car impacts that 

generally occur in accidents leading to the release of hazardous materials; namely, head 

and shell impacts. Figure 22 shows three particular instants in time from a generalized 

derailment simulation in which the post-derailment, car-to-car impacts can be simplified 

to a head impact and two shell impacts, one near the center of the tank and one near an 

end. Moreover, the simplified or generalized car-to-car impacts scenarios are used to 

examine the response of the tank structure for a prescribed closing speed.

(a) Derailment Simulation (b) Simplified Car-to-Car 

Impacts

Figure 22. Simulated and Generalized Car-to-Car Impact Scenarios

Figure 23 shows still photographs taken from a surveillance video that captured the 

occurrence of an actual freight train derailment. The sequence of the stills shows the 

evolution of the derailment pile-up and car-to-car impacts, which are similar to those 

produced by the derailment dynamics models. The similarity between actual and 

simulated car-to-car collisions provides confidence in the models for derailment 

dynamics, and suggests that they have been verified and validated.
22

Figure 23. Stills from Surveillance Video of an Actual Train Derailment
23

3. Structural Finite Element Analysis

The physics of impact are modeled using dynamic, nonlinear finite element analysis

(FEA). In the present context, nonlinear means elastic-plastic material behavior with 

large deformations. Finite element models of different tank car components, such as the 

head and the shell of the tank, are developed to examine their structural behavior when 

impacted by different objects (such as couplers, wheels, etc.). In general, structural 

behavior is quantified as force as a function of indentation, or force-indentation 

characteristic. Moreover, two commercial general-purpose finite element software 

programs for linear and nonlinear, static and dynamic analysis are used for this purpose: 

LS-DYNA [14] and ABAQUS [15].

The development of computational models that include impact dynamics as well as 

nonlinear material behavior is labor intensive. The combination of finite difference in 

time and nonlinear material behavior makes it difficult in practice to obtain good model 

performance without assuming extremely small time steps, which affects computational 

time. Therefore, the primary technical challenge in the present work is to develop an 

accurate and efficient model within practical computational limits. 

Solutions to structural behavior in dynamic, nonlinear FEA are achieved through direct 

integration methods, also referred to as step-by-step methods, which use a finite 

difference approximation to replace the time derivative at various time steps. The finite 

difference methods for direct integration can be either implicit or explicit. Implicit 

integration requires an iterative solution process to ensure equilibrium at each time step, 

and is unconditionally stable. The iterative process may require high computational time. 

No iterations are performed in explicit integration, but the time step assumed in the 

solution must be smaller than the critical time step for the solution to be stable. 

Moreover, explicit integration is conditionally stable. The critical time step varies during 

the solution process because it depends on the geometry and material conditions that 

change during the analysis. The number of time steps for explicit integration may be 100 

to 10,000 times more than would be used in an implicit calculation. If a step size larger 

than the critical time step is assumed in an explicit calculation, errors can accumulate and

grow, ultimately leading to numerical instability of the solution. 

In linear problems, numerical instabilities in finite element analysis are self-evident 

because the solution grows without limit. In nonlinear problems, with elastic-plastic or 

other energy dissipating materials, extra energy introduced into the system by numerical 

instabilities may be dissipated by plastic work, which makes it possible for the instability 

to be arrested. An arrested instability, which may be in error by 10 to 100 percent or 

more, may appear to be reasonable [16].

Elastic-plastic material behavior is generally modeled using the Ramberg-Osgood 

equation for strain as a function of stress:

n

E K

σ σ

ε

  = +     (1)
24

where ε is the strain, σ is the stress, and E is the modulus of elasticity (30,000 ksi 

assumed for tank car steel). Also, n and K are material constants. Table 2 lists the 

assumed values of these constants for different tank car steels. The table also lists the 

assumed values for yield strength and ultimate tensile strength, which correspond to the 

minimum requirements for these steels.

Table 2. Mechanical Properties and Constants Assumed for Tank Car Steels

n K

(ksi)

Yield 

Strength 

(ksi)

Tensile 

Strength 

(ksi)

TC-128B 9.41 96.8 50 81

AAR M-115 6.65 73.1 30 60

A516-70 8.08 82.0 38 70

A710 20.4 104.3 80 90

HPS70 11.9 118.2 75 96

HPS100 20.8 137.3 107 119

The various activities to build credibility into computational models are collectively 

referred to as Verification and Validation (V&V). The V&V activities described in this 

report are developed with specific objectives for each modeling phase, and do not adhere 

to any specific recommended guidelines or standards.2

[17

 In this context, verification means 

assessing the accuracy of the solution from the computational models by comparison with 

known solutions. Validation means assessing the accuracy of a computational simulation 

by comparison with data. Moreover, verification deals with the mathematics associated 

with the model, and validation deals with the physics of the model ]. Clearly 

verification and validation are separate activities, but verification precedes validation.

Head indentation models are validated through comparisons with data obtained from 

head impact tests conducted by the Railway Progress Institute (RPI) and the Association 

of American Railroads (AAR) Tank Car Safety Research and Test Project in the 1970s 

[19]. Shell indentation models are validated through comparisons with measurements 

from full-scale shell impact tests that were conducted as part of the Next Generation Rail 

Tank Car Project [20] in 2007. 

3.1 Verification

A numerically stable and accurate solution within practically reasonable computational 

times is affected by choices made in the modeling development regarding type of 

element, mesh density (element aspect ratio), and order of quadrature (i.e., fully 

 2 Professional organizations, such as the American Institute of Aeronautics and Astronautics and the 

American Society of Mechanical Engineers (ASME) [18] are actively developing guidelines for assessing 

the credibility of modeling and simulation in computational fluid dynamics and solid mechanics, 

respectively.
25

integrated elements or reduced integration to calculate element stiffness). Regular shapes 

generally provide greatest accuracy. Thus, in a good mesh, most elements would be 

approximately square in two dimensions or cubes in three dimensions. Moreover, grid or 

mesh convergence is a part of the verification process in the development of FEA 

models. Sensitivity studies are conducted to examine the effect of varying element type, 

element aspect ratio, and order of integration or quadrature on the calculations of forceindentation behavior. In addition, FEA results are compared with known closed-form 

solutions to relatively simple structures (i.e., flat circular plates and ellipsoidal caps).

3.1.1 Sensitivity Studies

Numerical experiments are conducted to examine the effect of development options on 

force-indentation behavior and computational times. The effect of these options on 

equivalent plastic strain is also examined, which is necessary in order to develop a 

criterion for material failure. Moreover, the development options that are examined in 

these numerical experiments or sensitivity studies are:

(1) Commercial FEA Code: Do ABAQUS and LS-DYNA give comparable results?

(2) Static and Dynamic Analyses

(3) Element Type: Solid or Shell Elements

(a) Element aspect ratios and through-the-thickness layers for solid elements

(b) Element sizes and through-the-thickness integration points for shell elements

(4) Integration Scheme: Full or Reduced Integration

Generally speaking, shell elements are commonly used to model thin-walled structures. 

Shell elements are formulated to include or neglect transverse shear deformations which 

affect resistance to bending. When shell elements are used, the number of integration 

points through the thickness must be specified to calculate the element stiffness via 

numerical integration (i.e., quadrature). A shell element may be regarded as a special 

form of a solid element made thin in one direction. Alternatively, three-dimensional solid 

elements may be used but the number of elements through the thickness must be chosen 

judiciously to account for bending properly.

In principle, finer mesh and more integration points tend to provide more accurate 

solutions in finite element modeling, but increase computational time. Modeling options 

are also restricted by available computer resources. The following in-house computers 

were used in the sensitivity studies:

(1) Dual Intel Xeon (64 bit), 2×3.6 GHz, 8 GB Memory,

(2) Dual Intel Xeon (32 bit), 2×3.4 GHz, 4 GB Memory, and

(3) Intel Xeon (32 bit), 3.4 GHz, 2 GB Memory.

Finite element models of a tank car head impacted by a rigid coupler are developed for 

the sensitivity studies. The relevant parameters of the head impact models are listed in

Table 3.
26

Table 3. Parameters for Simulated Head Impact Sensitivity Studies

Parameter Value

Tank head diameter 83 inches

Head thickness 0.4375 inch

Aspect ratio of ellipsoidal cap 2 to 1

Tank car weight 40,900 lb

Ram car weight 128,900 lb

Material AAR M-115

Impact location Center of head

Impact speed 8.5 mph

Simplifying assumptions are made in the sensitivity studies. For example, a fixed 

boundary condition is applied along the interface between the impacted head and the 

remaining structure which is not modeled. The backup cars are not included in the 

model. The ram car is modeled as a rigid body with a distributed mass. Scanned images 

of a coupler deformed during an accident are digitally processed to generate the shape of 

the impactor. Although the shape of the coupler is asymmetrical, a quarter-symmetric 

model of the tank car head was modeled for simplicity. 3

Figure 24(a) shows a schematic of the entire dynamic simulation. Figure 24(b) shows a 

zoomed view of the impact zone. Similarly, static analyses are conducted on the same 

tank car head (Figure 25) with the same boundary conditions as the dynamic simulations. 

In the static analyses, a traction load is applied over a circular area (93 square inches (in)) 

at the center of the head.

Both static and dynamic analyses are conducted to calculate the global force-indentation 

response and the distribution of equivalent plastic strain. In the static analyses, force is a 

resultant of the traction load. In the dynamic analyses, force is derived from the contact 

force output. The simulation time for the dynamic analyses is set to 0.35 seconds.

Table 4 lists the results from the sensitivity analyses using ABAQUS. The analyses are 

grouped according to analysis type (static or dynamic), element type (solid or shell), 

integration scheme (full or reduced), element aspect ratio for solid elements or element 

size for shells, and through the thickness characteristics (number of layers for solids and 

number of integration points for shells). For each analysis case, the exact computational 

or CPU time was recorded. The CPU time in the table was rounded to the nearest day or 

week. Similarly, Table 5 shows the results from the sensitivity analyses using LSDYNA.

 3 Strictly speaking, the asymmetrical shape of the coupler does not warrant a quarter-symmetric model. 

This approach is reasonable for the purpose of comparative studies. 
27

(a) Full View

(b) Zoomed View

Figure 24. Schematic of Dynamic Simulations for Sensitivity Studies

Figure 25. Schematic of Static Analysis for Sensitivity Studies
28

Table 4. Results from Sensitivity Analyses using ABAQUS

Analysis 

type

Element 

type

Integration 

scheme

Element aspect 

ratio or size (1)

Through the 

thickness 

characteristics

CPU time

Static

Solid Full 1:1

1 layer <1 day

2 layers 1-3 days

3 layers 1-2 weeks (2)

Shell Full 1t

2 points <1 day

3 points <1 day

4 points <1 day

5 points <1 day

0.5t 3 points 1-3 days

Dynamic

Solid

Full 1:1 1 layer <1 day

2:1 2 layers 1-3 days

Reduced with 

enhanced 

hourglass 

control

1:1 1 layer <1 day

1:1 2 layers 3-7 days

2:1 2 layers <1 day

3:1 3 layers 1-3 days

4:1 2 layers <1 day

4:1 4 layers 1-3 days

Shell Full

2t 3 points <1 day

1t

2 points

3 points 1-3 days

4 points

5 points <1 day (3)

6 points <1 day

7 points <1 day

15 points (4) <1 day

0.5t 3 points 3-7 days (5)

1t with 0.5t local 

refinement (6) 5 points 1-3 days

1t with t/3 local 

refinement (7) 5 points 1-2 weeks

(1) Refers to general characteristics of a mesh, whereas individual element characteristics may vary.

(2) Estimated for the simulation to reach a force level of 400 kips. Owing to an unknown system error, actual 

simulation was aborted after about 4.5 days with partial result obtained with a maximum force of 187 kips.

(3) Mass scaling technique was employed to increase the stable time increment from 3.8×10-7 to 8×10-7

, thus 

decreasing the CPU time from 1-3 days to <1 day. The resulting mass increase is 0.44 lb or 0.19 percent of the 

head mass.

(4) Simpson’s rule was applied in this case, whereas Gauss quadrature was applied in all the other shell cases.

(5) Mass scaling technique was employed to increase the stable time increment from 1.7×10-7 to 4×10-7

, thus 

decreasing the CPU time from an estimated 2 weeks to 5.7 days. The resulting mass increase is 0.42 lbs or 0.18

percent of the head mass.

(6) A 10×10square-inch area in the impact center was meshed with a characteristic element size of 0.5t, whereas

the remaining mesh was transitioned to a characteristic element size of 1t. (7) A 10×10-square-inch area in the impact center was meshed with a characteristic element size of t/3, whereas 

the remaining mesh was transitioned to a characteristic element size of 1t.
29

Table 5. Results from Sensitivity Analyses using LS-DYNA

Analysis 

type

Element 

type

Integration 

scheme

Element 

aspect ratio 

or size

Through the 

thickness 

characteristics

CPU time

Dynamic

Solid

Full

1:1 1 layer <1 day

2:1 2 layers <1 day

1:1 2 layers 3-7 days

1:1 3 layers 2 weeks

Reduced w/ 

default hourglass 

control

2:1 2 layers <1 day

4:1 2 layers <1 day

8:1 2 layers <1 day

Shell Full 1t

2 points <1 day

3 points <1 day

4 points <1 day

5 points <1 day

Static analyses were conducted using ABAQUS/Standard. For solid elements, only 1:1 

aspect ratio was considered, and 1 to 3 layers of elements were developed. For shell 

elements, two element sizes were considered: 1t and 0.5t, where t is the head thickness. 

