U.S. Department of

Transportation

Federal Railroad 

Administration

Detailed Puncture Analyses Tank Cars:

Analysis of Different Impactor Threats and Impact 

Conditions

Office of Research

and Development

Washington, DC 20590

DOT/FRA/ORD-13/17 Final Report

 March 2013
NOTICE

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1. AGENCY USE ONLY (Leave blank) 2. REPORT DATE

March 2013

3. REPORT TYPE AND DATES COVERED

Technical Report

April 2011-August 2012

4. TITLE AND SUBTITLE

Detailed Puncture Analyses of Tank Cars: Analysis of Different Impactor Threats and 

Impact Conditions

5. FUNDING NUMBERS

6. AUTHOR(S) and FRA COTR

Steven W. Kirkpatrick

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

Applied Research Associates, Inc.

2672 Bayshore Parkway, Suite 1035

Mountain View, CA 94043

8. PERFORMING ORGANIZATION 

REPORT NUMBER

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

U.S. Department of Transportation 

Federal Railroad Administration

Office of Research and Development

Washington, DC 20590

10. SPONSORING/MONITORING

AGENCY REPORT NUMBER

DOT/FRA/ORD-13/17

11. SUPPLEMENTARY NOTES

COTR: Francisco González ,III

12a. DISTRIBUTION/AVAILABILITY STATEMENT

This document is available to the public through the FRA Web site at www.fra.dot.gov, or by 

calling (202) 493-1300.

12b. DISTRIBUTION CODE

13. ABSTRACT (Maximum 200 words)

There has been significant research in recent years to analyze and improve the impact behavior and puncture resistance of railroad 

tank cars. Much of this research has been performed using detailed nonlinear finite element analyses supported by full scale 

impact testing. This use of detailed simulation methodologies has significantly improved our understanding of the tank impact 

behaviors and puncture prediction. However, the evaluations in these past studies were primarily performed for a few idealized 

impact scenarios. 

This report describes a research program to evaluate railroad tank car puncture behaviors under more general impact conditions. 

The approach used in this research program was to apply a tank impact and puncture prediction capability using detailed finite 

element analyses (FEA). The analysis methodologies apply advanced damage and failure models that were validated by a series 

of material tests under various loading conditions. In this study, the analyses were applied to investigate the tank puncture 

behaviors for a wide range of impact conditions.

14. SUBJECT TERMS

Tank car, Impactor, derailment, hazardous materials, hazmat

15. NUMBER OF PAGES

268

16. PRICE CODE

17. SECURITY CLASSIFICATION

OF REPORT

Unclassified

18. SECURITY CLASSIFICATION

OF THIS PAGE

Unclassified

19. SECURITY CLASSIFICATION

OF ABSTRACT

Unclassified

20. LIMITATION OF ABSTRACT

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

Prescribed by ANSI Std. 239-18

298-102
ii

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
iii

Contents

Executive Summary........................................................................................................................ 1

Overview......................................................................................................................................... 3

1. Introduction ........................................................................................................................... 20

1.1 Background ............................................................................................................... 20

1.2 Material Damage and Failure Behaviors................................................................... 21

1.3 Tank Car Puncture Modeling .................................................................................... 22

2 Material Constitutive and Damage Models........................................................................... 26

2.1 Introduction ............................................................................................................... 26

2.2 Material Stress-Strain Behavior ................................................................................ 26

2.2.1 TC128B Material Properties ..................................................................................... 26

2.3 Bao-Wierzbicki Failure Surface................................................................................ 31

2.4 Material Characterization Testing and Analyses....................................................... 33

2.4.1 Tensile Tests and Analyses ....................................................................................... 34

2.4.2 Notched Round Bar Tensile Tests and Analyses ...................................................... 35

2.4.3 Tensile-Shear Tests and Analyses............................................................................. 37

2.4.4 Punch Tests and Analyses......................................................................................... 40

3 Analysis of Different Size and Shape Impactors................................................................... 44

3.1 Introduction and Background.................................................................................... 44

3.1.1 Puncture Analysis Methodologies............................................................................. 44

3.2 Side Impact Analysis of Different Size and Shape Impactors .................................. 52

3.2.1 Effects of Impactor Size and Shape .......................................................................... 55

3.2.2 Definition of the Impactor Characteristic Size.......................................................... 62

3.2.3 Analysis of Impactor Edge Sharpness....................................................................... 65

3.2.4 Analysis of Complex Impactor Shapes..................................................................... 66

3.2.5 Analysis of Impactor Orientation Effects.................................................................. 78

3.3 Head Impact Analysis of Different Size and Shape Impactors................................. 83

3.3.1 Effects of Impactor Size and Shape .......................................................................... 83

3.3.2 Analysis of Complex Impactor Shapes..................................................................... 88

3.3.3 Analysis of Offset Head Impact Location Effects..................................................... 96

3.4 Analysis of Impact Speed Effects ............................................................................. 97

3.4.1 Analysis of Impact Speed for Side Impacts .............................................................. 97

3.4.2 Analysis of Impact Speed for Head Impacts........................................................... 102

3.5 Analysis of Tank and Lading Temperature Effects................................................. 104

4 Analysis of General Impact Conditions .............................................................................. 108
iv

4.1 Introduction ............................................................................................................. 108

4.2 Oblique Impacts ...................................................................................................... 108

4.3 Impact Boundary Condition Effects........................................................................ 114

4.3.1 Side Impact Constraint Effects................................................................................ 114

4.3.2 Head Impact Constraint Effects .............................................................................. 121

4.4 Lading Response Effects......................................................................................... 124

4.4.1 Lading Effects for Side Impacts.............................................................................. 124

4.4.2 Lading Effects for Head Impacts............................................................................. 130

4.5 Head Impact Test Configuration ............................................................................. 134

4.5.1 Draft Gear Effects for the Impactor ........................................................................ 134

4.5.2 Trailing Mass Effects for the Impactor ................................................................... 137

4.5.3 Summary of the Head Impact Test Evaluation ....................................................... 142

4.6 Analysis of Offset Side Impact Effects................................................................... 143

4.6.1 Analysis of Vertical Offset Side Impacts................................................................ 143

4.6.2 Analysis of Longitudinal Offset Side Impacts........................................................ 147

5 Impact Analyses on Other Tank Car Designs..................................................................... 152

5.1 Introduction and Background.................................................................................. 152

5.2 DOT 105J500 Chlorine Tank Cars.......................................................................... 153

5.3 Ethylene Oxide Tank Cars ...................................................................................... 158

5.3.1 Normal side Impacts of EO Tank Cars ................................................................... 159

5.3.2 Offset Impacts of EO Tank Cars............................................................................. 161

5.3.3 Oblique Impacts of EO Tank Cars.......................................................................... 162

5.3.4 Summary of EO Tank Car Puncture Performance .................................................. 164

5.4 Anhydrous Ammonia Tank Cars............................................................................. 166

5.4.1 Normal side Impacts of AA Tank Cars................................................................... 167

5.4.2 Oblique Impacts of AA Tank Cars.......................................................................... 168

5.4.3 Summary of AA Tank Car Puncture Performance.................................................. 170

5.5 Comparison of the Various Pressure tank Car designs ........................................... 171

5.6 DOT Class 111 tank cars......................................................................................... 172

5.6.1 Effects of Outage Volume....................................................................................... 174

5.6.2 Analyses of Different General Purpose Tank Designs............................................ 181

5.6.3 Offset Impact Analyses........................................................................................... 190

5.6.4 Summary of Analyses for General Purpose Tank Cars........................................... 191

6 Analytical Models for Tank Car Impacts............................................................................ 194

6.1 Introduction ............................................................................................................. 194

6.2 Head Impact Analyses............................................................................................. 194

6.2.1 Head Impact Analysis Algorithm............................................................................ 194
v

6.3 Side Impact Analyses.............................................................................................. 201

6.3.1 Supporting FE Tank Analyses................................................................................. 201

6.3.2 Side Impact Analysis Algorithm ............................................................................. 211

6.4 Development of the Characteristic Puncture Force................................................. 218

7 Analysis of Real World Threats.......................................................................................... 226

7.1 Introduction and Background.................................................................................. 226

7.2 Protection System Design ....................................................................................... 226

7.3 Side Impact Puncture Analyses............................................................................... 230

8 Conclusion........................................................................................................................... 237

9 References........................................................................................................................... 241

Appendix A. Tank Head Puncture Resistance Performance Standards..................................... 248

Abbreviations and Acronyms ..................................................................................................... 250
vi

Illustrations

Figure 1. Correlation of Side Impact Puncture Forces with Ram Characteristic Size................... 3

Figure 2. Correlation of Side Impact Puncture Energies with Ram Characteristic Size ............... 4

Figure 3. Puncture Forces for the 12x12-Inch Impactor at Various Orientations ......................... 5

Figure 4. Comparison of Puncture Forces for Normal and Oblique Impacts................................ 6

Figure 5. Comparison of Puncture Energies for Normal and Oblique Impacts............................. 7

Figure 6. Comparison of the Calculated Head and Side Impact Puncture Forces......................... 7

Figure 7. Comparison of the Calculated Head and Side Impact Puncture Energies...................... 8

Figure 8. The Effects of Constraint Conditions for the 15 mph Constant Velocity Impacts......... 9

Figure 9. The Effects of Tank Motion BCs on Head Impact Response ...................................... 10

Figure 10. Calculated Longitudinal Velocity Distribution in the SPH Lading............................ 11

Figure 11. The Effects of Lading on Unconstrained Head Impact Response.............................. 12

Figure 12. Normalized Side Impact Puncture Energies at 105 oF ............................................... 13

Figure 13. Comparison of Relative Puncture Performance of Various Tank Designs................ 14

Figure 14. Comparison of the 1D Model and FEA of Head Impact Behaviors........................... 15

Figure 15. Idealized Schematic of the Side Impact Spring Mass Model..................................... 16