The number of integration points for the shell elements ranged from 2 to 5. CPU times 

for analyses using shell elements were comparable to those using solid elements with 

similar mesh refinement.

Dynamic analyses were conducted using ABAQUS/Explicit and LS-DYNA. In certain 

cases, the dynamic analyses for solid elements used reduced integration. At the same 

level of mesh refinement, a dynamic analysis is generally more time consuming than a 

static analysis.

Commercial Codes

Comparisons between results from ABAQUS and LS-DYNA verify the accuracy of both 

codes. Figure 26(a) shows results from dynamic analyses using solid elements with two 

different meshes (1:1 element aspect ratio and 1 layer of elements through the thickness 

compared with 2:1 element aspect ratio and 2 layers) from both codes. Figure 26(b)

shows results from dynamic analyses using shell elements with different integration 

points through the thickness. The full-integration scheme is used to produce the results 

shown in these figures. Moreover, ABAQUS and LS-DYNA produced results that are 

nearly indistinguishable in the solid element cases. In the shell element cases, results 

from ABAQUS and LS-DYNA are nearly identical up to an indentation of about 17 in, 

beyond that the LS-DYNA results appear to be more compliant, with lower maximum 

forces and higher maximum and residual indentations, than the ABAQUS results. The 

differences in maximum forces and maximum and residual indentations between the two 

programs are within 6 percent.
30

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

ABAQUS 1:1 1-layer

ABAQUS 2:1 2-layers

LS-Dyna 1:1 1-layer

LS-Dyna 2:1 2-layers

Force (Kips)

Indentation (inch.)

(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

ABAQUS 1t 3-points

ABAQUS 1t 4-points

LS-Dyna 1t 3-points

LS-Dyna 1t 4-points

Force (Kips)

Indentation (inch.)

(b)

(a) Using Solid Elements (b) Using Shell Elements

Figure 26. Comparison of Force-Indentation Results

Figure 27 compares contours of equivalent plastic strain from different meshes using 

solid elements. Figure 28 compares contours from using shell elements. More 

specifically, residual equivalent plastic strains are plotted in these contours. The upper 

limit of the contour plots was set to 0.2 in all cases. The two finite element programs 

using either solid or shell elements predicted the same location of maximum equivalent 

plastic strain; for instance, along the coupler’s shorter edge in contact with the tank head. 

In the case of solid elements, the general trends of the distributions for equivalent plastic 

strain over the entire domain of interest are similar. In the case of shell elements, 

however, the maximum equivalent plastic strains are similar in magnitude but the contour 

distributions appear to show larger variations.

Static and Dynamic Analyses

Figure 29 compares the force-indentation responses obtained from static and dynamic 

finite element analyses. Figure 29(a) shows the results using 1 or 2 layers of solid 

elements through the thickness of the tank head and an element aspect ratio of 1:1. 

Figure 29(b) shows the results using shell elements with an element size of 1t and 3 

integration points through the thickness. Dynamic responses are expected to be stiffer 

than static responses due to inertial and frictional effects especially at larger indentations. 

The dynamic stiffening is evident in the shell element and 1-layer solid element cases, 

but the 2-layer solid element case displays the opposite; i.e., the static response is 

somewhat stiffer than the dynamic case. Use of solid elements will be discussed further 

in subsequent subsections.
31

(a) ABAQUS Solid 1:1 1-layer (b) ABAQUS Solid 2:1 2-layers

(c) LS-DYNA Solid 1:1 1-layer (d) LS-DYNA Solid 2:1 2-layer

Figure 27. Contours of Equivalent Plastic Strain using Solid Elements

 

(a) ABAQUS Shell 1t 3-points (b) ABAQUS Shell 1t 4-points

 

(c) LS-DYNA Shell 1t 3-points (d) LS-DYNA Shell 1t 4-points

Figure 28. Contours of Equivalent Plastic Strain using Shell Elements
32

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

Static 1:1 1-layer

Static 1:1 2-layers

Dynamic 1:1 1-layer

Dynamic 1:1 2-layers

Force (kips)

Indentation (inch.)

(a)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

Static 1t 3-points

Dynamic 1t 3-points

Force (kips)

Indentation (inch.)

(b)

(a) Using Solid Elements (b) Using Shell Elements

Figure 29. Comparison between Static and Dynamic Finite Element Analyses

Solid elements

Figure 30 compares results using solid elements with different meshes in both static and 

dynamic analyses. In the static case, the curve for 3 layers of elements through the 

thickness is incomplete for the reason stated in footnote (2) of Table 4. The available 

results for 2 and 3 layers of elements through the thickness are nearly identical, 

suggesting that results are converging as the characteristic element size becomes smaller. 

This is true in both static and dynamic analyses.

Stiffer responses are expected for poor element aspect ratios due to shear locking. This is 

confirmed by the results for the dynamic analyses. The force-indentation curve 

corresponding to a 2:1 element aspect ratio is stiffer than the others.

Figure 31 shows the contour plots for equivalent plastic strain from dynamic analyses 

using four different meshes. While all four contour plots show strain localization in the 

same general area at which impact occurs, the distribution over the whole domain is 

somewhat different in each. The contour plots for 2 and 3 layers of elements through the 

thickness with an aspect ratio of 1:1 show similar maximum values for equivalent plastic 

strain and somewhat similar distributions over the whole domain.
33

0

100

200

300

400

500

600

0 10 20 30 40 50

Static 1:1 1 layer

Static 1:1 2 layers

Static 1:1 3-layers

Force (kips)

Indentation (inch.)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

Dynamic 1:1 1-layer

Dynamic 1:1 2-layers

Dynamic 1:1 3-layers

Dynamic 2:1 2-layers

Force (kips)

Indentation (inch.)

(a) Static Analysis (b) Dynamic Analysis

Figure 30. Comparison between Static and Dynamic Finite Element Analyses

(a) Solid 1:1 1-layer (b) Solid 1:1 2-layers

(c) Solid 1:1 3-layers (d) Solid 2:1 2-layers

Figure 31. Contours of Equivalent Plastic Strain from Dynamic Analysis using 

Shell Elements
34

Shell Elements

Sensitivity to mesh size and the number of integration points through the thickness was 

examined for shell elements. Figure 32 compares static analyses for (a) a fixed mesh size

(equal to 1t) and varying number of integration points through the thickness (between 2 

and 5), and (b) a fixed number of integration points (equal to 3) and varying mesh sizes

(0.5t and 1t). Figure 33 shows the same comparison for dynamic analysis (with an 

additional mesh size of 2t). Based on the global force-indentation behavior, convergence 

appears to be achieved with three integration points and a mesh size of 2t. The noise in 

the curve for an element size of 0.5t is attributed to increased time increments as a result 

of mass scaling as described in footnote (5) of Table 4.

0

100

200

300

400

500

600

0 10 20 30 40 50

Static 1t 2-points

Static 1t 3-points

Static 1t 4-points

Static 1t 5-points

Force (kips)

Indentation (inch.)

0

100

200

300

400

500

600

0 10 20 30 40 50

Static 1t 3-points

Static 0.5t 3-points

Force (kips)

Indentation (inch.)

(a) Varying Number of Integration Points (b) Varying Mesh Size

Figure 32. Comparison Force-Indentation Curves from Static Analysis using Shell 

Elements

Solid versus Shell Elements

Figure 34 compares force-indentation curves obtained from (a) static analyses and (b) 

dynamic analyses using typical meshes for solid and shell elements. The static results 

shown in Figure 34(a) are almost identical.
35

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

Dynamic 1t 2-points

Dynamic 1t 3-points

Dynamic 1t 4-points

Dynamic 1t 5-points

Force (kips)

Indentation (inch.)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

Dynamic 2t 3-points

Dynamic 1t 3-points

Dynamic 0.5t 3-points

Force (kips)

Indentation (inch.)

(a) Fixed Mesh Size and Varying Integration 

Points Through the Thickness

(b) Fixed Number of Integration Points and 

Varying Mesh Size

Figure 33. Comparison Force-Indentation Curves from Dynamic Analysis using 

Shell Elements

0

100

200

300

400

500

600

0 10 20 30 40 50

Static shell 1t 5-points

Static solid 1:1 2-layers

Force (kips)

Indentation (inch.)

0

50

100

150

200

250

300

350

400

0 5 10 15 20 25 30

ABAQUS shell 1t 5-points

LS-Dyna shell 1t 3-points

Dynamic solid 1:1 2-layers

Dynamic solid 2:1 2-layers

Force (kips)

Indentation (inch.)

(a) Static Analyses (b) Dynamic Analyses

Figure 34. Force-Indentation Curves from Static and Dynamic Analysis using Solid 

and Shell Elements
36

Full versus Reduced Integration

Quadrature is used in finite element analysis to calculate the volume of each element 

which in turn is needed to determine the element stiffness. If the element shape is regular 

(i.e., straight edges) and cube-like (in three-dimensions), the element volume and 

stiffness can be calculated accurately. As the element shape deviates from a cube (i.e., as 

the height-to-width ratio, or element aspect ratio, increases), the element tends to stiffen 

and lose accuracy. A lower-order quadrature rule, called reduced integration, may be 

desirable. Since the expense of generating a stiffness matrix by numerical integration is 

proportional to the number of sampling points, using fewer sampling points means lower 

cost. A low-order rule tends to soften an element because strain energy of higher order 

deformation modes is not accounted for. However an inherent danger in using low-order 

integration is that zero-energy deformation modes may arise.

Single-point integration elements combined with various hourglass control methods may 

produce global force-indentation curves that are similar to those obtained using fully 

integrated elements, but the distributions for equivalent plastic strain are inconsistent. 

The so-called enhanced hourglass control in ABAQUS appears to provide reasonable 

strain distributions but the global force-indentation curves are much stiffer than LSDYNA. Use of reduced integration elements is recommended only for qualitative 

studies.

Summary 

Based upon the foregoing verification studies, the following conclusions regarding the 

estimation of global force-indentation curves were drawn.

(1) The solid element formulations in ABAQUS and LS-DYNA produce nearly 

identical results in dynamic analyses.

(2) The solid element results converge at a characteristic element size of 0.5t (1:1 

element aspect ratio, two layers through the thickness), in both static and dynamic 

analyses.

(3) The results using shell element in ABAQUS converge at a characteristic element 

size of 1t and 3 integration points through the thickness, in both static and 

dynamic analyses.

(4) Results from static analyses using solid and shell elements are in good agreement.

(5) Using solid elements, the structural response tends to stiffen as the element aspect 

ratio increases, most likely due to the shear locking effect.

(6) Maximum forces and indentations calculated using ABAQUS solid elements are 

within 4 percent ABAQUS shell element results.

(7) Maximum forces and indentations calculated by LS-DYNA using shell elements 

are within 6 percent of ABAQUS shell element results.

In addition, the following conclusions regarding the contours of equivalent plastic strain 

based on ABAQUS shell analyses are drawn.

(1) Six Gaussian integration points through the thickness are recommended.
37

(2) The predicted locations of the maximum equivalent plastic strain are consistent 

for element sizes less than or equal to 1t.

(3) The magnitude of the maximum equivalent plastic strain increases as the mesh 

becomes finer.

(4) A separate sensitivity analysis is needed to examine the mesh sensitivity on 

assumed failure criteria.

3.1.2 Static Case Studies

As part of the verification process, results from static FEA models are compared to 

known closed-form solutions for relatively simple cases. The verification case for the 

head deformation model is the rigid-plastic collapse of an ellipsoidal cap with a 

concentrated load applied at its apex. An analytical solution to the rigid-plastic 

rotationally symmetric deformation of a non-pressurized hemispherical shell was

developed by de Oliveria and Wierzbicki [21]. The solution was modified for ellipsoidal 

shells.

Figure 35 compares the force-deflection response from the closed-form solution and the 

finite element analysis. The ellipsoidal cap has an aspect ratio (major-axis length to 

minor-axis length) of 2 to 1, diameter of 87.5 in, thickness of 0.5 in. In the FEA model, 

the applied load is distributed over a 1-square-foot area at the center of the cap. In the 

closed-form solution, the applied load is assumed to be a concentrated load applied at the 

center of the shell. The closed-form solution also assumes a flow stress, which is a 

material property used to define the rigid-plastic limit. In the present case, the flow stress 

is assumed to be equal to the yield strength of the material (30 ksi). The solution 

algorithm in the finite element analysis uses Riks method [22], which is efficient when 

the static load-deflection curve is expected to exhibit snap-through or snap-back 

behavior. Considering the differences in applied loading (concentrated versus distributed 

load) and material behavior (rigid-plastic versus elastic-perfectly-plastic), the comparison 

appears to show reasonable agreement.

Wierzbicki and Suh [23] developed theoretical analyses of large plastic deformation of 

cylindrical tubes subjected to various loading conditions, including lateral loads, which 

may be used as a verification case for the shell impact model. The closed-form solution 

is sensitive to the assumed boundary conditions. Figure 36 compares the forceindentation curve obtained from the closed-form solution for a cylinder subjected to 

lateral loading with a static, nonlinear finite element calculation. The cylinder is assumed 

to be supported by a rigid surface on the side opposite from the applied load, and is free 

to slide and rotate at its ends.
38

Center Indentation (inches)

0 5 10 15 20 25 30 35 40

Force (kips)

0

100

200

300

400

500

Closed-Form Solution

Finite Element Analysis

Figure 35. Comparison of Force-Indentation Curves for Center Loaded Ellipsoidal 

Cap

Indentation (inches)

0 5 10 15 20

Force (kips)

0

100

200

300

400

500

Analytical solution

Finite element analysis

Figure 36. Comparison of Force-Indentation Curves for Cylindrical Shell
39

3.1.3 Dynamic Case Studies

Results from static and dynamic FEA are compared for additional verification of the 

modeling development. Figure 37 shows force-indentation curves for head impacts 

calculated by static and dynamic FEA. In the dynamic cases, off-center impacts are 

simulated at five different speeds. In the static cases, the location of load application 

was varied. Moreover, the figure shows that static and dynamic FEA produce practically 

the same force-indentation characteristic for head impacts. Similarly, Figure 38 shows 

that static and dynamic FEA calculate similar force-indentation characteristics for shell 

impacts.

The combination of finite difference in time to capture dynamics and nonlinear stressstrain analysis to capture elastic-plastic material behavior makes it difficult in practice to 

obtain good model performance without assuming extremely small time steps in FEA. 

Therefore, lumped-mass modeling was conducted to verify the dynamic, nonlinear FEA. 

For example, the spring characteristic in Figure 39 may represent the structural stiffness 

of the tank car head. Moreover, static nonlinear FEA is used to calculate the forceindentation curve for an ellipsoidal end cap, which is then used as the spring 

characteristic in the dynamic lumped-mass model.

Another alternative method to examine the structural response of the tank car head to 

impact is semi-empirical analysis. In addition to conducting tank car head impact tests, 

the RPI-AAR Tank Car Safety Research and Test Project conducted regression analyses 

with the head impact test data to develop equations for estimating impact force and 

indentation as functions of impact velocity or closing speed. The theoretical basis of 

these equations is Hertz contact. The equations derived from the regression analyses in 

combination with the theory of Hertz contact are referred to as the semi-empirical 

equations.

Figure 40 shows results from three different methods to calculate impact force as a 

function of closing speed on empty tank heads: (1) the solid line represents results from 

the semi-empirical equations; (2) the open square symbols represent results from the 

dynamic lumped-mass model; and (3) the solid triangles represent results from the 

dynamic, nonlinear FEA. The solid circles represent the test measurements.

Comparison of the dynamic nonlinear FEA calculations with the semi-empirical formula 

developed by the RPI-AAR shows that the latter accurately predicts the peak collision 

force for engagements at closing speeds from 7 to 15 mph. Also, for closing speeds from 

15 to 25 mph, the RPI-AAR semi-empirical formula predicts forces somewhat greater 

than those predicted by the finite element analyses.
40

Indentation (inches)

0 10 20 30 40 50

Force (kips)

0

200

400

600

800

Dynamic, 5 mph

Dynamic, 8.8 mph

Dynamic, 15 mph

Dynamic, 20 mph

Dynamic, 25 mph

Static, center load

Static, off-center load

Figure 37. Comparison between Static and Dynamic FEA for Head Indentation

Indentation (inches)

0 5 10 15 20

Force (kips)

0

100

200

300

400

500

Static

Dynamic (16 mph)

Dynamic (20 mph)

Figure 38. Comparison between Static and Dynamic FEA for Shell Indentation
41

m1 m2

k(x)

vo

z1 z2

x =z1-z2

Figure 39. Dynamic Lumped-Mass Model for Tank Car Impacts

Closing Speed (mph)

0 5 10 15 20 25

Impact Force (kips)

0

100

200

300

400

500

600

700

800

Semi-Empirical Equation

Lumped Mass Model

Dynamic FEA

RPI-AAR Data

AAR M-115

W1 = 128.9 kips

W2 = 48.5 kips

D = 87.5 inches

h = 0.5 inch

Figure 40. Impact Force as a Function of Closing Speed for Head Impacts

3.2 Validation

With appropriate choices in element type (shell vs. solid), element aspect ratio, and order 

of quadrature, results from the dynamic, nonlinear FEA models are compared to impact 

forces and indentations measured in tests. For head impacts, results from the FEA 

models are compared to data from tests conducted by the RPI-AAR Tank Car Safety 

Research and Test Project during the 1970s [19]. For shell impacts, FEA results are 

compared to data from tests conducted as part of the Next Generation Rail Tank Car 

project [20].
42

3.2.1 Head Impacts

Dynamic nonlinear (i.e., elastic-plastic material behavior with large deformations) finite 

element analysis was conducted using LS-DYNA3D (version 970) to simulate three 

impact speeds: 6, 8.8, and 11.5 mph. The analysis modeled a rigid coupler impacting an 

elastic-plastic ellipsoidal tank car head (i.e. end cap). The finite element mesh of the end 

cap comprised two layers of 8-noded hexahedron elements through the thickness of the 

tank car head with a nominal element aspect ratio of 8 to 1. Moreover, the explicit finite 

element solver with reduced integration to formulate the element stiffness was used in the 

finite element analysis. To minimize computational time, the tank container was 

modeled by a large area of rigid material and a smaller area of deformable material at 

impacted end of the tank (Figure 41). The impacting coupler was modeled as a rigid part 

with its density adjusted to reflect the weight of the entire ram car. All simulations were 

terminated after 0.25 seconds. Table 6 lists the relevant details of the RPI-AAR tank car 

head impact tests that were simulated by the FEA.

Figure 41. Rigid-Deformable Finite Element Model of Tank Container

Table 6. Details of Simulated Tank Car Head Impact Tests

Parameter Value

Impact location 1/3 down from center

Ram car weight 128,706 lb

Tank car weight 45,325 lb

Diameter 87.5 inches

Aspect ratio of ellipsoidal cap 2 to 1

Head thickness 0.5 inch

Outage 100%
43

The end caps in the tank car impact tests were made from AAR M-115 steel. Table 7

lists material properties assumed in the FEA for this tank car steel. Additional

assumptions regarding material behavior were listed previously in Table 2.

Table 7. Material Properties Assumed for Tank Car Head

Property Value

Density, ρ 0.283 lb/in3

Poisson’s ratio, ν 0.3

The RPI-AAR tank car head impact test data include measurements for residual dent 

depth, residual dent width, and maximum coupler force. Table 8 compares the results 

from the dynamic, nonlinear FEA with the test data for the three different impact speeds. 

The calculated residual dent depths are within 20 percent of the measurements. Although 

the FEA consistently underestimates the residual dent widths, the calculated widths are 

within 25 percent of the measurements. The FEA underestimates the maximum coupler 

forces at impact speeds of 8.8 and 11.5 mph, but the calculated impact forces are within 

10 percent of the measurements. At 6 mph, however, the calculated maximum coupler 

force overestimates the test result by more than 80 percent.

Table 8. Comparison between FEA and RPI-AAR Head Impact Tests with 100

Percent Outage

(a) Residual Dent Depth (inches)

Impact Speed

(mph)

Test FEA % diff

6.0 6.5 6.7 +3%

8.8 13.5 11.0 –19%

11.5 16.0 15.0 –6%

(b) Residual Dent Width (inches)

Impact Speed

(mph)

Test FEA % diff

6.0 53 43 –19%

8.8 62 54 –13%

11.5 80 60 –25%

(c) Maximum Coupler Impact Force (kips)

Impact Speed

(mph)

Test FEA % diff

6.0 59 108 +83%

8.8 137 151 +10%

11.5 208 192 –8%
44

The most conspicuous results are those at the impact speed of 6 mph. Numerical 

experiments are conducted to examine the effect of various modeling assumptions on the 

calculations at this impact speed. The variations in modeling assumptions include: 

element type, integration scheme (i.e., reduced versus fully integrated elements), and 

mesh density. Mesh density is related to the assumed element aspect ratio. In the case of 

shell elements, the number of integration points through the thickness is a modeling 

variable. In the case of solid elements, the number of layers through the thickness is 

related to the element aspect ratio.

Table 9 lists the various cases exercised in the numerical experiments for an impact speed 

of 6 mph. The table also shows the relative effect of the modeling assumptions on the 

calculated residual dent depths and maximum coupler forces. Considering only the cases 

with shell elements, the calculated maximum coupler forces vary by less than 9 percent

while the calculated dent depths vary by less than 4 percent. Much larger variations in 

the calculated results are evident when solid elements are used. The calculated results 

using solid elements are not sensitive to mesh density with reduced integration. 

Conversely, the calculated results using solid elements are sensitive to mesh density 

when fully integrated elements are used. Table 10 lists the cases and results for an 

impact speed of 11.5 mph.

Table 9. Effect of Modeling Assumptions on Results at Impact Speed of 6 mph

Element

Type

Integration 

Scheme

Element

Aspect

Ratio

Through 

Thickness

Attribute

Residual

Dent 

Depth

(inches)

Residual 

Dent 

Width 

(inches)

Maximum

Coupler

Force 

(kips)

Max. Eff. 

Plastic 

Strain

Shell

Reduced

4:1

2 points 6.4 41 108 0.04

4 points 6.5 41 107 0.06

8 points 6.5 40 107 0.07

1:1 2 points 6.3 40 110 0.10

5 points 6.4 40 108 0.15

Full

4:1

2 points 6.3 41 113 0.04

4 points 6.4 40 110 0.05

8 points 6.4 41 110 0.06

1:1 2 points 6.3 41 112 0.10

5 points 6.6 42 108 0.14

Solid

Reduced 8:1 2 layers 6.6 45 108 0.04

2:1 2 layers 6.7 42 107 0.11

Full 8:1 2 layers 4.7 39 135 0.07

2:1 2 layers 6.1 40 112 0.10
45

Table 10. Effect of Modeling Assumptions on Results at Impact Speed of 11.5 mph

Element

Type

Integration 

Scheme

Element

Aspect

Ratio

Through 

Thickness

Attribute

Residual

Dent 

Depth

(inches)

Residual 

Dent 

Width 

(inches)

Maximum

Coupler

Force 

(kips)

Max. Eff. 

Plastic 

Strain

Shell

Reduced

4:1 2 points 15.1 58 170 -

5 points 15.3 59 174 -

1:1 2 points 14.7 55 173 -

5 points 15.0 59 168 -

Full

4:1 2 points 14.4 62 200 0.07

5 points 14.8 62 195 0.08

1:1 2 points 14.2 60 199 0.17

5 points 14.3 58 194 0.20

Solid

Reduced 8:1 2 layers 15.0 60 192 0.07

2:1 2 layers 15.0 57 193 0.18

Full 8:1 2 layers 11.6 54 241 0.08

2:1 2 layers 14.3 56 200 0.13

Fluid-structure interaction is included in the finite element modeling to account for the 

inertial effects of fluid in the tank. The finite element analysis with fluid-structure 

interaction uses Arbitrary-Lagrangian-Eulerian (ALE) coupling.4

Table 11

The finite element 

model with fluid-structure interaction consists of four parts: (1) the tank car structure 

(Lagrangian mesh), (2) an air block surrounding the tank car structure (Eulerian mesh), 

(3) the liquid inside the tank (Eulerian mesh), and (4) vapor outage that fills the 

remainder of the tank (Eulerian mesh). The physical properties of the fluid inside the 

tank are adjusted according to the lightweight and test weight recorded for a given impact 

test.

compares the results from the dynamic, nonlinear FEA with fluid-structure 

interaction to the test data for three different impact speeds. In these impact tests, the 

coupler struck the tank car head at the center of the end cap. The impact force measured 

at 10.2 mph is less than the impact force measured at 8.7 mph. In each case, the 

calculations for impact forces and residual dent dimensions (depth and width) overpredict the measurements.