Figure 16. Comparison of the FEA and Impact Algorithm for Different Speed Impacts ........... 17

Figure 17. Initial Set of Tank Puncture Forces under Various Impact Conditions...................... 17

Figure 18. Correlation of Characteristic Puncture Forces for Various Impact Conditions ......... 18

Figure 19. Number of Accidents with at Least One Car Releasing Hazardous Materials [2]..... 21

Figure 20. Calculated Derailment Behavior for the 36-Car Train Model [10]............................ 22

Figure 21. Calculated Puncture Behavior of a Head and Head Shield ........................................ 23

Figure 22. Calculated Puncture Forces as a Function of System Thickness ............................... 24

Figure 23. Loading and Failure Mechanism for the Tank Impact and Puncture ......................... 25

Figure 24. Material Testing Data for Different TC128B Materials............................................. 27

Figure 25. Comparison of Engineering and True Stress-Strain Data for TC128B...................... 29

Figure 26. Tabular True Stress Curve Developed for the TC128B Constitutive Model ............. 29

Figure 27. Comparison of the Measured and Calculated TC128B Tensile Test ......................... 30

Figure 28. Local Damage Criterion for Tensile Ductile Fracture Analyses................................ 32

Figure 29. Bao-Wierzbicki Failure Surface and Tests Used for Model Calibration ................... 33

Figure 30. Dimensions of the Specimen Used in Tensile Testing............................................... 34

Figure 31. Necking Behavior Observed in the TC128B Round Bar Specimens......................... 34
vii

Figure 32. Validation of the Tensile Test Behavior for TC128B ................................................ 35

Figure 33. Test Setup for the TC128B Notched Round Bar Specimens ..................................... 36

Figure 34. Validation of the Notched Round Bar Test Behavior for TC128B............................ 37

Figure 35. Specimen Geometries for the Combined Tensile Shear Tests ................................... 38

Figure 36. Photograph of the Combined Tensile Shear Test Configuration................................ 38

Figure 37. Analysis of the Specimen Behavior in the Pure Shear Orientation............................ 39

Figure 38. Validation of the Combined Tensile Shear Test Behavior for TC128B .................... 39

Figure 39. Simulation of the Punch Test on the Thin TC128B Plate Material............................ 40

Figure 40. Punch Test Failure Mode for the Thin TC128B Plate Material ................................. 41

Figure 41. Simulation of the Punch Test on the Thin TC128B Plate Material............................ 42

Figure 42. Force-Deflection Curves for Three Punch Test Configurations on TC128B............. 42

Figure 43. Comparison of the Calculated and Measured Punch Test Plate Profile..................... 43

Figure 44. Tank Model and Impact Zone Mesh Used for Side Impact Puncture Analyses ........ 45

Figure 45. Tank Head Model and Impact Zone Mesh Used for the Head Puncture Analyses.... 46

Figure 46. Calculated Tank Car Impact Behavior Using Two Different Lading Models ........... 46

Figure 47. Pressure-Volume Relationship Used for the Tank Control Volume (10.6 percent

outage)................................................................................................................................... 47

Figure 48. Effect of Variable Internal Pressure on 500-Pound Tank Impact Response .............. 48

Figure 49. Calculated Internal Pressure Variations in the 500-Pound Tank Impact Analyses.... 49

Figure 50. Simplified Tank Model Analysis with Bao-Wierzbicki Failure Assessment............. 50

Figure 51. Comparison of the Calculated and Measured Test 2 Impact and Puncture Behavior 51

Figure 52. Detailed Impact and Puncture Sequence for a 600-Pound Chlorine Car ................... 53

Figure 53. Calculated Puncture Initiation and Fracture Progression ........................................... 54

Figure 54. Calculated Energy Balance for the 600-Pound Chlorine Tank Car Impact (R10F)... 54

Figure 55. Tank Model and Impact Zone Mesh Used for the 12x12 Inch Impactor................... 55

Figure 56. Models of the Different Size Square Impactors......................................................... 56

Figure 57. Updated 600-Pound Tank Impact Analysis with Different Size Impactors............... 57

Figure 58. Puncture Forces for the 600-Pound Tank Impacts with Different Size Impactors..... 57

Figure 59. Calculated Puncture Behaviors (3x3- and 12x12-Inch Impactors) ............................ 58

Figure 60. Models of the Different Size Rectangular Iimpactors................................................ 58

Figure 61. Puncture Forces for the 600-Pound Tank Impacts with Different Size Impactors..... 59

Figure 62. Calculated Puncture Behaviors (3x3- and 12x12-Inch Impactors) ............................ 60

Figure 63. Models of the Different Size Round Impactors.......................................................... 61
viii

Figure 64. Puncture Forces for the 600-Pound Tank Impact Analyses with Different Size and 

Shape Impactors.................................................................................................................... 61

Figure 65. Calculated Puncture Behaviors for Different Size Round Impactors......................... 62

Figure 66. Correlation of the Puncture Forces with Ram Characteristic Size ............................. 64

Figure 67. Correlation of the Puncture Energies with Ram Characteristic Size.......................... 64

Figure 68. Calculated Force-Deflection Behaviors for the Impactor Edge Radii Evaluations.... 66

Figure 69. Calculated Puncture Behavior for the 3x12 Impactor with 0.5 and 0.1 in Edge Radii

............................................................................................................................................... 67

Figure 70. Model for the Rail Section Impactor.......................................................................... 67

Figure 71. Geometry for the Rail Section Impactor .................................................................... 68

Figure 72. Calculated Side Impact Puncture Behavior for the Rail Section Impactor ................ 69

Figure 73. Puncture Forces for the 600-Pound Tank Impact Analyses with the Rail Impactor.. 70

Figure 74. Model for the Coupler Head Impactor ....................................................................... 71

Figure 75. Calculated Puncture Behavior for the Coupler Head Normal Impact........................ 72

Figure 76. Calculated Force-Deflection Behavior for the Coupler Head Normal Impact........... 73

Figure 77. Calculated Puncture Behavior for the Coupler Head 15-Degree Rotation Impact .... 74

Figure 78. Calculated Force-Deflection Behavior for the Coupler 15-Degree Rotation Impact. 75

Figure 79. Calculated Puncture Behavior for the Coupler 15-Degree Rotation Impact.............. 76

Figure 80. Calculated Force-Deflection Behavior for the Coupler 15-Degree Rotation Impact. 77

Figure 81. Puncture Forces for the 600-Pound Tank Impact Analyses with the Coupler Head 

Impactor................................................................................................................................ 77

Figure 82. Example Impactor Orientation Analyses Performed for Side Impacts...................... 78

Figure 83. Calculated Force-Deflection Behaviors for the 12x12-Inch Impactor and Various 

Levels of Yaw Rotations....................................................................................................... 79

Figure 84. Puncture Forces for the 12x12-Inch Impactor at Various Orientations ..................... 81

Figure 85. Puncture Behavior for the 12x12-Inch Impactor with Face, Edge, and Corner Impacts

............................................................................................................................................... 82

Figure 86. Analysis of the Tank Head Puncture Behavior for the 6x6-Inch Impactor................ 84

Figure 87. Calculated Head Impact Force-Deflection Behaviors for the Square Impactors....... 85

Figure 88. Calculated Head Impact Puncture Forces for Various Impactors.............................. 85

Figure 89. Calculated Head Puncture Behaviors for the 3x12 and 12x3 Impactors.................... 86

Figure 90. Comparison of the Calculated Head and Side Impact Puncture Forces..................... 87

Figure 91. Comparison of the Calculated Head and Sside impact puncture energies. ................ 87

Figure 92. Analysis of the 11 mph Rail Section Impact Behavior on the Constrained Head...... 89
ix

Figure 93. Calculated Head Impact Puncture Behavior for the Rail Section Impactor............... 89

Figure 94. Calculated Head Puncture Impact Response for the Rail Section Impactor .............. 90

Figure 95. Calculated Head Impact Puncture Forces for Various Impactors.............................. 90

Figure 96. Calculated Head Puncture Behavior for the Upside Down Rail Impactor................. 91

Figure 97. Calculated Head Impact Response for the Rail Section Impactors............................ 91

Figure 98. Analysis of the 18 mph Coupler Impact Behavior on the Constrained Head ............ 92

Figure 99. Calculated Damage for the 18 mph Coupler Impact on the Constrained Head ......... 93

Figure 100. Calculated Damage for the 25 mph Coupler Impact on the Constrained Head ....... 94

Figure 101. Calculated Head Puncture Impact Response for the Rigid Coupler Impactor......... 95

Figure 102. Calculated Head Impact Puncture Forces for Various Impactors............................ 95

Figure 103. Impact Scenarios Used in the Vertical Offset Impact Analyses............................... 96

Figure 104. Calculated Force-Deflection Behaviors for Variable Offset Head Impacts............. 97

Figure 105. Comparison of Side Impact Behaviors at Different Impact Speeds......................... 98

Figure 106. Comparison of Side Impact Puncture Forces at Different Impact Speeds............... 99

Figure 107. Comparison of Side Impact Puncture Energies at Different Impact Speeds............ 99

Figure 108. Comparison of the Tank Side Loading Response at Different Speeds .................. 100

Figure 109. Comparison of the Tank Side Loading Response at Different Speeds .................. 101

Figure 110. Comparison of the Tank Side Loading Response at Different Speeds .................. 102

Figure 111. Comparison of Head Impact Behaviors at Different Impact Speeds ..................... 103

Figure 112. Physical Properties of Chlorine as a Function of Temperature.............................. 104

Figure 113. Pressure-Volume Relationships for the Chlorine Tank Car at 78 oF and 105 oF ... 105

Figure 114. Comparison of Side Impact Puncture Forces at 78 oF and 105 oF ......................... 106

Figure 115. Comparison of the Side Impact Puncture Energies at 78 oF and 105 oF ................ 106

Figure 116. Normalized Side Impact Puncture Energies at 105 oF ........................................... 107