 4 In the present context, a Lagrangian mesh is one that transforms according to its deformation; an Eulerian 

mesh is a fixed mesh in space through which material flows.
46

Table 11. Comparison between FEA and RPI-AAR Head Impact Tests with 2% 

Outage

(a) Residual Dent Depth (inches)

Impact Speed

(mph)

Test FEA % diff

7.2 6.5 12.5 +92%

8.7 8.25 12.7 +54%

10.2 11.25 15.9 +41%

(b) Residual Depth Width (inches)

Impact Speed

(mph)

Test FEA % diff

7.2 40 54.4 +36%

8.7 48 57.5 +20%

10.2 60 63.9 +7%

(c) Maximum Coupler Force (kips)

Impact Speed

(mph)

Test FEA % diff

7.2 89 174 +96%

8.7 200.8 300 +49%

10.2 141 372 +164%

Figures 42 through 44 compare the calculated and measured impact forces and 

indentation dimensions (depth and width) for the various cases involving bare tank heads 

with different levels of outage. The calculated values for the case of 2 percent outage are 

clearly stiffer than the observed behavior, and required further refinement. The 

horizontal error bars in these figures indicate the range of calculated impact forces and 

indentation dimensions depending on the modeling assumptions for mesh density, 

element type, and integration scheme. The dynamic nonlinear finite element calculations 

for indentations and maximum coupler forces in empty tanks were within 25 percent of 

the RPI-AAR impact test data with the exception of the maximum coupler force at 

relatively low impact speed.
47

Calculated Impact Force (kips)

0 100 200 300 400

Measured Impact Force (kips)

0

100

200

300

400

2% Outage

100% Outage

vo=6.0 mph

vo=8.8 mph

vo=11.5 mph

vo=7.2 mph

vo=8.7 mph

vo=10.2 mph

under-prediction

over-prediction

Figure 42. Comparison between Calculated and Measured Impact Forces

Calculated Residual Dent Depth (inches)

0 5 10 15 20

Measured Residual Dent Depth (inches)

0

5

10

15

20

2% Outage

100% Outage

vo=6.0 mph

vo=8.8 mph

vo=11.5 mph

vo=7.2 mph

vo=10.2 mph

vo=8.7 mph

under-prediction

over-prediction

Figure 43. Comparison between Calculated and Measured Residual Dent Depths
48

Calculated Residual Dent Width (inches)

0 20 40 60 80 100

Measured Residual Dent Width (inches)

0

20

40

60

80

100

vo=6.0 mph

vo=8.8 mph

vo=11.5 mph

vo=7.2 mph

vo=8.7 mph

vo=10.2 mph

under-prediction

over-prediction

Figure 44. Comparison between Calculated and Measured Residual Dent Widths

Finite element analyses were performed with different combinations of element types 

(solid and shell elements), integration schemes (reduced and fully integrated), and 

through-the-thickness characteristics (element aspect ratio or mesh density). Based upon 

these variations, the following results were observed:

(1) Different analyses calculated similar indentations and coupler forces with the 

exception of the analysis with a relatively coarse mesh and fully integrated solid 

elements, which calculated stiffer behavior compared to the other analyses.

(2) Maximum strains are consistent and reasonable for the analyses with finer meshes 

at low impact speed.

(3) At higher impact speeds, maximum strains are consistent with the exception of 

the analyses with reduced integrated shell elements.

3.2.2 Shell Impacts

As part of the Next Generation Rail Tank Car Project, a series of full-scale tests were 

conducted to examine the structural behavior of chlorine tank cars under shell impacts. 

In these tests, a stationary tank car was positioned next to a concrete wall, as shown in 

Figure 45. The tank car contained water mixed with clay slurry to produce the density 

approximately equal to that of liquid chlorine. The outage in the tests was 10.6 percent 

with an internal pressure of 100 psi. A ram car weighing 286,000 lb with a rigid indenter 

was used to strike the side of the tank car at its center on the beltline. Moreover, these 

tests were conducted to provide data for validating the FEA models developed for shell 

impacts.
49

Figure 45. Position of Tank Car in Full-Scale Tests

Table 12 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 indenter sizes were 

used in the tests, which are denoted in the table. The indenter shape was a rectangular 

cross-section with rounded edges. The dimensions for each indenter face are listed in 

Table 13.

Table 12. Summary of Full-Scale Shell Impact Tests

Impact 

Speed

(mph)

Indenter

Type

Outcome

Test 0 10 Large Tank integrity maintained

Test 1 14 Large Tank integrity maintained

Test 2 15 Small Tank punctured

Table 13. Indenter Face Dimensions

Indenter Type Height

(inches)

Width

(inches)

Edge Radii

(inch)

Large 17 23 1

Small 6 6 1⁄2
50

Different mesh representations are used in the FEA 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.

The FEA 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 outer steel 

jacket and thermal protection is ignored.

In all of the tests, the ram car was instrumented with accelerometers. The accelerometer 

data were filtered, and processed to provide forces. Figure 46 compares the force-time 

history as measured in Test 0 with those calculated from the FEA models using different 

fluid representations to account for fluid-structure interaction. The results suggest that 

the Eulerian fluid formulation provides more 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 46. Comparison of Force-Time Histories for Test 0

Table 14 compares the maximum impact force measured in Test 0 with FEA results with 

different fluid formulations. The maximum impact force calculated using LS-DYNA 

with the Eulerian fluid formulation is within 5 percent of the test data, which is excellent 

agreement.
51

Table 14. Comparison of Maximum Forces in Assurance Test

Maximum Force

(kips)

Assurance Test 837

LS-DYNA, Eulerian 877

ABAQUS, Lagrangian 707

Figure 47 compares the force-time histories from the data in Test 1 and the FEA results 

with different fluid formulations. The FEA results with the Eulerian fluid formulation 

again show excellent agreement with the data in Test 1.

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 Data

LS-DYNA, Eulerian

ABAQUS, Lagrangian

Figure 47. Comparison of Force-Time Histories for Test 1

Table 15 compares the maximum impact forces and maximum indentations from Test 1 

and the FEA results using LS-DYNA and the Eulerian fluid formulation. The maximum 

impact forces are within 10 percent. The maximum indentation of 26 in was measured in 

the test with string potentiometers. The FEA prediction of 30 in for maximum 

indentation assumed mechanical properties based on minimum requirements for TC128B 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 performed with the actual properties, which resulted in slightly better 

agreement for both maximum impact force and maximum indentation.
52

Table 15. Comparison between Test 1 and FEA

Maximum

Force

(kips)

Maximum 

Indentation

(inches)

Test 1 1290 26

LS-DYNA, Eulerian (1) 1223 29

LS-DYNA, Eulerian (2) 1170 30

NOTES:

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

(2) Based on assumed properties based on minimum requirements 

Figure 48 compares force-indentation curves from Test 1 data and the FEA results. The 

curve representing the test data is a cross-plot of indentation-time history obtained from 

string potentiometers and force-time history from processed accelerometer data. The 

force-indentation curve from the FEA shows qualitative agreement with the test. 

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

ABAQUS, Lagrangian

Figure 48. Comparison of Force-Indentation Curves for Test 1

The second full-scale shell impact test used an impactor with a smaller cross-sectional 

area than the previous tests to increase the likelihood of rupturing the tank. Moreover, 

the ram car in this test struck the side of the stationary tank car at impact speed of 15 

mph, and punctured the tank.
53

Analyses of Test 0 and Test 1 demonstrated that the FEA with the Eulerian fluid 

formulation provides results that are in close agreement with 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 [25]. Material failure criteria are discussed in greater 

detail in the following section of this report.

The accelerometer measurements in Shell Impact Test 2 were filtered and processed in 

the same manner as the previous tests. Figure 49 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

(ms), 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 ms. 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 49. Comparison of Force-Time Histories for Test 2
54

3.2.3 Unnotched Charpy Tests

The pendulum impact tests, which are described in the section on Tank Car Steels 

Characterization, provided data that can be used to examine the effect of different 

material failure criteria on fracture energy. Elastic-plastic finite element analysis (FEA), 

assuming different criteria, was conducted to calculate the fracture energy and simulate 

the Bulk Fracture Charpy Machine (BFCM) tests [26]. Three material failure criteria are 

described briefly as follows.

1) Gurson-Tvergaard–This criterion was developed by Gurson [27] and Tvergaard [28]

and [29] specifically for failure by ductile fracture. FEA applying this criterion to 

examine the puncture resistance of tank cars was proposed by Anderson and 

Kirkpatrick [30], and performed by Anderson et al. [31].

2) Constant strain–This criterion is the simplest to implement in FEA, and assumes that 

failure initiates when the effective strain reaches a critical level (e.g., 20 percent).

3) Bao-Wierzbicki–Effective strain to initiate failure depends on the general state of 

stress in terms of stress triaxiality [25].

Stress triaxiality is the portion of the stress tensor that is hydrostatic. Mathematically, it 

is the ratio of mean stress to von Mises equivalent stress, or

m

e

σ

η

σ = (2)

In terms of principle stresses, the mean stress and the effective or von Mises equivalent 

stress are defined as

( 123 ) 1

3

σ σσσ m = ++ (3)

( ) ( ) ( ) 2 22

12 23 31

1

2

σ σσ σσ σσ e = − +− +−     (4)

Mean or hydrostatic stress is associated with dilatation or the change in volume of a 

material element as it deforms. Effective or von Mises stress is directly related to 

distortional energy or the energy to change the shape of a material element as it deforms. 

Therefore, a physical interpretation of stress triaxiality is that it describes the general state

of stress in a material element and is the ratio of volume change to shape change.

Figure 50 shows a schematic of effective strain to initiate failure as a function of stress 

triaxiality. The failure initiation envelope for the Bao-Wierzbicki (B-W) criterion is 

shown to consist of three regions representing different modes of failure. Region I is 

characterized by high values of stress triaxiality which promote the nucleation, growth, 

and coalescence of voids leading to ductile fracture. Region III is associated with 

negative stress triaxiality which represents shear fracture due to shear band localization. 

Region II comprises positive but low values of stress triaxiality representing mixed mode 
55

fracture. The schematic also shows that zero stress triaxiality (i.e., η equal to 0) is equal 

to a stress state of pure shear, and that the cusp between Regions I and II (which 

corresponds to η equal to 1⁄3) is equal to s stress state of uniaxial tension. In theory, the 

failure initiation envelope for a given material is developed through a series of physical 

tests. The complete series entails 11 tests with different specimen geometries to 

characterize different levels of near-constant stress triaxiality in the vicinity of failure. 

Such tests were conducted previously to develop failure initiation envelopes for 2024-

T351 aluminum [32] and A710 steel [33]. In the FEA implementation, the failure 

initiation envelope is developed from a calibration method using measurements from 

standard uniaxial tensile tests [34]. The constant strain criterion is also shown in the 

schematic for comparison. Clearly, constant strain may be a considered as a special case 

of the B-W failure envelope in which effective strain to initiate failure is independent of 

stress triaxiality. In addition, the Gurson-Tvergaard criterion may be considered as 

accounting for only Region I of the B-W failure envelope.

Figure 50. Schematic of Failure Initiation Envelope based on Stress Triaxiality

Failure initiation occurs when loading conditions induce effective plastic strains at levels 

above the limits suggested by Figure 50. Once failure initiates, damage is assumed to 

progress in the form of linear strain softening. Figure 51 illustrates this concept, in which 

the stress-strain behavior of a material element exhibits a linear decrease in stress with 

increasing strain beyond the strain to initiate failure, εi. Modeling damage progression by 

strain softening helps minimize the mesh dependency of the numerical results [35].
56

Figure 51. Schematic of Linear Strain Softening

Figure 52 compares BFCM test data for normalized TC-128B tank car steel using the two 

different strikers with FEA results based on the B-W criterion. The solid curve in the 

figure represents the result of a best-fit regression analysis through the BFCM data. Error 

bars on the data are two standard deviations above and below the mean value for a given 

specimen thickness. The close agreement between the test data and analysis is selfevident especially for the thicker specimens.

Specimen Thickness (inches)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fracture Energy (ft-lb)

0

1000

2000

3000

4000

5000

6000

7000

8000

Test Data

Average

FEA

Normalized TC-128B tank car steel

Error bars represent ±2 standard deviations

Nominal specimen width is 1.0 inch

(a) Sharp Tup

Specimen Thickness (inches)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fracture Energy (ft-lb)

0

1000

2000

3000

4000

5000

6000

7000

8000

Test Data

Average

FEA

Normalized TC-128B tank car steel

Error bars represent ±2 standard deviations

Nominal specimen width is 1.0 inch

(b) Blunt Tup

Figure 52. Comparison of BFCM data for Normalized TC-128B with FEA 

assuming Bao-Wierzbicki Criterion
57

Figure 53 compares the BFCM test data (using a blunt striker) with FEA results assuming 

three different criteria. FEA results using the Gurson-Tvergaard (G-T) criterion were 

reported by Anderson et al. [31]. FEA results using constant strain and the BaoWierzbicki (B-W) criteria were reported by Yu et al. [26]. In applying the constant strain 

criterion, a critical value of 20 percent strain was assumed. Fracture energies calculated 

using the G-T criterion appear to varying linearly with specimen thickness. Assuming 

constant strain, the variation is nonlinear. The variation is also nonlinear in the case of 

the B-W criterion. In addition, the calculated fracture energies for the thinner specimens 

are not as accurate as those for the thicker specimens in the case of the B-W criterion. 

Mesh refinement may improve the calculated energies for the thinner specimens. 

However, the thicknesses of commodity tanks are usually greater than 0.5 inch. 

Moreover, for thicknesses of interest in tank car designs, fracture energies calculated 

using the B-W criterion are within excellent agreement of the measured fracture energies.

Gurson-Tvergaard

Specimen Thickness (inch)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Fracture Energy (ft-lb)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Experiment

Average

FEA

Constant Strain

Specimen Thickness (inch)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Fracture Energy (ft-lb)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Experiment

Average

FEA

Bao-Wierzbicki

Specimen Thickness (inch)

0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9

Fracture Energy (ft-lb)

0

1000

2000

3000

4000

5000

6000

7000

8000

9000

10000

Experiment

Average

FEA

Error bars for experimental data represent ±2 standard deviations

Figure 53. Comparison of Different Failure Criteria with BFCM Test Data for TC128B Tank Car Steel

Figure 54 compares measured BFCM fracture energies (using the blunt striker) with 

those calculated using elastic-plastic FEA with the B-W criterion for different tank car 

steels. The mechanical properties for these materials are listed in Table 2. The figure 

shows excellent agreement between the experimental and calculated values for fracture 

energy. The close agreement provides confidence in applying the B-W criterion to 

examine material failure. Moreover, the application of the B-W criterion to the BFCM 

tests provides a benchmark to calculate puncture in the full-scale for application, which 

was accomplished and described previously.
58

Calculated Fracture Energy (ft-lb)

0 1000 2000 3000 4000 5000 6000 7000 8000

Measured Fracture Energy (ft-lb)

0

1000

2000

3000

4000

5000

6000

7000

8000

TC-128B

HPS 70

HPS 100

A710

under-prediction

over-prediction

Error bars represent ±2 standard deviations

Figure 54. Comparison of Measured and Calculated Fracture Energies for 

Different Steels (Blunt Striker)

Sensitivity studies were performed with the FEA model to simulate the BFCM test to 

examine the relative effect of different factors on calculated impact energy. The factors 

examined in the studies can be grouped into four categories: (1) plasticity (yield and 

ultimate tensile strengths), (2) fracture initiation (C1 and C2), (3) softening (failure 

displacement, uf), and (4) contact (coefficient of friction). In the sensitivity studies, each 

factor was varied from its baseline value, one at a time, while the other factors remained 

equal to the baseline values. Figure 55 summarizes the results of the sensitivity studies. 

The figure shows that varying the failure displacement by ±100 percent changes the 

impact energy from about –30 percent to about +20 percent. Moreover, the slopes of the 

lines for each factor indicate their relative effect on the calculated impact energy. Thus, 

the plasticity parameters have the most significant effect on the calculated impact energy. 

The failure initiation parameters and the failure displacement have moderate effects. The 

coefficient of friction has a less significant effect. 
59

Percent Change in Parameter

-150 -100 -50 0 50 100 150

Percent Change in Impact Energy

-60

-40

-20

0

20

40

60

Yield Strength

Ultimate Tensile Strength

C1

C2

uf

Coefficient of friction

Figure 55. Percent Variation in Impact Energy with Parameter Changes

3.3 Discussion and Summary

Finite element analysis (FEA) models are developed to estimate the response of the tank 

structure to collision events, such as the impact of a coupler from an adjacent rail car on 

the end cap (i.e., head) or side (i.e., shell) of a tank car. The structural response is 

calculated in terms of impact force as a function of indentation, or force-indentation 

characteristic.

Results from static FEA models are compared to closed-form solutions for ellipsoidal 

heads and cylindrical tubes. The closed-form or analytical solutions assume rigid-plastic 

material behavior, whereas the FEA models assume elastic-plastic material. The closedform solutions also assume a concentrated load, whereas the FEA models assume that the 

load is applied through a rigid punch. Despite these differences, the force-indentation 

characteristics calculated by the FEA models and the closed-form solutions are in 

reasonable agreement for both head and shell deformations.

Static and dynamic, nonlinear FEA models produce nearly identical force-indentation 

characteristics for both head and shell impacts. Dynamic, nonlinear FEA models for 

head impact are also compared with lumped-parameter models, which give similar results 

in terms of impact force as a function of closing speed.
60

The comparisons between FEA models and closed-form solutions are valid for empty 

tanks. Similar comparisons for tanks containing lading cannot be made because no 

closed-form solutions are available. 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 FEA models to account for fluid-structure 

interaction. Development of computational models that include the multi-physics of 

fluid-structure interaction is a topic on the forefront of current research and development

[36].

Results from dynamic nonlinear FEA with different fluid formulations are compared to 

data from full-scale tank car shell impact tests, which are shown to be in excellent 

agreement. Figure 56 overlays the measured and calculated force-indentation curves for 

the two full-scale shell impact tests (i.e., Tests 1 and 2). The figure also shows a 

regression curve that was generated from the calculated and measured curves for both 

tests. Moreover, the figure suggests indenter size has a relatively weak effect on forcedeformation behavior for indentations less than 20 in, but indenter size appears to have a 

relatively strong effect on tank car puncture. Additional analyses confirm this conclusion

[37].

Indentation (inches)

0 5 10 15 20 25 30

Force (kips)

0

200

400

600

800

1000

1200

1400

1600

1800

TEST 1 MEASUREMENT (14.0 mph, LARGE PUNCH)

TEST 1 ANALYSIS (14.0 mph, LARGE PUNCH)

TEST 2 MEASUREMENT (15.1 mph, SMALL PUNCH)

TEST 2 ANALYSIS (15.1 mph, SMALL PUNCH)

Regression Curve

Figure 56. Force-Indentation Characteristic for Shell Impact

Material failure was predicted using a strain-based criterion, referred to as the BaoWierzbicki (B-W) criterion. In this criterion, the effective plastic strain to initiate failure 

depends on the general state of stress in the tank structure in terms of stress triaxiality. 

Implementation of the B-W criterion was validated using data from pendulum impact 
61

tests conduced on unnotched Charpy specimens made from tank car steel. Results from 

the FEA simulations were shown to be in excellent agreement with the experimental 

measurements of fracture energy over a range of test specimen thicknesses. Moreover, 

FEA produced results within the narrow scatter band of test results for all specimens of 

thickness greater than 0.5 inch. These results are significant because the range of 

specimen thickness for which the analysis most accurately reproduced the experiment 

corresponds to that used in typical tank car construction.

The favorable FEA results of the unnotched Charpy specimens suggested that the failure 

criterion can be applied to examine puncture in the full-scale shell impact tests. In 

modeling material failure, accurate FEA results were obtained when solid (i.e., brick) 

elements were used at and around the impact location. For the simulation of the 

pendulum impact tests, sensitivity studies suggested that these elements must have an 

aspect ratio equal to one with a minimum of six elements through the thickness. This is 

accomplished by meshing a patch of solid elements of sufficient size at the impact 

location. This patch can be coupled to shell elements at locations away from the impact

zone that do not require this special treatment. Shell elements in the impact zone do not 

produce accurate results when used in conjunction with the B-W criterion. 

These mesh considerations were applied in the FEA simulations of the full-scale tank car

shell impact tests. Figure 57 shows this patch of solid elements in the impact zone for the 

tank. In this figure, the patch of brick elements in the impact area is so fine that it is 

depicted as a solid area.

Figure 57. Typical FEA Mesh for Full-Scale Shell Impact Simulations

Moreover, an FEA framework for shell impacts has been developed that accounts for the 

following effects: (1) nonlinear material behavior using elastic-plastic constitutive 

models allowing for large deformations, (2) fluid-structure interaction using Lagrangian 

and Eulerian fluid mesh formulations while modeling the tank structure with a 

Lagrangian mesh, (3) material failure using a strain-based criterion that depends on the 

general state of stress in the tank structure. 
62

The FEA framework was applied to examine the structural performance for a variety of 

tank car configurations under generalized head and shell impact scenarios. Figure 58

shows schematics of the generalized head and shell impact scenarios examined using the 

FEA framework. In the case of the head impact, the tank car travels into a rigid barrier 

with the indenter protruding from it. In the shell impact case, the tank car is stationary 

and is struck by a moving ram car with a rigid indenter protruding from it. The ram car 

weight is 286,000 lb. In addition, the figure shows that the impact location for head 

scenario is below the tank centerline, while the impact location for the shell scenario is 

coincident with the tank centerline. In both impact scenarios, the indenter face is 6 in by 

6 in with edge radii of one-half inch.

(a) Head

(b) Shell

Figure 58. Generalized Impact Scenarios Examined by FEA

The FEA framework is applied to examine the structural performance of generic tank car 

configurations under the generalized head and shell impact scenarios. Table 16 lists the 

general attributes of these configurations. The baseline configuration is the same as the 

tank cars used in the full-scale shell impact tests described earlier. The second design 

configuration is the baseline tank with increased head and shell thicknesses. The thicker 

tank translates to a heavier car. In cases for the generalized head impact, the presence of 

a head shield is examined for both tank car configurations. In these cases, full-height, 

one-half-inch thick head shields are modeled. The mechanical properties assumed for the 

head shield material (A516-70) are listed in Table 2. In the baseline cases for both head 

and shell impacts and the case of the thicker baseline for the shell impact, the presence of 

the jacket (11-gage) is included.
63

Table 16. Tank Car Configurations Examined by FEA

Baseline Baseline with 

Increased Thickness

Nominal Tank Car Weight 263,000 lb. 286,000 lb.

Tank Inner Diameter 1005⁄8 inches 1005⁄8 inches

Outage 11% 11%

Internal pressure 100 psi 100 psi

Head thickness 0.828 inch 1.136 inches

Head material TC-128B A516-70

Shell thickness 0.777 inch 0.975 inch

Shell material TC-128B TC-128B

Structural performance is quantified in terms of puncture velocity, which is defined as the 

velocity at which puncture of the tank may be expected to occur, under the prescribed 

conditions. Table 17 lists the range of puncture velocities estimated from applying the 

FEA framework described in this document to the generalized head impact scenario. The 

table also lists the range of kinetic energies associated with the puncture velocities. The 

presence of a head shield and thickening the baseline tank increase the estimated 

puncture velocity slightly. Similarly, Table 18 lists the estimated ranges for puncture 

velocity and kinetic energy for the generalized shell impact scenario. The results from 

the FEA framework suggest a slight increase in puncture velocity from thickening the 

baseline tank.

Table 17. Estimated Range of Puncture Velocity and Associated Kinetic Energy for 

Generalized Head Impact Scenario

Configuration Puncture

Velocity

Range

(mph)

Kinetic

Energy

Range

(Million ft-lb)

Baseline 8 – 10 0.6 – 0.9

Baseline with Head Shield 9.5 – 11.5 0.7 – 1.2

Baseline with Increased Thickness and 

Head Shield 10 – 12 0.9 – 1.4
64

Table 18: Estimated Range of Puncture Velocity and Associated Kinetic Energy for 

Generalized Shell Impact Scenario

Configuration Puncture

Velocity

Range

(mph)

Kinetic

Energy

Range

(Million ft-lb)

Baseline 11 – 13 1.2 – 1.6

Baseline with Increased Thickness 12 – 14 1.4 – 1.9
65

4. TANK CAR STEELS CHARACTERIZATION

Southwest Research Institute (SwRI) carried out a laboratory testing program, under a 

task order contract with the Volpe Center, to examine the mechanical behavior of 

different tank car steels. Moreover, the testing program was conducted in response to

recommendations made by the National Transportation Safety Board (NTSB) regarding 

the Minot derailment (Appendix A). This section briefly summarizes test results, and 

provides supplemental analysis and information. The SwRI testing program comprised 

three parts:

1) Basic Material Characterization–Basic material characterization included:

(a) Analysis of chemical composition; 

(b) Testing for tensile properties, such as yield strength, ultimate tensile strength, 

percent elongation, and reduction in cross-sectional area; and 

(c) Charpy V-Notch (CVN) impact testing at three temperatures: 0oF and ±50oF.

2) High-Rate Fracture Toughness Testing–Fracture toughness was measured at high 

strain rates, such as might be experienced in derailments, at two temperatures: 

0oF and –50oF.

3) Pendulum Impact Testing for Bulk Fracture Behavior–An oversized, nonstandard 

pendulum impacting device was built to measure the energy to fracture unnotched 

Charpy specimens. The measurement of fracture energy was used to assess 

puncture resistance.

Specific details of the tests and results are described and presented in an extensive report 

prepared by SwRI [38].

A data dump from the Universal Machine Language Equipment Register (UMLER) 

database was performed by the AAR in April 2005 to examine the state of the pressure 

tank car fleet in terms of material distribution and year of manufacture. Figure 59 shows 

the makeup of the pre-1989 pressure tank car fleet in terms of fabrication material. The 

figure indicates that the vast majority of the fleet is fabricated from TC-128B. Other tank 

car steels makeup less than 7 percent of the fleet. Some entries in the UMLER database 

did not include material type, and are grouped in the “other” category.

Material for the testing program was obtained from 34 tank cars that were either retired 

from revenue service or were involved in an accident. For example, material was 

obtained from cars involved in the Minot accident that were examined by SwRI in 

litigation support for GATX (e.g., [39] and [40]). The tank car steels included: TC-128B 

(both non-normalized and normalized), A212, A515, and A285. Thirty-two of the 34 

cars that were provided for this testing program were built prior to 1989. Samples were 

taken from both the head and shell of the tank.

Given cost and scheduling constraints, an engineering estimate of at least one car per year 

was sought as a sample rate. The adequacy of the sample size to draw definitive 

conclusions depends on the purpose of the study, population size, level of precision, level 

of confidence, and degree of variability. Estimates of minimum sample size for different 

levels of confidence and precision are given in Appendix B.
66

Figure 59. Distribution of Steels in Pre-1989 Pressure Tank Car Fleet

Figure 60 is an overlay of two plots. The bottom plot shows the cumulative percentage

of pressure tank cars as a function of year of manufacture (i.e., built year) for (a) the 

whole fleet (represented by the green triangles) and (b) the pre-1989 fleet (blue squares). 