Figure 117. Various Oblique Impact Conditions Investigated for Side Impacts....................... 108

Figure 118. The Effects of Impact Obliquity on the Tank Impact and Puncture Response ...... 109

Figure 119. Oblique Impact Damage Development and Puncture Behavior for Side Impacts. 110

Figure 120. The Effects of Impact Obliquity on the Tank Impact Response and Puncture ...... 111

Figure 121. Effect of Impactor Angle on Oblique Impact Response for Side Impacts............. 112

Figure 122. The Effects of Impact Obliquity on the Tank Impact Response and Puncture ...... 112

Figure 123. Comparison of Puncture Forces for Normal and Oblique Impacts........................ 113

Figure 124. Comparison of Puncture Energies for Normal and Oblique Impacts..................... 113

Figure 125. Various Tank Motion Constraint BCs for Side Impacts ........................................ 115
x

Figure 126. The Effects of Constraint Conditions for a 25 mph Impact and 9.55-inch-Diameter 

Impactor with Differing Tank Weights............................................................................... 116

Figure 127. The Effects of Constraint Conditions for the 15 mph Constant Velocity Impacts. 117

Figure 128. The Effects of Impact Speed on the Highly Constrained Side Impacts................. 118

Figure 129. Calculated Response for the Symmetric Tank Side Impact Scenario .................... 119

Figure 130. The Effects of Constraint BCs on the Side Impact Response ................................ 120

Figure 131. The Effects of Constraint BCs on the Side Impact Response ................................ 120

Figure 132. Various Tank Motion Constraint BCs for Side Impacts ........................................ 121

Figure 133. The Effects of BC Restraint on Head Impact Response (18 mph Impacts).......... 122

Figure 134. The Effects of BC Restraint on Head Impact Response (25 mph Coupler Impacts)

............................................................................................................................................. 123

Figure 135. Updated Model Generated for a 105J500W Pressure Tank Car ............................ 125

Figure 136. Calculated Test 1 Impact Response with Cutaway Showing Lading..................... 126

Figure 137. Comparison of the Measured and Predicted Test 1 Force-Deflection Curves....... 126

Figure 138. Various Model Support BCs for a 105J500W Pressure Tank Car......................... 127

Figure 139. Calculated Tank Car Impact Behavior Using Three Different Support BCs......... 128

Figure 140. Calculated Side Impact Response with SPH Lading Model .................................. 129

Figure 141. Calculated Tank Car Impact Behavior Using Two Different Lading Models ....... 130

Figure 142. Calculated Head Impact Response with SPH Lading Model................................. 131

Figure 143. Calculated Tank Car Head Impact Behavior Using Different Lading Models...... 132

Figure 144. Calculated Longitudinal Velocity Distribution in the SPH Lading........................ 132

Figure 145. Calculated Tank Car Head Impact Behavior Using Different Lading Models...... 133

Figure 146. Tank Head Impact Analysis Model Geometry....................................................... 134

Figure 147. Model of the 263,000 Coupler Impactor Sled........................................................ 135

Figure 148. Force-Deflection Characteristics Used for the Energy Absorbing Raft Gear........ 136

Figure 149. Comparison of 25 mph Coupler Impact and Puncture Behaviors.......................... 137

Figure 150. Momentum Transfer for the Tank Car Head Impact Analysis............................... 139

Figure 151. Velocity Histories for the 1.3X Lading Head Impact Analysis.............................. 140

Figure 152. Calculated Impact Behavior Using the 1.3X Lading Model .................................. 140

Figure 153. Velocity Histories for the Smeared Full Lading Head Impact Analysis................ 141

Figure 154. Calculated Head Impact Behavior Using the Smeared Full Lading Models.......... 141

Figure 155. Impact Scenarios Used in the Vertical Offset Impact Analyses............................. 144

Figure 156. Comparison of the Calculated Side Impact Behavior with Vertical Offsets.......... 145
xi

Figure 157. Calculated Puncture Behavior for the 25-inch Vertical Offset Side Impact .......... 145

Figure 158. Calculated Puncture Forces for the Various Vertical Offset Side Impacts............ 146

Figure 159. Calculated Puncture Energies for the Various Vertical Offset Side Impacts......... 147

Figure 160. Various Impact Locations Investigated for Unconstrained Side Impacts.............. 148

Figure 161. The Effects of Longitudinal Offsets on Unconstrained Side Impact Behavior...... 149

Figure 162. Longitudinal Offset Impact Locations Investigated for Constrained Side Impacts 150

Figure 163. Offset Impact Effects on a Constrained Tank, Constant 15 mph Impact............... 151

Figure 164. Offset Impact Effects on a Constrained Tank, 25 mph Initial................................ 151

Figure 165. Comparison of Physical Properties of Common Pressure Tank Car Commodities152

Figure 166. Tank Pressure-Volume Relationships for Various Commodities (10.6 Percent 

Outage)................................................................................................................................ 153

Figure 167. Puncture Force Comparisons for the 105J500 and 105J600 Tank Cars................. 156

Figure 168. Puncture Energy Comparisons for the 105J500 and 105J600 Tank Cars.............. 156

Figure 169. Comparison of the Offset Impact Puncture Energies for the 105J500 and 105J600 

Tank Cars............................................................................................................................ 157

Figure 170. Comparison of the 45-Degree Oblique Impact Puncture Energies for the 105J500 

and 105J600 Tank Cars....................................................................................................... 157

Figure 171. Normalized Puncture Energy Summary for the 105J500 and 105J600 Tank Cars 158

Figure 172. Calculated Baseline EO Tank Puncture Forces for Various Size and Shape 

Impactors............................................................................................................................. 160

Figure 173. Calculated Baseline EO Tank Puncture Energies for Various Size and Shape 

Impactors............................................................................................................................. 160

Figure 174. Calculated Puncture Forces for the Various Vertical Offset Side Impacts............ 161

Figure 175. Calculated Puncture Energies for the Various Vertical Offset Side Impacts......... 162

Figure 176. Impact Scenario for the 45-Degree Oblique Side Impact Analyses....................... 163

Figure 177. Comparison of Puncture Forces for Normal and Oblique Impacts........................ 163

Figure 178. Comparison of Puncture Energies for Normal and Oblique Impacts..................... 164

Figure 179. Comparison of Relative Puncture Performance of the Baseline EO Tank Designs165

Figure 180. Comparison of Relative Puncture Performance of EO and Chlorine Tank Designs

............................................................................................................................................. 166

Figure 181. Calculated Baseline AA Tank Puncture Forces for Various Size and Shape 

Impactors............................................................................................................................. 167

Figure 182. Calculated Baseline AA Tank Puncture Energies for Various Size and Shape 

Impactors............................................................................................................................. 168

Figure 183. Comparison of Puncture Forces for Normal and Oblique Impacts........................ 169
xii

Figure 184. Comparison of Puncture Energies for Normal and Oblique Impacts..................... 169

Figure 185. Comparison of Relative Puncture Performance of AA and Chlorine Tank Designs

............................................................................................................................................. 170

Figure 186. Comparison of Relative Puncture Performance of Various Tank Cars.................. 171

Figure 187. Comparison of Relative Puncture Performance of Various Tank Designs............ 172

Figure 188. Model of a 23,000 Gallon DOT-111A100W Tank for Analysis of Outage Volume 

Effects................................................................................................................................. 175

Figure 189. Control Volume Pressure Curves for Various Outages between 1 and 18 Percent 176

Figure 190. Calculated Impact and Puncture Behaviors for Different Outage Volumes .......... 177

Figure 191. Force-Deflection Curves and Puncture Energies for Different Outage Volumes.. 178

Figure 192. Control Volume Pressures for Impacts with Different Outage Volumes............... 179

Figure 193. Effect of the Outage Volume on the Puncture Energy in Side Impacts................. 180

Figure 194. Force-Deflection Curve and Impact Energy Dissipation for an Empty Tank ........ 180

Figure 195. Side Impact Damage Distribution for 1 Percent and 18 Percent Outage Volumes 181

Figure 196. Correlation of the Side Impact Puncture Forces with the Impactor Characteristic 

Size...................................................................................................................................... 182

Figure 197. Comparison of the Normalized Side Impact Puncture Forces ............................... 183

Figure 198. Correlation of the Side Impact Puncture Energies with the Ram Face Characteristic 

Size...................................................................................................................................... 184

Figure 199. Calculated Force-Deflection Curves for the 105J600 and 111A100W3 Tank Cars

............................................................................................................................................. 185

Figure 200. Calculated Pressure-Deflection Curves for the 105J600 and 111A100W3 Tank Cars

............................................................................................................................................. 186

Figure 201. Comparison of Calculated Puncture Forces for 1 Percent and 3 Percent Outage .. 187

Figure 202. Comparison of Calculated Puncture Energies for 1 Percent and 3 Percent Outage188

Figure 203. Comparison of Force-Deflection Characteristics for 1Percent and 3 Percent Outage

............................................................................................................................................. 189

Figure 204. Comparison of Calculated Tank Pressures for Analyses with 1 Percent and 3 Percent 

Outage ................................................................................................................................. 189

Figure 205. Calculated Puncture Forces for the Various Vertical Offset Side Impacts............ 190

Figure 206. Calculated Puncture Energies for the Various Vertical Offset Side Impacts......... 191

Figure 207. Normalized Puncture Energies for the Various Vertical Offset Side Impacts....... 192

Figure 208. Normalized Puncture Energies for the Various Vertical Offset............................. 193

Figure 209. The Effects of BC Restraint on Head Impact Response......................................... 195
xiii

Figure 210. Comparison of the 1D Model and FEA Predictions for Tank Impact Forces (18 mph 

Impacts)............................................................................................................................... 196

Figure 211. Comparison of the FEA Analyses with Unloading Behaviors............................... 197

Figure 212. Comparison of the 1D Model and FEA Predictions with Unloading (18 mph 

Impacts)............................................................................................................................... 198

Figure 213. The Effects of BC Restraint on Head Impact Response (25 mph Coupler Impacts)

............................................................................................................................................. 199

Figure 214. Comparison of the 1D Model and FEA Predictions with Unloading (25 mph 

Coupler Impacts)................................................................................................................. 200

Figure 215. Comparison of the FEA and Constant Stiffness Approximation ........................... 200

Figure 216. Comparison of the 1D Model and FEA Predictions with Unloading (Fixed Head 

Stiffness – 18 and 25 mph Impacts).................................................................................... 201

Figure 217. The Effects of Constraint BCs on the Side Impact Response ................................ 202

Figure 218. Comparison of Models Used to Investigate Reaction Wall Size Effects............... 203

Figure 219. The Effects of Constraint Wall Width on the Reaction Loads............................... 204

Figure 220. The Effects of Wall Width on the Tank Compression Stiffness............................ 204

Figure 221. The Effects of Wall Width on the Tank Impact Behavior...................................... 205

Figure 222. The Effects of Wall Width on the Impact Force Histories..................................... 206

Figure 223. The Effects of Constraint Wall Height on the Reaction Loads.............................. 207

Figure 224. Comparison of Tank Deformations with Different Wall Heights.......................... 207

Figure 225. The Effects of Tank Thickness on Quasi-Static Compression Loads.................... 208

Figure 226. The Effects of Tank Thickness on Quasi-Static Compression Stiffness................ 209

Figure 227. The Effects of Tank Radius on Quasi-Static Compression Loads......................... 209

Figure 228. The Effects of Tank Pressure on Quasi-Static Compression Loads....................... 210

Figure 229. The Effects of Tank Pressure on Quasi-Static Compression Stiffness................... 211

Figure 230. Idealized Schematic of the Side Impact Spring Mass Model................................. 212

Figure 231. Idealized Elastic-Plastic Spring Behavior and Calculated Unloading Response ... 213

Figure 232. Comparison of the FEA and Impact Algorithm for Different Speed Impacts ....... 214

Figure 233. Comparison of the FEA and Impact Algorithm for Different BCs........................ 215

Figure 234. Idealized Schematic of the Offset Side Impact Model Kinematics........................ 216

Figure 235. Comparison of the FEA and Impact Algorithm for Offset Side Impacts............... 216

Figure 236. Comparison of the FEA and Impact Algorithm for an EO Tank Car .................... 217

Figure 237. Initial Set of Tank Puncture Forces Under Various Impact Conditions................. 218

Figure 238. Effects of Tank Thickness on Puncture Force for Various Size Impactors ........... 219
xiv

Figure 239. Tank Thickness Correction for the Characteristic Puncture Force ........................ 220

Figure 240. Effects of Impact Face Orientation on Puncture Force .......................................... 221

Figure 241. Effects of Impactor Shape on Puncture Force in 45-Degree Oblique Impacts ...... 222

Figure 242. Effects of Impactor Shape on Puncture Force in 30-Degree Oblique Impacts ...... 222

Figure 243. Effects of Impactor Shape on Puncture Force in 15-Degree Oblique Impacts ...... 223

Figure 244. Impactor Shape Corrected Puncture Forces for 45-Degree Oblique Impacts........ 223

Figure 245. Impactor Shape Corrected Puncture Forces for Various Oblique Impacts ............ 224

Figure 246. Impactor Size Correction for Oblique Impact Puncture Forces............................. 225

Figure 247. Correlation of Characteristic Puncture Forces for Various Impact Conditions ..... 225

Figure 248. Configuration of the Layered Punched Plate Protection Concept [78].................. 228

Figure 249. Simulated Tensile Test Behavior for the High Hard Steel..................................... 229

Figure 250. Simulated Tensile Behavior of the Punched Plate Material................................... 229

Figure 251. Comparison of the Solid and Punched Plate Tensile Behavior.............................. 230

Figure 252. Model for the Punched Plate Concept Impact Analyses........................................ 231

Figure 253. Details of the Model for the Punched Plate Impact Patch...................................... 231

Figure 254. Impact and Puncture of the 500-Pound Chlorine Car and Punched Plate Protection

............................................................................................................................................. 232

Figure 255. Calculated Tank Impact Damage and Puncture Initiation...................................... 233

Figure 256. Calculated Punched Plate Impact Damage and Puncture Behavior....................... 233

Figure 257. Comparison of Side Impact Puncture Forces for Different Tank Designs............. 235

Figure 258. Comparison of Side Impact Puncture Energies for Different Tank Designs ......... 235

Figure 259. Comparison of Side Impact Puncture Energies for Different Tank Designs ......... 236
xv

Tables

Table 1. Tabular TC128B stress-strain curve values................................................................... 30

Table 2. Summary of the baseline side impact analyses for the 105J600 tank car...................... 63

Table 3. Summary of the analyses to assess the impactor face edge radius. ............................... 65

Table 4. Summary of the analyses to assess the impactor orientation effects. ............................ 80

Table 5. Summary of the baseline head impact analyses............................................................. 84

Table 6. Summary of the vertical offset side impact analyses................................................... 146

Table 7. Summary of the baseline side impact analyses on the 105J500 tank car .................... 154

Table 8. Summary of the vertical offset side impact analyses on the 105J500 tank car. .......... 154

Table 9. Summary of the 45-degree oblique side impact analyses on the 105J500 tank car..... 155

Table 10. Summary of the ethylene oxide tank car design parameters. .................................... 159

Table 11. Summary of the anhydrous ammonia tank car design parameters. ........................... 166

Table 12. Summary of the general purpose tank car design parameters. .................................. 174

Table 13. Summary of impact analyses to assess outage volume effects.................................. 178

Table 14. Parameter values for the spring-mass side impact algorithm .................................... 214

Table 15. Summary of side impact analyses for the 105J500 tank and punched plate concept 234
xvi

Acknowledgements

This report primarily describes analyses performed under the Federal Railroad Administration 

(FRA) Contract DTFR53-11-C-00017. The analysis methodologies used in this report build on 

the work previously performed under Next Generation Rail Tank Car (NGRTC) Project funded 

by The Dow Chemical Company. The development of the puncture modeling methodologies 

and the testing used to validate the models and develop the constitutive and failure models were 

performed under the NGRTC project. 

The analyses of Ethylene oxide tank cars in this report were performed under Contract No. 5058 

with the American Chemistry Council on behalf of its Ethylene Oxide Panel. The analyses apply 

the same methodologies used for the other tank car designs included in this study. 
1

Executive Summary

This report describes a research program to improve the safety and security of railroad tank cars. 

The approach used in the program involved applying a tank impact and puncture prediction 

capability using previously developed and validated detailed finite element (FE) analyses. This 

validated puncture modeling capability allowed for rapid evaluation of many different tank car 

design and impact condition alternatives. 

The FE modeling approach used for all of the above impact analyses is useful for understanding 

the mechanics of tank impacts and punctures. However, at times, a simplified analysis 

methodology or impact algorithm is more suitable for the assessment of various factors on tank 

impact safety. Accordingly, in the final phase of this study, we developed analytical tank impact 

algorithms that can be applied to future analyses of tank car safety. When assessing potentially 

applicable analysis methodologies, we examined the response characteristics of both head and 

side impacts. We found that the behaviors for these two impact conditions were sufficiently 

unique that different analysis methodologies were appropriate. The resulting models were 

compared with the FE analyses of different impact conditions and found to provide good 

correlation with the FE results.

In the initial phase of this program, the effects of different size and shape impactors were 

investigated. A DOT 105J600 chlorine tank car was used as the baseline target tank for these 

analyses. Rectangular and round impactors of various sizes were used to assess the 

corresponding tank puncture conditions. Based on the results of these analyses, a new parameter 

was developed to characterize the effective size of the impactor. This impactor characteristic 

size is the square root of the area of the impactor face. The impactor characteristic size 

parameter provided a good linear correlation to the calculated puncture forces for the range of 

different impactor sizes and shapes analyzed. 

In the second phase of the program, impactors with more complex geometries were used. These 

included a section of a rail, a coupler head, and the edges or corner of a rotated rectangular 

impactor. In this phase, the impactor characteristic size parameter was useful for quantifying the 

puncture potential of the impactors. For example, a rail section impactor has a characteristic size 

of approximately 5 inches—equivalent to the 5x5 inch square impactor. With the characteristic 

size parameter, a more complex impactor such as a coupler head can also be assessed, in spite of 

having an impactor face profile that is not flat. In addition, the puncture force can vary 

significantly with relatively small changes in the orientation of the impact. For a limited set of 

impact orientations analyzed, the coupler head was found to have a characteristic size as small as 

5 inches and as large as 12 inches. 

Two different series of analyses were performed to investigate the effects of the impactor 

orientation. The first series of analyses rotated the impactor orientation and maintained the 

normal impact trajectory. The second series of analyses used an oblique impact configuration. 

Both sets of analyses found that rotation of the impactor face relative to the tank surface results 

in load concentrations at the edge of the impactor and significant reductions in the puncture 

force. As a result, the characteristic size of the 12x12 impactor drops from 12 inches in the 

normal impact to approximately 4.5 to 5 inches in an edge impact. The characteristic size is 

further reduced to approximately 3 inches for the corner impact. These results show that 
2

impacting objects with corners and edges can have the penetration potential of a much smaller 

object if the orientation of the impactor concentrates the loading to the edge or corner. 

A significant finding from the first phases of the study is that there are many potential impact 

threats with a relatively small characteristic size. When the combinations of complex impactor 

shapes and off-axis impactor orientations are considered, many objects will have the puncture 

potential of an impactor with a characteristic size equal to or smaller than the 6-inch impactor 

used in previous tank car tests.

In the next phase of the program, analyses were performed to assess the effects of the tank 

constraint levels (boundary conditions) on the impact response. The first series of analyses were

performed to investigate the effects of the constraint level on the tank side impact response. 