The top plot shows the makeup of the cars from which test material was obtained. 

4.1 Basic Material Characterization

Material characterization was conducted in accordance with the following standard test 

methods, which are published by the American Society for Testing and Materials 

(ASTM):

1) Chemical analysis–ASTM E415, “Standard Test Method for Optical Emission 

Vacuum Spectrometric Analysis of Carbon and Low-alloy Steel”

2) Tensile properties–ASTM A370–Standard Test Methods and Definitions for 

Mechanical Testing of Steel Products”

3) Charpy impact energy–ASTM E23, “Standard Test Methods for Notch Bar 

Impact Testing of Metallic Materials”

In the chemical analysis, 16 elements were measured and reported, even though the TC128B composition specification calls for controlling only nine distinct elements. In 

summary, 59 of 61 samples (97 percent) met composition requirements for TC-128B.
 

67

Figure 60. Cumulative Distribution of Pressure Tank Car Fleet and Tank Cars used for Testing

UMLER: April 2005 data

Year of Manufacture

19561958196019621964196619681970197219741976197819801982198419861988199019921994199619982000200220042006

% of Pressure Car Fleet Produced Before

0

10

20

30

40

50

60

70

80

90

100

whole fleet

pre-1989 fleet only

1960's 1970's

1980's

1990's

2000's

1950's 1956 1958 1960

19621964196619681970197219741976197819801982198419861988199019921994199619982000200220042006

No. of Candidate 

Tank Cars/Material

0

1

2

3

4 TC128-B 

A212-B/G 

A515-Gr70 

A285-C 
68

Tensile properties of interest were yield strength, ultimate strength, percent elongation at 

failure, and reduction of area. The gage length was generally 2 in, although material 

limitations occasionally required the use of sub-size specimens with smaller gage-lengths 

(1 in or 1.4 in). Tensile specimens were oriented transverse to the primary plate axis for 

the shell specimens. Head specimens were arbitrarily removed since the orientation of 

the plate prior to hot pressing the head was not known. Two replicate specimens were 

tested in all cases.

Tensile test measurements for TC-128B tank car steel are summarized in Table 19 in 

terms of the mean or average value and standard deviation. The table lists includes the 

number of test samples taken from the head and shell locations, N. For comparison, 

minimum requirements for TC-128B are listed in Table 20. In summary, 82 percent of 

the tested samples met the minimum requirement properties.

Table 19. Summary of Tensile Test Measurements for TC-128B

N Ultimate 

Tensile 

Strength (ksi)

Yield

Strength

(ksi)

Elongation

(%)

Reduction in 

Area

(%)

Mean SD Mean SD Mean SD Mean SD

Head 42 87.7 5.23 62.3 4.01 29.2 2.76 62.1 4.35

Shell 80 89.3 7.36 60.5 7.66 24.8 2.95 50.2 4.91

H&S 122 88.8 6.61 61.1 6.67 26.3 3.58 54.3 7.39

Table 20. Tensile Property Specifications for TC-128B

Property Allowable

Ultimate Tensile Strength 81 to 101 ksi

Yield Strength Greater than 50 ksi

Elongation Greater than 22%

Similarly CVN impact energies at three different temperatures are listed in Table 21. The 

relatively high values for standard deviation listed in the table indicate large scatter in 

impact energy for the range of temperatures.

Table 21. Summary of CVN Impact Energies (ft-lb) at Three Temperatures

–50oF 0oF 50oF

N Mean SD N Mean SD N Mean SD

Head 36 16.9 10.92 45 35.5 20.72 36 54.4 30.35

Shell 74 6.3 4.59 96 12.5 6.78 74 21.0 9.39

H&S 110 9.8 8.79 141 19.9 16.80 110 31.9 24.54
69

Figure 61 compares CVN data from tank cars involved in three different accidents: three 

cars from Minot (GATX 47814, GATX 47837, and GATX 47982), one car from 

Graniteville (UTLX 900270), and one car from Macdona (ACFX 86305). The Charpy 

tests were conducted on material extracted from the shells of the tank cars. The Charpy 

test specimens were oriented in the transverse direction. The figure also shows 

measurements made by SwRI [40] (represented by the open symbols in the figure) and by

NTSB [41] (solid symbols) for the three cars involved in the Minot accident. The SwRI 

measurements were all taken at 0oF, while the NTSB data cover a range of temperatures. 

Regression curves are fit to the NTSB data. The figure shows significant scatter among 

different cars. Moreover, the figure also shows inherent scatter associated with CVN 

impact energy as a measure of impact resistance, as characterized by the error bars for 

measurements at the same temperature.

Temperature (o

F)

-250 -200 -150 -100 -50 0 50 100 150 200 250

CVN Energy (ft-lb)

0

10

20

30

40

50

60

70

80

GATX 47814 - NTSB

GATX 47814 - SwRI

GATX 47837 - NTSB

GATX 47837 - SwRI

GATX 47982 - NTSB

GATX 47982 - SwRI

UTLX 900270 - NTSB

ACFX 86305 - NTSB

Error bars represent ±1 standard deviation

Figure 61. CVN Data for Cars Involved in Three Different Accidents
70

4.2 High-Rate Fracture Toughness

Toughness is a term that is loosely used to characterize the resistance to failure of metal

with a sharp crack, notch, or similar stress concentrator. Moreover high values of 

toughness are generally recognized as a desirable property for structural steel.

The word ‘toughness’ is used for two separate quantities: impact toughness and fracture 

toughness. Impact toughness is an energy measurement (e.g., Joules or ft-lb) which is 

commonly obtained from the CVN test. Fracture toughness is a calculated value for the 

critical stress intensity factor (in units of MPa-√m or ksi-√inch) based on standard tests. 

Relationships between these quantities are empirical. The relationships have been 

validated over many years for structural steels in moderate section thickness. This has 

permitted the more readily available Charpy impact data to be used as an indicator to the 

adequacy of the fracture toughness. The widespread use of the CVN test stems from 

economics—it is the least expensive compared to other tests. But the conversion from 

Charpy impact energy to fracture toughness is somewhat problematic because the CVN 

test uses a specimen that contains a blunt notch rather than a sharp crack.

Fracture toughness changes with temperature—as temperature decreases, steel becomes

more brittle and is more susceptible to fracture. Such changes occur gradually over a 

range of temperature. The temperature at which the fracture behavior of steel changes 

from ductile to brittle is called the ductile-to-brittle transition temperature. The transition 

temperature for normalized steel is lower than that of non-normalized steel.

AAR Specification M-1002 requires that heads and shells of all pressure tank cars built 

after January 1, 1989, must be constructed of normalized steel. Normalization is a heat 

treating process that produces a finer and more abundant pearlitic microstructure, which 

is intended to make the steel stronger and harder compared to non-normalized steel.

Fracture toughness is also affected by loading rate—as the rate of loading or strain rate

increases, steel becomes more susceptible to fracture. Performing a fracture mechanics 

test at relatively high loading rates rather than a CVN test is intended to provide a more 

realistic assessment of impact resistance. Moreover, measurement of high-rate fracture 

toughness in tank car steels has been limited to those conducted previously by SwRI in 

litigation support for GATX (e.g., [39] and [40]).

The tests performed by SwRI did not adhere precisely to ASTM standards for fracture 

toughness5

 5 For example, ASTM E399: “Standard Test Method for Linear-Elastic Plane-Strain Fracture Toughness 

KIC of Metallic Materials,” and ASTM E1820, “Standard Test Method for Measurement of Fracture 

Toughness,” addendum for Rapid Loading Fracture Toughness Determination.

due to inherent circumstances. For example, the material obtained for the 

testing program is thinner than what is typically considered for plane-strain conditions. 

In addition, since the material was obtained from tank cars, it is curved, which limits the 

size of the test specimens. Finally, testing is performed at both low temperature and high 

loading rate with strain rates on the order of 5 inch per inch per second, which has serious 

implications with regard to transducer performance and data integrity. For example, 
71

applying the method described in ASTM E1820 requires highly accurate crack extension 

measurements which are not practical when the time to peak load is on the order of 

1/1000th of a second.

A consequence of the somewhat nonstandard testing procedure adopted by SwRI is that 

fracture toughness is reported in terms of Kmax (maximum stress intensity factor 

calculated using peak load observed in the fracture test) rather than KIC (plane-strain 

fracture toughness calculated using procedures in ASTM E399). The merits of applying 

this so-called Kmax approach are discussed in detail in the technical report prepared by 

SwRI [38].

A framework for interpreting fracture toughness values was developed previously by 

Anderson and McKeighan [42]. Classifications for different values of fracture toughness 

obtained from the Kmax approach were defined as follows: 

• Less than 50 ksi-√in Poor toughness

• 50 – 100 ksi-√in Adequate toughness

• 100 – 200 ksi-√in Good toughness

• Greater than 200 ksi-√in Excellent toughness

The vast majority of material in the testing program fell into the adequate or good 

category. A limited number of samples fell into the poor category, but were confined to 

the lowest temperature results (–50oF). 

Table 22 summarizes the high-rate fracture toughness tests conducted on TC-128B tank 

car steel obtained from retired cars built prior to 1989. The table lists the number of tests, 

average or mean value, and standard deviation at the two test temperatures (–50oF and 

0oF) for material taken from the head and the shell of the retired cars. For instance, 51 

tests were performed on shell material; 24 tests on material from heads. The statistics are 

based Kmax measurements reported by McKeighan [38]. The average fracture toughness 

for the head material is generally higher than that for the shell. In addition, average 

fracture toughness values for both head and shell material decrease with lower 

temperature. The standard deviation indicates the variability in the data.

Similarly, Table 23 summarizes the high-rate fracture toughness data from six cars 

involved in the Minot accident, each of which was also built prior to 1989. The material 

in these tests was also TC-128B, and was obtained from the shells of the tank cars. The 

statistics are based on Kmax measurements conducted as part of litigation support for 

GATX [40]. The trend of decreasing fracture toughness with temperature is evident 

again in these data. The average fracture toughness at 0oF is slightly higher for the Minot 

cars than for the retired cars. In addition, the standard deviations for the Minot cars are 

slightly less than those for the retired cars, indicating less scatter in the data.
72

Table 22. Summary of High-Rate Fracture Toughness Data for Retired Cars

Temperature 

(oF)

Number of 

tests

Average

(ksi-√in)

Standard 

Deviation

(ksi-√in)

Shell –50 16 53.8 17.8

0 35 82.1 22.6

Head –50 8 73.5 24.2

0 16 98.8 25.4

Table 23. Summary of High-Rate Fracture Toughness Data from Minot Cars

Temperature

(oF)

Number of

tests

Average

(ksi-√in)

Standard 

Deviation

(ksi-√in)

0 13 90.6 17.2

37 21 98.7 10.7

Fracture toughness data for steels tend to be highly scattered, especially in the ductile-tobrittle transition region. The SwRI high-rate fracture toughness data confirms this 

tendency. Two methods to quantify scatter in fracture toughness data have been 

developed previously, and are described briefly as follows.

1) Master Curve Method–ASTM standard E1921-03 [43] describes a methodology6

2) Basis Tolerance Limits

to account for scatter in fracture toughness data in the ductile-to-brittle transition 

region, which is based on two general observations: 

(a) Scatter in fracture toughness data in the transition region follows a 

characteristic statistical distribution that is the same for all ferritic steels, and

(b) The shape of the fracture toughness versus temperature curve in the transition 

range is virtually identical for all ferritic steels. The only difference between 

steels is the absolute position of the curve on the temperature axis.

In this methodology, fracture toughness data are assumed to vary according to a 

Weibull distribution function.

[45]–Statistical tolerance limits provide a range in which 

some percentage of a sample population will lie. In quality control applications, 

the extreme (lower) percentile of the distribution is targeted as the tolerance limit. 

For example, a tolerance limit called the B-basis is defined as the value at which 

10 percent of the total population will lie below with a 95 percent confidence 

level. A more stringent tolerance limit is the A-basis, which is the value at which 

1 percent of the total population will lie below at 95 percent confidence level. 

 6 The master curve method has been used to establish fracture toughness requirements for crack initiation 

and crack arrest conditions in nuclear reactor pressure vessel steels [44].
73

The procedures to calculate A- and B-basis values depend on the assumed 

statistical distribution function and sample size. 

Figure 62 shows results from applying these two methods to the SwRI fracture toughness 

(Kmax) data from the shells of retired cars made from TC-128B. Fracture toughness data 

for the two different temperatures are included to show the extent of scatter. The figure 

shows three curves estimated from applying the master curve method: the dotted curve 

labeled Kmax(0.90) represents 90th percentile or upper bound, the solid curve labeled 

Kmax(0.50) represents the median or 50th percentile curve, and the dashed curve labeled 

Kmax(0.10) represents 10th percentile or lower bound of the data. The fracture toughness 

master curves were generated from applying procedures described by McCabe et al. [44], 

but without censoring the data.7 Nonparametric B-basis values8

Temperature (oF)

-100 -50 0 50 100

Fracture Toughness (ksi-in1/2)

0

50

100

150

200

250

Kmax data @-50o

F

Kmax data @0oF

Nonparametric B-basis value Kmax(0.90)

Kmax(0.10)

Kmax(0.50)

for the two test 

temperatures are also shown in the figure for comparison, which are less than the 10th 

percentile values calculated from the master curve method. 