Varying the tank boundary constraints resulted in significantly different late-time behaviors and 

puncture energies. However, the initial portion of the loading was dominated by the inertial 

resistance of the tank. Puncture occurred in this initial phase of the impact for many 

combinations of impactor sizes and impact speeds. Thus for many side impacts, the constraint 

on the back side of the tank was not significant. 

A corresponding second series of analyses were performed to investigate the effects of the 

constraint level on the tank head impact response. The constraint conditions were found to be 

more significant for head impacts. The tank constraint effects for head impacts were observed 

much earlier than they were for side impacts for two main reasons. The first is that the tank 

cylinder was much stiffer in axial loading than in lateral loading. Thus, the head impact forces 

were very rapidly transmitted to translations of the tank center of gravity (CG). The second 

reason for increased constraint effects in head impacts is the behavior of the lading. For the 

duration of the impact, only a fraction of the total lading mass was coupled to the motions of the 

unconstrained tank. Analyses to quantify the lading effect showed that less than 10 percent of 

the lading was coupled to the motion of the tank for a typical head impact scenario. These 

factors are important in the development of a new head impact specification. The current 18-

mile per hour coupler impact test requirements are not tightly controlled in terms of target tank 

constraints and impactor geometry effects. Therefore, significantly different impact severities 

can be obtained within the test requirements. 

In addition to the analyses performed on the 105J600 chlorine tank car, a series of other tank car 

types were analyzed. The evaluations were performed for the 500-pound chlorine tank car, the 

340- and 500-pound anhydrous ammonia (AA) tank cars, and the 300-, 400-, and 500-pound

ethylene oxide (EO) tank cars. These analyses determined the relative puncture energies for the 

different commodities and tank car designs which can be helpful for guiding future decisions on 

tank car designs and safety regulations. 

A series of analyses were also performed to assess the impact and puncture behavior of DOT 

class 111 tank cars. The designs included the baseline DOT 111A100W1 tank car design and 

different alternative designs with modified tank materials, added jackets, and increased 

thicknesses to improve puncture resistance. In addition to the tank design parameters, other 

factors such as the effects of outage volume were also investigated and found to be important for 

puncture resistance. Again, the relative puncture energies calculated for the different design 

alternatives are useful in guiding decisions about future safety requirements for this class of tank 

cars. 
3

Overview

This report describes a research program to improve the safety and security of railroad tank cars. 

The approach used in the research and development program involved applying a tank impact 

and puncture prediction capability using detailed finite element analyses (FEA). The FEA 

capability was developed and validated previously in the NGRTC program. The analysis 

methodologies apply advanced damage and failure models that were validated by a series of 

material tests under various loading conditions. In this study, the analyses were applied to 

investigate the tank puncture behaviors for a wide range of impact conditions. 

Different Size and Shape Impactors

In the initial phase of this program, different size and shape impactors were investigated. The 

impactors used included square, rectangular, and round impact face geometries. A new 

parameter was developed to characterize the effective size of the impactor. This impactor 

characteristic size is the square root of the area of the impactor face. The summary of the 

puncture forces for the various impactors is plotted against the impactor characteristic size in

Figure 1. The figure shows that the impactor characteristic size parameter provides a good 

correlation for all of the different impactor sizes and shapes analyzed. Overall, there is a strong 

linear correlation of the puncture force with the characteristic size of the impactor. 

Figure 1. Correlation of Side Impact Puncture Forces with Ram Characteristic Size

A similar summary of the puncture energies for the various impactors is shown in Figure 2. The 

figure shows that the impactor characteristic size parameter also correlates well to the impact 

energy for the range of impactors considered. There is more scatter in the correlation of the 

impact energies, but that is expected since various factors such as the impact speed and boundary 
4

conditions (BCs) have been shown to introduce variations in the impact energy for different 

impact scenarios. The comparison of impact energies in Figure 2 shows that the correlation is 

roughly with the square of the characteristic size of the impactor. This is a result of the linear 

increase in the puncture force combined with a similar increase in the displacements required to 

reach the impact force (the puncture energy is obtained by integrating the force-deflection curve 

of the impact up to the point of the tank puncture). 

Figure 2. Correlation of Side Impact Puncture Energies with Ram Characteristic Size

The linear correlation between the puncture force and the impactor characteristic size is useful 

for defining the effective size of complex impactors. For example, the rail section impactor has a

cross-sectional profile that includes both convex and concave regions. The puncture force for

the rail has a characteristic size of approximately 5 inches (in) in a normal side impact. This falls 

within the expected range of values estimated from the rail profile. Alternatively, a more 

complex impactor, such as a coupler head can be assessed. Here the behavior is complicated by 

an impactor face profile that is not flat. As a result, the puncture force was found to vary 

significantly with relatively small changes in the orientation of the impact. For a limited set of 

impact orientations analyzed, the coupler head was found to have a characteristic size as small as 

5 in and as large as 12 in. 

Impact Orientation Effects

To investigate the effects of the impactor orientation, a series of analyses were performed with a 

12x12 in square impactor with a 0.1-inch edge radius. A summary of the analyses is provided in 

Figure 3 where the calculated puncture forces are plotted against the impactor rotation angles. 

The effects for the pitch rotation are similar to those for the yaw rotation, but with a slight 

variation in the puncture forces resulting from the relative stiffness of the tank when bending in 
5

the longitudinal and radial directions in the impact zone. The analyses where the yaw rotation 

was maintained at 45 degrees and various levels of pitch rotation were added further concentrates 

the load and damage at the corner of the impactor. 

Figure 3. Puncture Forces for the 12x12-Inch Impactor at Various Orientations

For comparison, the puncture forces calculated for the rotated 12x12-inch impactor were used to

calculate the impactor characteristic size, shown on the right axis of Figure 3. The plot shows 

that the characteristic size of the impactor decreases rapidly as the rotation increases from 0 to 

approximately 30 degrees. Between 30 and 45 degrees the contact is primarily with the edge or 

corner of the impactor and the puncture force (or characteristic size) is relatively constant. The 

characteristic size of the 12x12 impactor drops from 12 in for the normal impact to 

approximately 4.5 to 5 in for an edge impact. The characteristic size is further reduced to 

approximately 3 in for the corner impact. These results show that impacting objects with corners 

and edges can have the penetration potential of a much smaller object if the orientation of the 

impactor concentrates the loading to the edge or corner. 

An impact condition with similarities to the rotated impactor is where the impact occurs at an 

oblique angle to the tank. A set of analyses was performed with the full range of impactor sizes 

and shapes at 15, 30, and 45-degree oblique impact angles. Comparisons of the normal and 

oblique impact puncture forces and energies are provided in Figure 4 and Figure 5, respectively. 

The puncture forces are reduced with increasing obliquity angles and at the 45-degree impact the 

puncture forces are more than 50 percent lower for the largest impactors. However, as the 

impactor size is reduced, the differences in puncture force are also reduced. At a 6-inch

characteristic size the oblique impact puncture force is only reduced by 40 percent compared to

the normal impact puncture force. Finally, for the 3x3-inch impactor there is significantly less

difference between the normal and oblique impact puncture forces. 
6

Figure 4. Comparison of Puncture Forces for Normal and Oblique Impacts

The puncture energies and puncture forces are similar for the oblique impact. The puncture 

energies for the largest impactors are reduced by roughly 60 percent. Again, as the impactor size 

is reduced, the differences in puncture energies are also reduced. At a 6-inch characteristic size, 

the oblique impact puncture energy is only reduced by 50 percent compared to the normal 

impact. Finally, for the 3x3-inch impactor, there is very little difference between the normal and 

oblique impact puncture energies. 

Head Impacts

The calculated head impact puncture forces and puncture energies for various size and shape 

impactors are compared to the side impact forces and energies in Figure 6 and Figure 7, 

respectively. The slope of the puncture force fit is approximately 10 percent greater than that of 

the side impact puncture forces. The difference is a combination of two competing factors. First 

the combined head and head shield thickness is almost 50 percent more than the combined 

thickness of the tank shell and jacket. However, this increase in thickness is partially negated by 

the fact that the offset head impact scenario produces larger stress and strain concentrations at 

the top edge of the impactor which essentially reduces the puncture force. 

The comparison of the side and head puncture energies in Figure 7 shows that again the head 

impacts have a similar fit to the square of the ram characteristic size, but the puncture energies 

are 30 to 35 percent lower for the head than for the shell. The difference results primarily from 

the head deformation mode and rigidly constrained impact scenario that are much stiffer than for 

the shell side impacts. As a result, the puncture forces are reached at significantly lower ram 

displacements resulting in the reduction of puncture energies. 
7

Figure 5. Comparison of Puncture Energies for Normal and Oblique Impacts

Figure 6. Comparison of the Calculated Head and Side Impact Puncture Forces
8

Figure 7. Comparison of the Calculated Head and Side Impact Puncture Energies

Side Impact Boundary Condition Effects

A series of analyses were performed to investigate the effects of the constraint level on the tank 

side impact response. The analyses were for the side impact of the 600-pound chlorine tank car. 

The impactor selected for these analyses was the 9.55-inch-diameter round impactor. Three 

different levels of constraint were considered: (1) highly constrained, (2) moderately 

constrained, and (3) unconstrained. The highly constrained boundary condition (BC) is the tank 

backed by the rigid impact wall that has been used for the majority of the side impact analyses in 

this report (as well as the NGRTC analyses in Reference 1). The moderately constrained 

boundary condition is two deformable tanks sitting side by side. The unconstrained boundary 

condition is a single tank that is free to translate. 

The impactor was prescribed to have a 15 mph constant velocity during the entire impact 

duration. This is more representative of the loading for an impactor that is attached to a longer 

section of train in a derailment where the very large mass results in small changes in impactor 

velocity over the duration of any individual impact event. A comparison of the force-deflection 

characteristics for the side impact response with the three different constraint conditions (wall, 

tank, free) is shown in Figure 8. For reference, a corresponding force-deflection curve for a 25 

mph impact with the 295,000 lb impactor is also shown on the graph. 