Figure 62. Fracture Toughness Master Curve Applied to Shell Data from Retired 

Cars

 7 The data should be censored to exclude tests in which evidence exists of significant ductile tearing [46]. 8 Nonparametric means that no statistical distribution function was assumed.
74

Similarly Figure 63 shows the results from applying the master curve method and 

estimating the basis tolerance limits to Kmax data from the shells of Minot cars made from 

TC-128B tank car steel. The variability or scatter appears to reduce with increased 

temperature. The master curves for the Minot cars are shifted toward the right on the 

temperature scale compared to those for retired cars. The shift in temperature is reflected 

through the reference temperature, which by definition is the temperature at which the 

median fracture toughness is equal to 100 MPa-√m or 91 ksi-√in. 

Table 24 lists the reference temperatures for the two sets of data as estimated by the 

master curve method. Generally speaking, high toughness steels have a low reference 

temperature and low toughness steels have a high reference temperature. Moreover, the 

basic premise of the master curve method is that a wide range of ferritic steels fit one 

universal curve for toughness as a function of temperature, and the only difference 

between different grades and heats of steels is the absolute position of the curve with 

respect to temperature.

Temperature (oF)

-100 -50 0 50 100

Fracture Toughness (ksi-in1/2)

0

50

100

150

200

250

Kmax data @0o

F

Kmax data @37o

F

Nonparametric B-basis value

Kmax(0.90)

Kmax(0.10)

Kmax(0.50)

Figure 63. Fracture Toughness Master Curve Applied to Shell Data from Minot 

Cars
75

Table 24. Estimated Reference Temperatures

To (oF)

Retired Cars Only 10.0

Minot Cars Only 19.0

Table 25 lists the tolerance limits estimated for high-rate fracture toughness based on the 

data from the retired cars and the Minot cars. The 10th percentile limit is calculated 

using the master curve method. Procedures to calculate the B-basis depend on the 

assumed statistical distribution function and sample size. The B-basis values shown in 

the two previous figures are calculated assuming nonparametric statistics using the 

Hanson-Koopmans method [47]. Except for the retired cars at –50oF, the nonparametric 

B-basis value is the most conservative (i.e., pessimistic or worst case) tolerance limit. 

Moreover, in two previous figures, the test data lie above or close to the nonparametric 

B-basis tolerance limit, and some of the data lie below the 10th percentile curve from the 

master curve method.

Table 25. Estimated Tolerance Limits for High-Rate Fracture Toughness (in ksi-

√in)

Retired Cars Minot Cars

–50oF 0oF 0oF 37oF

10th percentile 45.0 59.8 56.5 72.2

Normal B-basis 17.5 42.9 53.6 78.4

Lognormal B-basis 27.2 46.0 57.2 78.7

Weibull B-basis 18.8 45.3 54.7 77.6

Nonparametric B-basis 24.1 37.8 41.1 65.2

Figure 64 shows the test data from the retired cars plotted as high-rate fracture toughness 

(Kmax) as a function of CVN energy at a temperature of 0oF. The error bars represent 

variability in the measurements in terms of one standard deviation above and below the 

mean value. The figure also shows the Roberts-Newton equation, which is assumed to be 

a lower-bound relation for CVN energy and fracture toughness [48]. Similarly, Figure 65

shows measurements of high-rate fracture toughness as a function of CVN energy at a 

temperature of –50oF. Except for a few outliers, the test data lie above the RobertsNewton equation. In two of the outliers, the variability in both CVN energy and 

measured fracture toughness was quite large in comparison to the other data. Moreover, 

it appears that Roberts-Newton equation provides a reasonable lower-bound relationship 

between CVN energy and Kmax for non-normalized TC-128B tank car steel.
76

CVN Energy (ft-lb)

0 20 40 60 80 100 120

High-Rate Fracture Toughness (ksi-in1/2)

0

50

100

150

200

Head Tests

Shell Tests

Roberts-Newton

Kc=9.35(CVN)0.63

Error bars represent ±1 standard deviation

Figure 64. High-Rate Fracture Toughness as a Function of CVN Energy at 0oF

CVN Energy (ft-lb)

0 20 40 60 80 100 120

High-Rate Fracture Toughness (ksi-in1/2)

0

50

100

150

200

Roberts-Newton

Kc=9.35(CVN)0.63

Error bars represent ±1 standard deviation
77

Figure 65. High-Rate Fracture Toughness as a Function of CVN Energy at –50oF

4.3 Pendulum Impact Testing of Bulk Fracture Behavior

Standard tests for toughness contain stress concentrations (e.g., a blunt notch in the 

Charpy test and a sharp crack in the ASTM fracture mechanics tests) to ensure that 

material failure will initiate and propagate. In a structure without preexisting stress 

raisers, the mechanics of material failure under impact loading conditions are not well 

understood. Moreover, the meaning of fracture toughness in a structure without a 

preexisting crack is unclear.

A nonstandard pendulum impact test was developed to measure the energy to fracture 

unnotched Charpy specimens. An oversized pendulum test fixture, BFCM, was built by 

SwRI to accommodate the energy levels needed to break the unnotched specimens 

(Figure 66). The measurement of fracture energy was used to assess puncture resistance.

\

Figure 66. Oversized, Nonstandard Pendulum Impactor

Figure 67 shows a drawing of BFCM test specimen. The trapezoidal ends of the 

specimen self-engage into the test fixture so they are held fixed as the impact load is 

applied through the pendulum. In this drawing, the test section is 6-inches long, and the 

specimen width is 1 in. Two impact tups were used in the tests: a blunt tup with a 0.5-

inch wide contact surface and a sharp tup with a 0.125-inch wide contact surface. Figure 

68 shows the dimensions of the two impact tups. 
78

Figure 67: BFCM Test Specimen

(a) Blunt Tup (b) Sharp Tup

Figure 68. Impact Tups Used in BFCM Tests

Figure 69 shows data from the BFCM tests conducted on specimens made from 

normalized TC-128B tank car steel with varying thicknesses and using the two different 

strikers or tups. The figure also shows regression curves of the test data for the two 

different tups. The error bars represent variability in the test measurements for fracture 

energy in terms of two standard deviations above and below the average for a given 

specimen thickness. The data in the figure indicates that more energy is required to 

fracture an unnotched specimen with the blunt tup than with the sharp tup. The data can 

be used to validate potential material failure criteria that are incorporated into finite 

element analysis to examine tank integrity.
79

Blunt Striker

Specimen Thickness (inch)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fracture Energy (ft-lb)

0

1000

2000

3000

4000

5000

6000

7000

8000

Test Data

Average

Error bars represent ±2 standard deviations. Nominal specimen width is 1.0 inch

Sharp Striker

Specimen Thickness (inch)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fracture Energy (ft-lb)

0

1000

2000

3000

4000

5000

6000

7000

8000

Test Data

Average

Figure 69. Fracture Energies for TC-128B Measured in BFCM Tests

4.4 Discussion and Summary

The results of the fracture toughness tests are scattered by a factor of about four. This 

would require a safety factor of at least two in a quality assurance (QA) specification. In 

other words, the samples taken from a production heat would have to average at least 

twice the toughness required for service.

At present, the cause of the scatter is unknown. If it is the test protocol, then a better 

procedure might reduce the scatter enough to allow a more reasonable safety factor in a 

QA specification. However, inherent material variability might be the cause of the 

scatter. In the latter case, it is doubtful that a workable QA specification could be 

devised, for two reasons.

First, the performance goal may require a very expensive material. Alternatively, an 

unacceptable gain in structure weight may be required in order to decrease applied 

stresses enough to meet the safety factor with achievable material performance.

Second, the specification does not provide an absolute safety guarantee because some 

small percentage of the material might not have the minimum necessary toughness. For 

example, even an A-basis specification (no more than one percent below minimum) 

leaves the risk that one thousand cars in a fleet of one hundred thousand might have 

insufficient toughness. Also a subtle potential for error exists in the specification itself. 

A- and B-basis values are usually derived from given numbers of samples, without regard 

to the relation between sample and production volume. There is no problem when the 

samples are items such as light bulbs—one sample “volume” is the same as one 
80

production “volume.” However, using a few samples to measure the toughness of a heat 

of steel is equivalent to testing on the order of one ten-thousandth of the material volume. 

One must question whether an A- or B-basis derived from such tests reflects the true 

scatter in performance.

The large scatter observed in the high-rate fracture toughness measurements makes it 

unlikely that a practical specification of minimum fracture toughness can be devised to 

guarantee the prevention of unstable fracture in railroad tank cars subject to derailment 

forces. A specification of average fracture toughness is possible and could serve to 

decrease the population of cars at risk of fracture.

With respect to the pressure tank car fleet as a whole, the cold weather risk associated 

with non-normalized tank car steel may be mitigated by taking some combination of any 

of the following actions on such cars: (1) retire early, (2) reconfigure for nonhazardous/non-pressure commodities, and (3) transfer to service on exclusively southern 

routes.
81

5. Conclus ions

This report describes engineering studies conducted and managed by the Volpe Center on 

the structural integrity of railroad tank cars under accident loading conditions. The 

following conclusions are made based upon the results to date.

Derailment Dynamics

The lumped-parameter models developed to examine the gross motions of rail cars in a 

generalized train derailment were verified through various comparisons. 

(1) The similarity of results from the purpose-built and ADAMS models suggests that the 

dynamics are being correctly calculated for the assumed scenarios in both models.

(2) The purpose-built and ADAMS models produce similar results to those from a 

simulation model developed previously. The previous model reproduced the number 

of derailed cars in an actual derailment.

Sensitivity studies using the derailment dynamics models indicate that train speed and 

friction have the most significant effect on the derailment outcome in terms of either the 

number of derailed cars, maximum closing speed, or peak coupler force.

For flat terrain and train speeds not exceeding roughly 40 mph, the maximum closing 

speeds between cars engaging in post-derailment collisions appear to average about onehalf the initial train speed.

The derailment dynamics models produce simulated car-to-car impacts that generally 

occur in accidents and lead to release of lading; namely, head and shell impacts. 

Moreover, the simulated car-to-car impacts are useful to represent idealized scenarios that 

can be analyzed for performance evaluations.

Structural Response

The nonlinear (i.e., elastic-plastic material behavior with large deformations) FEA 

models developed to examine the structural response (i.e., force-indentation behavior) for 

head and shell deformations were also verified through various comparisons.

(1) The force-indentation behavior calculated by static, nonlinear FEA for head and shell 

deformations are in reasonable agreement with closed-form solutions.

(2) Static and dynamic, nonlinear FEA models produce nearly identical force-indentation 

characteristics.

(3) Dynamic, nonlinear FEA, and lumped-parameter models produce nearly identical 

results for impact force as a function of closing speed.

Dynamic, nonlinear FEA models for shell impacts with fluid-structure interaction were 

validated with data obtained from full-scale tank car tests:

(1) Calculated peak impact forces are within 10 percent of test data, and maximum 

indentations are within 15 to 20 percent.
82

(2) Puncture in the second full-scale shell impact test was predicted using a material 

failure criterion based on the general state of stress in the shell, or stress triaxiality.

Based on comparisons between FEA and full-scale shell impact test data, peak impact 

forces and maximum indentations depend on impact speed. In addition, indenter size 

appears to have a relatively weak effect on the force-indentation characteristic, but a 

strong effect on puncture.

Elastic-plastic FEA of unnotched Charpy specimens made from different tank car steels 

provided a benchmark case to examine material failure criteria. FEA used in conjunction 

with a criterion based on the general state of stress in terms of stress triaxiality (i.e., BaoWierzbicki [25]) were in excellent agreement with measured fracture energies.

Finite element procedures will remain useful for predicting structural response of any 

new car designs that might differ from current practice. Research employing these 

procedures is ongoing to develop alternative or improved designs for tank cars carrying 

hazardous materials [49] and [50].

Tank Car Steels Characterization

No clear trends were observed between chemical composition, tensile properties, Charpy 

impact energies, or fracture toughness values and tank car build date.

The extent of scatter observed in the measurements of fracture toughness was quite large, 

which obscures making definitive conclusions regarding toughness variation with age. 

The large scatter makes it is unlikely that a practical specification of minimum fracture 

toughness can be devised to guarantee the prevention of unstable fracture in railroad tank 

cars subject to derailment forces. A specification of average fracture toughness is 

possible and could serve to decrease the population of cars at risk of fracture.
83

6. References

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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] National Transportation Safety Board, “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.

[5] 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.

[6] Yang, T.H., Manos, W.B., Johnstone, B., “Dynamic Analysis of Train 

Derailments,” ASME Winter Annual Meeting, ASME Paper 72-WA/RT-5, 1972.