The comparison shows that the initial portion of the force-deflection curves for all three 15 mph 

impacts are identical (up to approximately 30 in of displacement). All three impacts reach an 

initial peak force that was very close to the failure level before the dynamic response of the tank 

results in a temporary drop in the impact force (at approximately 40 in of displacement). Beyond 

this time, the tank constraint BCs begin to play a large role in the behavior. With the highly 

constrained (wall) impact scenario the impact force quickly recovers and the tank is punctured at 
9

approximately 48 in of ram displacement. With the moderately constrained side-by-side tank 

scenario the impact force more slowly recovers and the tank is punctured at approximately 56 in 

of ram displacement. Finally, with the unrestrained (free) tank the impact force never fully 

recovers to the puncture force level and the tank does not puncture. 

Figure 8. The Effects of Constraint Conditions for the 15 mph Constant Velocity Impacts

The comparison of the different tank boundary constraints shows that the effects on the late time 

behavior and puncture energy can be significant. However, the initial portion of the loading is 

dominated by the inertial resistance of the tank and the puncture will occur in this initial phase of 

the impact for many combinations of impactor sizes and impact speeds. Thus, for many side 

impacts, the constraint on the back side of the tank is not significant. 

Head Impact Boundary Condition Effects

A series of analyses were performed to investigate the effects of the constraint level on the tank 

head impact response. The analyses were for the head impact of the 600-pound chlorine tank 

with a 0.5-inch-thick head shield. The impactor selected for these analyses was the 9.55-inchdiameter round impactor. 

The baseline head impact conditions, adapted from the NGRTC program [1], were for a highlyconstrained tank head mounted on a test frame that does not allow for any motion at the 

specimen support. The head impact specimen included the tank head and head shield, supported 

by a short length of the tank shell and jacket, which were welded to a rigid test frame. An 

unconstrained tank model was developed to investigate the constraint effects in head impacts. 

The model included the entire tank which was free to translate. Gravity was included in the 

analyses to develop appropriate vertical forces and motions in the offset impact scenario. 
10

Without the test frame support, a model of the ground was needed to resist the gravitational freefall motions of the tank. The tank was free to slide along the ground as a result of the impact. 

In the analysis of the unconstrained tank, the mesh-free Smoothed Particle Hydrodynamics 

(SPH) approach was used to model the lading. This had the advantage of being able to capture 

the fluid sloshing without mesh distortion effects and possible numerical instability of classical 

Lagrangian analyses. The SPH methodology was also compatible with the traditional 

Lagrangian analysis methodologies being used to evaluate the tank response. As a result, it was 

more computationally efficient than the Arbitrary Lagrangian Eulerian (ALE) methodology. 

The comparison of the force-displacement behaviors for 18 mph impacts with the 9.55-inchdiameter round impactor on the constrained and unconstrained tank heads is shown in Figure 9. 

For the constrained tank head, the force increased approximately linearly with displacement up 

to approximately a 1.8 million lb force at a displacement of approximately 25 in. At this point 

the constrained tank head was punctured. However, the behavior for the head impact on the 

unconstrained tank was significantly different. The force-displacement curves for the 

unconstrained tank model started along the same force deflection curve. However, the force 

levels began to drop below those of the constrained tank head at early displacement levels. This 

resulted from the impact forces pushing the tank away from the impactor thereby reducing the 

rate of the impactor head intrusion (dent formation). The impact forces leveled off and began to 

drop at a force of approximately 1 million lb and a displacement of 20 in. The impact severity 

was well below the level needed to puncture the tank head for the unconstrained tank condition. 

Figure 9. The Effects of Tank Motion BCs on Head Impact Response

The effect of the tank constraints for head impacts is observed much earlier in the response than 

for side impacts for two reasons. The first reason is that the tank cylinder is much stiffer in axial 

loading compared to lateral loading. Consequently, the head impact forces are very rapidly 

transmitted to translations of the tank center of gravity (CG). The second reason for increased 
11

constraint effects in head impacts is the behavior of the lading. For the duration of the impact, 

only a fraction of the total lading mass is coupled to the motions of the unconstrained tank. The

effect of this is shown by fringes of longitudinal velocity in the lading in Figure 10. The time 

shown is well past peak load, half way through unloading. However, the bulk of the lading is 

still stationary (blue fringes in the figure). Only the regions of the fluid very near the tank wall 

or directly behind the impacted tank head are moving. 

(a) Full Tank Profile (time = 0.18 s)

(b) Impact Zone (time=0.18 s)

Figure 10. Calculated Longitudinal Velocity Distribution in the SPH Lading

To investigate the effective weight of the fluid lading contributing to the motion in the head 

impact, we ran analyses at different smeared lading tank weights and iterated on an approximate 

equivalent weight of the tank. The value that matched the analysis best was a tank weight of 130

percent of the empty weight. The comparison of the analysis with the 130 percent tank weight 

with the empty tank model, the full weight model (smeared mass), and the model with SPH 

lading is shown in Figure 11. The agreement of the SPH model with the 130 percent tank weight 

model is quite good. Note that the 130 percent weight model increases the tank from an empty 

weight of 61,300 lb to a weight of 79,690 lb. The full weight of the tank is 263,000 lb which is 

the empty tank plus approximately 200,000 lb for the lading. As a result, these analyses show 

that less than 10 percent of the lading is coupled to the motion of the tank for this head impact

scenario. 
12

Figure 11. The Effects of Lading on Unconstrained Head Impact Response

Analysis of Other Tank Conditions and Car Designs

A set of analyses was performed to assess the effects of the tank and lading temperature. As the 

equilibrium temperature of the tank rises, the vapor pressure increases and the liquid density is 

reduced. A decrease in the liquid density will produce an increase in the liquid volume with a 

corresponding reduction in the outage volume. Both increasing the pressure and reducing the 

outage can reduce the puncture resistance of a tank car. 

The condition analyzed is a 105J600W chlorine tank car at an equilibrium temperature of 105 o

F. 

This temperature increases the internal vapor pressure for the tank to 155 pound-force per square 

inch (psi) and lowers the corresponding outage volume for a tank loaded to the specified limit of 

7.5 percent. These compare to the 100 psi internal pressure and outage volume of 10.6 percent at 

a tank temperature of 78 o

F. 

A summary of results for both normal and oblique side impacts for the tank at higher temperature 

is given in Figure 12. In the figure, the calculated puncture energies at 105 o

F are normalized by 

the puncture energies at 78 oF for the corresponding impact conditions. On average, the increase 

in temperature dropped the puncture energies by 20 percent. However, the puncture energies for 

smaller impactor sizes are more similar at the two temperatures. This is because the impact 

response for small impactors is dominated more by structural stiffness. The internal pressure 

(and pressure increase) plays a smaller role in the small dent sizes prior to puncture with the 

small impactor sizes. 
13

Figure 12. Normalized Side Impact Puncture Energies at 105 o

F

In addition to the analyses performed on the 105J600 tank car, a series of other tank car types 

were analyzed. The evaluations were performed for the 500-pound chlorine tank car, the 340 

and 500-pound anhydrous ammonia (AA) tank cars, and 300, 400, and 500-pound ethylene oxide 

(EO) tank cars. A full set of normal and 45-degree oblique side impacts was performed for each 

of the chlorine, EO, and AA tank car designs considered. For comparison of the various designs, 

we normalized the calculated puncture energies for the various designs to those of the 105J500W 

chlorine tank car. The comparison for these normalized results is provided in Figure 13. 

In this comparison, the puncture energies for the 105J500W EO tank car design are considerably 

higher than for any of the other tank car designs. The EO tanks have relatively high puncture 

energies as a result of the lower tank pressures and larger diameter tanks. The 105J500W, 

105J400W, and 105J300W EO tank cars have puncture energies on average 82 percent higher, 

17 percent higher, and 12 percent lower, respectively, than the 105J500W chlorine tank car. The 

puncture energies for the 105J600W chlorine tank car were on average 37 percent higher than 

the 105J500W chlorine tank car. The puncture energies for the 112J500W and 112J340W AA 

tank cars are on average 10 percent above and 39 percent below the 105J500W chlorine tank car, 

respectively. 
14

Figure 13. Comparison of Relative Puncture Performance of Various Tank Designs

Analytical Models of Tank Car Impacts

The FE modeling approach is very useful for determining the mechanics of tank impacts and 

punctures. However, at times, a simplified analysis methodology or impact algorithm is useful 

for the assessment of various factors related to tank impact safety. In this study, we developed

analytical tank impact algorithms that can be applied to future analyses of tank car safety. When 

evaluating appropriate analysis methodologies, we examined the response characteristics of both 

head and side impacts. We found that the behaviors for these two impact conditions are 

sufficiently unique that different analysis methodologies were appropriate. 

The head impact response has several characteristics that influenced the simplified impact 

algorithm. The tank head is a stiffer structure under impact and the impact behavior for a 

constrained head is relatively independent of the impact speed. The most common head impact 

scenario is with the motions and orientations of the impacted and impacting cars nearly aligned 

with the original direction of travel. As a result, the motions can be assumed to be primarily one 

dimensional. In addition, the contributions of the lading response are significantly different for 

head impacts on unconstrained tanks. 

A simple 1D algorithm was developed for the head impact tank motions with the different 

constraint conditions. The algorithm uses a known force-deflection curve of the fully 

constrained tank head as a characteristic property of the tank structure. The forces are then used 

to update the tank and impactor motions. The relative displacement of the impactor and tank are 

used to calculate an updated tank depth and corresponding change in impact force. 

The force-deflection behaviors predicted by the simple 1D algorithm for the two unconstrained 

tank impacts with the empty and full tank weights are compared to the detailed FE analyses in
15

Figure 14. The comparison shows that the simple algorithm accurately reproduces the force 

versus dent depth interaction and tank motions for the full impact and unloading behavior. 