[7] Birk, A.M., Anderson, R.J., Coppens, A.J., “Computer Simulation of a

Derailment Accident, Part I – Model Basis,” Journal of Hazardous Materials 25, 

pp. 121-147, 1990.

[8] Birk, A.M., Anderson, R.J., Coppens, A.J., “Computer Simulation of a 

Derailment Accident, Part II – Sample Simulation,” Journal of Hazardous 

Materials 25, pp. 149-165, 1990.

[9] Toma, E.E., “A Computer Model of a Train Derailment,” Ph.D. Thesis, Kingston, 

Ontario, Canada: Department of Mechanical Engineering, Queen’s University, 

1998.

[10] Han, H.S., Koo, J.S., “Simulation of Train Crash in Three Dimensions,” Vehicle 

System Dynamics 20, pp. 435-450, 2003.

[11] Jeong, D.Y., Lyons, M.L., Orringer, O., Perlman, A.B., “Equations of Motion for 

Train Derailments,” Proceedings of the 2007 ASME Rail Transportation Division 

Fall Technical Conference, RTDF2007-46009, September 2007.
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Derailments,” Proceedings of 2006 ASME International Mechanical Engineering 

Congress and Exposition, IMECE2006-14607, November 2006.

[13] Grange, J.S., Report of the Mississauga Railway Accident Inquiry, Hull, Quebec:

Canadian Government Publishing Centre,1981.

[14] LS-DYNA3D User’s Manual, Version 940, Livermore, CA: Livermore Software 

Technology Company.

[15] ABAQUS User’s Manual, Pawtucket, RI: Hibbit, Karlsson & Sorensen Inc.

[16] Cook, R.D., Malkus, D.S., Plesha, M.E., Concepts and Applications of Finite 

Element Analysis, 3rd Ed., New York, NY: John Wiley & Sons, 1989.

[17] Roache, P.J., Verification and Validation of Computational Science and 

Engineering, Albuquerque, NM, Hermosa Publishers, 1998.

[18] American Society of Mechanical Engineers, “Guide for Verification and 

Validation in Computational Solid Mechanics,” ASME V&V 10-2006, New 

York, NY, December 2006.

[19] Phillips, E.A., Olsen, L., “Final Phase 05 Report on Tank Car Head Study,” RPIAAR Tank Car Safety Research and Test Project, Report No. RA-05-1-17, July 

1972.

[20] Tang, Y.H., Yu, H., Gordon, J.E., Priante, M., Jeong, D.Y., Tyrell, D.C., Perlman, 

A.B., “Analyses of Full-Scale Tank Car Shell Impact Tests,” Proceedings of the 

2007 ASME Rail Transportation Division Fall Technical Conference,

RTDF2007-46010, September 2007.

[21] de Oliveria, J.G., Weirzbicki, T., “Crushing Analysis of Rotationally Symmetric 

Plastic Shells,” Journal of Strain Analysis for Engineering Design 17, pp. 229-23, 

1982.

[22] Riks, E., “An Incremental Approach to the Solution of Snapping and Buckling 

Problems,” International Journal of Solids and Structures 15, pp. 524-551, 1979.

[23] Wierzbicki, T., Suh, M.S., “Indentation of Tubes Under Combined Loading,” 

International Journal of Mechanical Sciences 30, pp. 229-248, 1988.

[24] Jeong, D.Y., Tang, Y.H., Yu, H., Perlman, A.B., “Engineering Analyses for 

Railroad Tank Car Head Puncture Resistance,” Proceedings of 2006 ASME 

International Mechanical Engineering Congress and Exposition, IMECE2006-

13212, September 2006.
85

[25] Bao, Y., Wierzbicki, T., “On fracture locus in the equivalent strain and stress 

triaxiality space,” International Journal of Mechanical Sciences 46, pp. 81-98, 

2004.

[26] 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.

[27] Gurson, A.L., “Continuum Theory of Ductile Rupture by Void Nucleation and 

Growth: Part 1 – Yield Criterion and Flow Rules for Porous Ductile Media,” 

Journal of Engineering Materials and Technology 99, pp. 2-15, 1977.

[28] Tvergaard, V., “Influence of Voids on Shear Band Instabilities under Plane Strain 

Conditions,” International Journal of Fracture 17, pp. 389-407, 1981.

[29] Tvergaard, V., “On Localization in Ductile Materials Containing Spherical 

Voids,” International Journal of Fracture 18, pp. 237-252, 1982.

[30] Anderson, T.L., Kirkpatrick, S.W., “Quantifying and Enhancing Puncture 

Resistance in Railroad Tank Cars Carrying Hazardous Materials, Phase I: 

Preliminary Study,” Structural Reliability Technology, Inc. Draft Report Prepared 

for The Chlorine Institute, 2006.

[31] Anderson, T.L., Rose, B., McKeighan, P.C., Kirkpatrick, S.W., “Quantifying and 

Enhancing Puncture Resistance in Railroad Tank Cars Carrying Hazardous 

Materials, Phase II: Development and Validation of a Puncture Resistance 

Evaluation Methodology,” Quest Reliability LLC Draft Report Prepared for The 

Chlorine Institute, 2007.

[32] Bao, Y., Wierzbicki, T., “Determination of Fracture Locus for the 2024-T351 

Aluminum,” Impact & Crashworthiness Laboratory, Massachusetts Institute of 

Technology, Report No. 81, 2002.

[33] Bao, Y., Bai, Y., Wierzbicki, T., “Calibration of A710 Steel for Fracture,” Impact 

& Crashworthiness Laboratory, Massachusetts Institute of Technology, Report 

No. 135, 2004.

[34] Lee, Y.W., Wierzbicki, T., “Quick Calibration for Industrial Use,” Impact & 

Crashworthiness Laboratory, Massachusetts Institute of Technology, Report No. 

115, 2004.

[35] Hillerborg, A., Modeer, M., Petersson, P.E., “Analysis of crack formation and 

crack growth in concrete by means of fracture mechanics and finite elements,” 

Cement and Concrete Research 6, 1976, pp. 773-782.
86

[36] Thilmany, T., “Tying Two Forces,” Mechanical Engineering 129, New York: 

American Society of Mechanical Engineers, May 2007: 34-37.

[37] Tang, Y.H., Yu, H., Gordon, J.E.., Jeong, D.Y., Perlman, A.B. “Analysis of 

Railroad Tank Car Shell Impacts Using Finite Element Method,” Proceedings of 

the 2008 IEEE/ASME Joint Rail Conference, JRC2008-63014, April 2008.

[38] McKeighan, P.C., “Mechanical Properties of Tank Car Steels Retired from the 

Fleet,” Southwest Research Institute Report to the Volpe Center, August 2008.

[39] McKeighan, P.C., “High Rate Fracture Toughness, Tensile Properties, CVN and 

Composition of Various TC-128B Steels, Phase A: Pre-1989 GATX Tank Cars 

and Modern Vintage Plate,” Interim Report, Southwest Research Institute Project 

No. 18.11388, June 2005.

[40] McKeighan, P.C., “High Rate Fracture Toughness, Tensile Properties, CVN and 

Composition of Various TC-128B Steels, Phase B: Tank Cars Involved in the 

2002 Minot Incident,” Interim Report, Southwest Research Institute Project No. 

18.11388, June 2005.

[41] National Transportation Safety Board, Materials Laboratory Factual Report, 

Report No. 03-042, April 2003.

[42] Anderson, T.L., McKeighan, P.C., “The Interpretation of Fracture Toughness 

Magnitudes for Tank Car Steels: Relating K-based Toughness Range to Material 

Adequacy,” August 2005.

[43] ASTM Standard E1921-03, “Standard Test Method for Determination of 

Reference Temperature, To, for Ferritic Steels in the Transition Range,” Annual

Book of ASTM Standards, Vol. 03.01, West Conshohocken, PA: ASTM 

International, 1998.

[44] McCabe, D.E., Merkle, J.G., Wallin, K., Introduction to the Development and Use 

of the Master Curve Method, West Conshohocken, PA: ASTM International,

2005.

[45] Department of Defense, “Metallic Materials and Elements for Aerospace Vehicle 

Structures,” Department of Defense Handbook, MIL-HDBK-5J, 2003.

[46] E-mail communication with T.L. Anderson.

[47] Hanson, D.L., Koopmans, L.H., “Tolerance Limits for the Class of Distribution 

with Increasing Hazard Rates,” Annals of Mathematical Statistics 35, pp. 1561-

1570, 1964.
87

[48] Barsom, J.M., Rolfe, S.T., Fracture and Fatigue Control in Structures: 

Applications of Fracture Mechanics, 3rd ed. West Conshohocken, PA: ASTM 

International, 1999; 126.

[49] Tyrell, D.C., Jacobsen, K., Talamini, B., Carolan, M., “Developing Strategies for 

Maintaining Tank Car Integrity During Train Accidents,” Proceedings of the 

2007 ASME Rail Transportation Division Fall Technical Conference,

RTDF2007-46015, September 2007.

[50] Carolan, M., Talamini, B., Tyrell, D.C., “Update on Ongoing Tank Car 

Crashworthiness Research: Predicted Performance and Fabrication Approach,” 

Proceedings of the 2008 IEEE/ASME Joint Rail Conference, JRC2008-63052, 

April 2008.
88

APPENDIX A - NTSB RECOMMENDATIONS FROM THE MINOT ACCIDENT

The NTSB released its accident report on the Minot derailment on March 15, 2004, and 

made the following recommendations to the FRA:

Require all railroads with continuous welded rail track to include procedures (in the programs 

that are filed with the Federal Railroad Administration) that prescribe on-the-ground visual 

inspections and nondestructive testing techniques for identifying cracks in rail joint bars before 

they grow to critical size. (R-04-1)

Establish a program to periodically review continuous welded rail joint bar inspection data from 

railroads and Federal Railroad Administration track inspectors and, when determined necessary, 

require railroads to increase the frequency or improve the methods of inspection of joint bars in 

continuous welded rail. (R-04-2)

Instruct Federal Railroad Administration track inspectors to obtain copies of the most recent 

continuous welded rail programs of the railroads that fall within the inspectors’ areas of 

responsibility and require that inspectors use those programs when conducting track inspections. 

(R-04-3) 

Conduct a comprehensive analysis to determine the impact resistance of the steels in the shells of 

pressure tank cars constructed before 1989. At a minimum, the safety analysis should include the 

results of dynamic fracture toughness tests and/or the results of nondestructive testing techniques 

that provide information on material ductility and fracture toughness. The data should come from 

samples of steel from the tank shells from original manufacturing or from a statistically 

representative sampling of the shells of the pre-1989 pressure tank car fleet. (R-04-4)

Based on the results of the Federal Railroad Administration’s comprehensive analysis to 

determine the impact resistance of the steels in the shells of pressure tank cars constructed before 

1989, as addressed in Safety Recommendation R-04-4, establish a program to rank those cars 

according to their risk of catastrophic fracture and separation and implement measures to 

eliminate or mitigate this risk. This ranking should take into consideration operating 

temperatures, pressures, and maximum train speeds. (R-04-5)

Validate the predictive model the Federal Railroad Administration is developing to quantify the 

maximum dynamic forces acting on railroad tank cars under accident conditions. (R-04-6)

Develop and implement tank car design-specific fracture toughness standards, such as a 

minimum average Charpy value, for steels and other materials of construction for pressure tank 

cars used for the transportation of U.S. Department of Transportation class 2 hazardous 

materials, including those in low-temperature service. The performance criteria must apply to the 

material orientation with the minimum impact resistance and take into account the entire range 

of operating temperatures of the tank car. (R-04-7)
89

APPENDIX B – ESTIMATION OF SAMPLE SIZE AND CONFIDENCE LEVEL

Determining an appropriate sample size is affected by a number of factors, including the 

purpose of the study, population size, level of precision, level of confidence or risk, and 

degree of variability. One method is to use a formula for sample size for the mean:9

2

/ 2 z

n

E

  α ⋅σ =    

where zα/2 is the abscissa of the standard normal distribution curve that cuts off an area α

at the tail, σ is the standard deviation, and E is the desired level of precision. Table B.1 

lists the values of zα/2 depending on the level of confidence.

Table B.1: Critical Values for Different Levels of Confidence

Level of Confidence za/2

95% 1.96

90% 1.645

80% 1.282

This formula states that higher levels of confidence and greater precision require larger 

sample sizes. Table B.2 lists results from using this formula to estimate the minimum 

sample sizes at different levels of confidence and precision.

Table B.2: Minimum Sample Sizes for Different Levels of Confidence and Precision

Level of Confidence E=σ E=0.5σ E=0.25σ

95% 4 16 62

90% 3 11 44

80% 2 7 27

For example, Table B.2 indicates that at least four samples are needed in order to achieve 

a 95% level of confidence that the average fracture toughness for a given population will

be within one standard deviation. At least 16 samples are needed in order to achieve the 

same level of confidence that the average fracture toughness will be within one-half 

 9 iSixSigma Staff. "How to Determine Sample Size, Determining Sample Size," iSixSigma.com (July 9,

2000). http://www.isixsigma.com/library/content/c000709a.asp
90

standard deviation. In this method, the sample size estimate is strongly influenced by the 

population variance.