Figure 14. Comparison of the 1D Model and FEA of Head Impact Behaviors

The side impact response also has several characteristics that influenced the methodology 

applied for the simplified impact algorithm. The tank is a more compliant structure under side 

impacts, and the impact behavior is not independent of the impact speed (dynamic effects – see 

Section 3.4). The side impact scenarios typically occur as a result of large scale lateral buckling 

behaviors in a derailment where the motions of the various cars are chaotic. As a result, the side 

impacts will include a greater range of variability in impact location and orientation and the 

motions will be at least two dimensional. These characteristics required a unique analytical 

methodology for side impacts. 

The approach used to develop a side impact analysis algorithm is to develop a spring-mass 

model for the tank that can replicate the force-deflection characteristics for side loading against 

various objects (e.g., impactor, reaction wall). These loads can then be applied with equations 

for the tank kinematics under the combined actions of the loads. A schematic of the spring-mass 

system used for the side impact algorithm is shown in Figure 15. The tank is represented by a 

series of five symmetric masses connected by springs. The outer masses (M1) are small and 

represent a small region of the tank that is involved in the initial interaction with the impactor or 

reaction structures. The secondary masses (M2) represent the region of the tank in the 

deformation zone around the impactor or reaction structures that become significant as the 

deformation progresses. The central mass (M3) is the remainder of the tank mass. 
16

Figure 15. Idealized Schematic of the Side Impact Spring Mass Model

The values used for the spring-mass model parameters were derived in a two-step fitting process. 

Initially, a series of Monte-Carlo analyses were performed where the parameters were allowed to 

vary randomly, within ranges determined by physical constraints. Results were compared with a 

series of FE impact analyses and the correlation for each set of parameters was determined. 

Subsequently, the parameters that provided the best fit with the impact data were optimized by 

finding the minimum error in the parameter space around the initial Monte-Carlo parameter set. 

The resulting model was then applied to simulate a series of impact behaviors, and the results 

were compared to the corresponding FE analyses. For example, a series of impacts with the 

9.55-inch-diameter impactor at different impact speeds are compared in Figure 16. The 

comparison shows that the spring-mass model does a good job of reproducing the variations in 

impact behaviors produced by different speed impacts. Note that the spring-mass model does 

not include puncture prediction so the comparison of the higher speed impacts is only 

appropriate up to the point of the calculated tank punctures in the FEA. 

Development of the Characteristic Puncture Force

The above sections describe analyses that can predict the force-deflection behaviors. However, 

the point along the force-deflection curve at which the tank is punctured also needs to be 

determined. This puncture force will be dependent on both tank geometry (materials and 

thicknesses) and the impact conditions (impactor size and impact orientation). 

Our approach to developing a tank puncture criterion for the tank impact algorithm(s) was to use 

puncture data from all the detailed FE puncture analyses described in this report and develop a 

“characteristic puncture force” parameter that is a function of the impactor characteristic size. A 

collection of the calculated puncture forces for various tank and impact conditions is shown in 

Figure 17. As expected, the larger ram characteristic sizes result in higher puncture loads. 

However, for any given ram characteristic size, there is a large spread in puncture forces. This is 

because the puncture force for an oblique impact against a 111A100W1 tank car will be much 

lower than the puncture force for a normal impact against a 105J600 tank car. 
17

Figure 16. Comparison of the FEA and Impact Algorithm for Different Speed Impacts

Figure 17. Initial Set of Tank Puncture Forces under Various Impact Conditions
18

To develop a characteristic puncture force, we applied a series of correction factors for the tank 

thickness, impact orientation, and impactor shape. When we apply all of the corrections, we 

obtain the characteristic puncture force correlation as shown in Figure 18. Using this 

characteristic puncture force allows us to assess the puncture conditions for a wide range of tank 

and impact parameters. The uncertainties in the puncture force can be assessed by comparing the 

range of errors in the corrected data for the detailed FE analyses to the puncture data fitting line. 

Figure 18. Correlation of Characteristic Puncture Forces for Various Impact Conditions
19

Analysis of Real World Threats

The majority of this study was focused on the safety of tank cars in accidents and derailments. 

These events are the most common that lead to releases of hazardous materials in rail operations. 

However, the security of tank cars from an intentional attack is also a consideration for these 

designs. The Department of Homeland Security (DHS) has done several small and full scale 

tests of components and tank cars subjected to different acts of terrorism. The objective of the 

analyses performed in this effort was to assess the puncture performance in impacts (safety) of a 

protection concept developed by DHS for security against various threats. 

The protection system concept analyzed was the punched plate concept. The system consists of 

two 1⁄4-inch-thick perforated panels made of High Hard Steel (HHS) and used in an offset 

configuration. The perforations were 3⁄8-inch diameter holes in a hexagonal pattern with 1⁄2-inch

spacing between the nearest neighboring hole positions. A series of tank side impact puncture 

analyses were performed on the punched plate protection concept. The analyses showed that the 

protection concept performs reasonably well in impact conditions. A comparison with other 

jacket designs found that the punched plate system provided equal or better impact protection 

than an equivalent weight TC128B jacket. Thus, this concept looks like a good design 

alternative that can provide protection for both safety and security concerns.
20

1. Introduction

There is ongoing research to develop strategies for improving railroad tank cars so they can 

maintain tank integrity in the event of severe accident conditions. Research results are being 

used to develop improved tank car designs and to inform rulemaking by the Federal Railroad 

Administration (FRA). 

A significant portion of the tank car research was performed under the Next Generation Railroad 

Tank Car (NGRTC) Program [1]. A key effort in the NGRTC Program was the development 

and validation of detailed finite element models of tank car equipment which can accurately 

predict the puncture resistance under different impact conditions. To date, these analysis tools 

have been developed and validated for the puncture of the baseline tank cars for both side and 

head impact conditions. These validated tools are being applied in this study to assess the 

puncture resistance of various tank car designs under different impact conditions. 

This report describes the application of the validated puncture analysis to assess the effects of

different impactor threats and impact conditions. This effort includes the development of 

detailed finite element models for tank cars and impactors, and the use of those models to assess 

puncture conditions for various impact scenarios. 

1.1 Background

Accident statistics show that the rail industry’s safety performance has generally improved over 

the last few decades. The FRA’s Railroad Accident and Incident Reporting System (RAIRS) 

shows that the number of accidents per year with at least one car releasing hazardous materials 

has decreased significantly over the past 25 years, as shown in Figure 19 [2]. However, a series 

of three recent accidents or derailments involving the release of hazardous material have focused 

attention on the structural integrity of railroad tank cars. These events include (1) Minot, ND, on 

January 18, 2002; (2) Macdona, TX, on June 28, 2004; and (3) Graniteville, SC, on January 6, 

2005 [3–5]. 

To better define the collision threat, studies have been performed to both evaluate the accident 

statistics [e.g. 6–8] and analyze the kinematics of freight trains in derailments and collisions [e.g. 

9, 10]. Evaluation of the derailments and collisions has shown that these are complex events 

with a wide range of collisions between the various cars in the train. A 40-mph derailment of a 

large freight train may involve thirty or more cars and the derailment event would last on the 

order of a minute before the train comes completely to rest. An example of a derailment 

simulation for a 36-car train model is shown in Figure 20. Impacts on tank cars can include both 

head impacts and side impacts from objects as small as a broken rail or from very blunt objects, 

such as another tank head. Thus, the objective of the tank car development effort is to increase 

protection in both head and side impacts for a range of impact conditions. The approach used 

was to develop the ability to predict the impact conditions that would lead to tank car punctures 

then apply the analysis tools to develop improved puncture resistant tank car designs. 
21

Figure 19. Number of Accidents with at Least One Car Releasing Hazardous Materials [2] 

1.2 Material Damage and Failure Behaviors

A necessary component of a predictive tank car puncture modeling capability is a detailed model 

that can be used to determine the impact damage and failure of the tank and protective system 

materials. An extensive series of laboratory materials testing was performed by the NGRTC 

Program [1] to characterize the tank car materials of interest. The tests included various material 

characterization tests, such as notched tensile tests and combined tension/shear tests, used to 

calibrate the material constitutive and failure behavior. Strain rate effects on the tank car 

materials were investigated and found not to have a significant effect on the tank puncture

behavior. Additional component tests, such as punch tests and bend tests, were performed to 

validate the constitutive models. 

The material damage and failure model applied is the Bao-Wierzbicki (BW) model that defines 

the material damage development based on the current stress state in the material and the plastic 

strain increments. The critical strain function is that proposed in the BW criterion and contains 

multiple branches depending on the range of stress state. For completeness, the NGRTC 

material testing and failure model development efforts are summarized in Section 2 of this 

report.
22

(a) 36-car train derailment model

(b) Calculated response 25 seconds after derailment

Figure 20. Calculated Derailment Behavior for the 36-Car Train Model [10] 

1.3 Tank Car Puncture Modeling

The BW failure modeling capability was combined with the tank car model to complete the tank 

car puncture prediction capability. This combined tank car impact and puncture modeling 

capability was applied in the NGRTC program [1] to evaluate a wide range of tank/jacket and 

head/head shield geometries. The side impact condition was a normal impact centered on the 

belt line of the tank. The head impact condition was an offset impact point approximately 29 in 

vertically downward from the center of the head. 

A sample head impact and puncture analysis is shown in Figure 21. The head impact analyses 

included the head, head shield, and a sufficient length of the side shell and jacket to allow for 

buckling to initiate in the jacket support from the loads transmitted by the head shield, as seen in 

Figure 21. 
23

(a) Initial impact conditions (b) Puncture response of the head

Figure 21. Calculated Puncture Behavior of a Head and Head Shield

The calculated head and shell puncture force as a function of the combined tank and jacket (or 

head shield) thickness is shown in Figure 22. All of the analyses included in the figure are 

performed with the 6x6-inch impactor with a 1⁄2-inch edge radius (the standard impactor in the 

NGRTC program). The figure shows the analyses are mostly consistent with a linear 

relationship between puncture force and total thickness of the protective layers. 

The linear relationship between the puncture force and total tank system thickness provides an 

indication of the primary failure mechanism initiating the tank puncture. The geometry of the 

ram impacting and indenting a pressurized tank shell is shown in Figure 23(a). A force balance 

analysis in the direction of the impact on a patch of tank shell material is shown in Figure 23(b). 

The forces resisting the impact loads are the pressure on the inside surface of the contact patch 

and the shear stress around the perimeter of the contact patch. For a 100 psi tank pressure and a 

6x6-inch impactor, the resultant force from the pressure is less than 4 kips on the contact patch. 

Thus, the average shear stress is approximately equal to the impact force divided by the product 

of the impactor face perimeter and tank thickness. 
24

Figure 22. Calculated Puncture Forces as a Function of System Thickness

The slope of the linear fit in Figure 22 corresponds to an average shear stress in the tank layers 

around the perimeter of the impactor of 39 ksi. By comparison, the yield and ultimate stress 

levels of the TC128B in pure shear are 33 ksi and 49 ksi, respectively (approximately 58 percent 

of the stress values in pure tension using a Von Mises yield criterion). Thus, the force balance 

indicates that the failure mode is primarily exceeding the shear capacity around the perimeter of 

the impact patch. 

The calculated puncture forces for pressurized heads and thicker head systems tended to fall 

slightly below the linear fit in Figure 22. The reason for these lower forces is that, for the stiffer 

head systems, the offset impact creates a larger stress concentration along the upper edge of the 

impactor face and the failure initiates at that location at a lower total force. The more compliant 

head systems allow for a larger dent to form and the impactor develops a more uniform stress 

distribution in the impact patch around the ram face perimeter. 
25

(a) Geometry of the tank indentation

(b) Free body diagram for the tank contact patch

Figure 23. Loading and Failure Mechanism for the Tank Impact and Puncture
26

2 Material Constitutive and Damage Models

2.1 Introduction

The tank car impact analyses require a model for the material constitutive and damage behaviors 

to accurately predict the puncture threshold under various impact conditions. A piecewise linear 

elastic-plastic constitutive model was modified for this purpose to include a version of the BaoWierzbicki (BW) failure criterion [11–13]. This model has been applied by other researchers to 

assess tank car puncture conditions [14] and is capable of reproducing both the nonlinear stressstrain behavior of the material as it deforms into the plastic regime and the fracture and failure 

behavior that depends on the state of stress and plastic strain history in the material. The 

material parameters used in these constitutive models were developed from the material test data 

on TC128B steel, developed under the NGRTC program [15–22]. 

The following sections describe the development of the constitutive and damage parameters used 

in the subsequent tank car puncture analyses. 

2.2 Material Stress-Strain Behavior

The first step in the development of a constitutive model is the development of the nonlinear 

stress-strain behavior. This governs the mechanical response of the material and prescribes the 

internal forces (stress) that are developed as the material is deformed (strained). 

2.2.1 TC128B Material Properties 

A tabular stress-strain curve was developed based on testing of different samples of TC128B 

[15]. A series of standard tensile tests were performed on different batches of TC128B, as 

shown in Figure 24. The data is consistent within each batch of material but significant variation 

can be found in tank car material obtained from different sources. The new material that was 

tested was at the upper range of strength for TC128B and the material recovered from the tank 

cars used in the test was more consistent with previous test data [23, 24]. As a result, the 

material recovered from the tank car used as the Test 2 target vehicle was used as the baseline 

material for the analyses in this report. 

The data shown in Figure 24 is the measured engineering stress-strain behavior. Engineering 

stress was obtained by dividing the measured loads by the original cross-sectional area of the 

specimen. Similarly, engineering strain was obtained by dividing the change in the specimen 

gauge-section length by the original length. 

The constitutive model in the finite element analyses requires that the engineering data be 

converted to true stress and true strain. This conversion accounts for the changing cross section 

of the specimen as it was deformed. The specimen cross section changes (shrinks) significantly 

during the test, and the engineering stress does not yield the “true” stress in this cross section. 

Similarly, the engineering strain is not representative of the material behavior, especially when a 

general three-dimensional state of strain exists. As a result, the engineering stress decreases as 

some materials approach failure, implying a weakening of the material. In reality, the stress in 

the cross section is increasing due to the reduction in the cross-sectional area (i.e. necking).
27

Figure 24. Material Testing Data for Different TC128B Materials

There are several different ways to measure stress and strain based on the coordinate system used 

[16]. Some are based on material (Lagrangian) coordinates and some on spatial (Eulerian) 

coordinates. The evaluation of strains in different coordinate reference systems gives rise to 

terms such as “Green” and “Almansi” strain tensors; these terms are useful for writing computer 

codes to solve large strain problems. An alternate approach is to define a “true” or “natural” 

stress and strain. The true stress is based on the load divided by the actual cross-sectional area of 

the specimen and is equal to the engineering stress multiplied by a term to correct for the change 

in cross section.

(1 e) σ T = σ eng + (1)

where σ T and σ eng are the true and engineering stresses, respectively, and e is the engineering 

strain.

Prior to the onset of localization (necking), the natural or true strain, T ε , is defined as

ln( ) ln(1 e) l

l

o

ε T = = + (2)

This definition comes about from defining the incremental true or “natural” strain as the current 

“change in length” divided by the current length, or

l

dl dε T = (3)
28

This is in contrast with the definition of engineering strain that references the change in length, 

∆l , divided by the original length, 0l , or

0l

l

e

∆ = (4)

After the onset of localization, the determination of the true strain in the necked region becomes 

more complex and requires measurement of the local neck geometry.

The TC128B engineering test results are compared to the converted true stress and true strain 

data in Figure 25. The true stress curves from the tests do not include a correction for the 

necking behavior. As a result, they are only valid up to the onset of necking at a true strain of 

approximately 15 percent. The actual true stress and true strain curves for the material continue 

to have an increasing slope from strain hardening throughout the loading if the effects of 

necking are corrected. An extrapolated true stress curve that corrects for the effects of the 

necking behavior is added to Figure 25 (solid black line). It is this extrapolated curve that is 

used in the material constitutive model. 

The final step in obtaining the tabular stress-strain parameters for the TC128B constitutive model 

was to fit a smooth set of points to the extrapolated true stress data. This final tabular fit for the 

TC128B is shown in the true stress versus plastic strain curve in Figure 26. The specific values 

for the tabular stress-strain curve are also listed in Table 1. As a validation that this curve 

accurately captures the true stress-strain behavior of the material, a tensile specimen model was 

generated and the constitutive parameters were applied to simulate the tensile test response. The 

calculation was analyzed to determine the engineering stress-strain behavior consistent with the 

tests (e.g. using equivalent gauge section length). A plot of the calculated engineering behavior 

compared to the test data is shown in Figure 27. The data shows that the constitutive parameters 

accurately reproduce the material behaviors, including the onset and development of necking in 

the specimen. 
29

Figure 25. Comparison of Engineering and True Stress-Strain Data for TC128B

Figure 26. Tabular True Stress Curve Developed for the TC128B Constitutive Model
30

Figure 27. Comparison of the Measured and Calculated TC128B Tensile Test

Table 1. Tabular TC128B Stress-Strain Curve Values

Point No. Plastic Strain (in/in) True Stress (ksi)

1 0.00e+00 58.0

2 8.22e-04 54.6

3 1.30e-02 54.8

4 2.76e-02 66.5

5 5.41e-02 79.5

6 9.87e-02 90.2

7 1.49e-01 96.0

8 1.15e+00 165.0
31

2.3 Bao-Wierzbicki Failure Surface

Accurate prediction of the puncture energies of tank cars for various impact conditions requires 

the addition of a detailed damage and failure assessment capability to the material model. These 

damage mechanics, or so-called local fracture mechanics (LFM) approaches, provide enhanced 

capabilities for tank car design and puncture assessment. Local fracture mechanics model the 

microstructural deformation and failure processes leading to fracture in terms of continuum 

parameters averaged over a small volume of material [25-32]. In contrast to classical linear 

elastic and elastic-plastic fracture mechanics (LEFM and EPFM, respectively), which 

characterize fracture in terms of the conditions at the boundary of the fracture process zone while 

ignoring the details of the processes occurring in that zone, LFM focuses on the evolution of the 

process zone itself. Although LFM may initially seem more complex to formulate and more 

difficult to apply than LEFM/EPFM, it is more versatile and more general than the latter 

approaches. Local fracture mechanics methodologies are also ideally suited to implementation 

into finite element analyses where damage can be evaluated at the local element level. 

The key mechanism that needs to be included in the ductile local fracture model for tank car 

puncture analyses is the influence of the stress state on the rate of damage development as the 

material is undergoing plastic deformation. The primary stress state factor that controls the rate 

of damage development is the stress triaxiality, defined as the ratio of the mean stress to the 

equivalent stress (σmean/σeq). The mean stress (or hydrostatic stress) is the average of the three 

principal stresses (stresses on three orthogonal axes perpendicular to the principal planes upon 

which no shear stress exists). The equivalent stress, also referred to as the effective stress or the 

Von Mises stress, is defined as

[( ) ( ) ( ) ]

1/ 2 2

3 1

2

2 3

2

1 2

2

1

σ eq = σ −σ + σ −σ + σ −σ (7)

where σ1, σ2, and σ3 are the three principal stresses. 

There are many models that include the effects of stress triaxiality on damage development and 

ductility. Several of these have previously been applied within LS-DYNA to analyze various 

ductile fracture problems [e.g. 33–35] including the use of the Gurson-Tvergaard model [36–38] 

for the puncture assessment of pressure tank cars [39]. These models have the ability to include 

the stress triaxiality effects on ductility for tensile loading as illustrated in Figure 28. The 

deficiency with many of these previous local damage models is that they do not include the

changes in damage development and failure for low triaxiality where the tensile damage and 

failure behavior transitions into a shear dominated fracture behavior. The concern that shear 

loads are important for tank car puncture assessments led to the selection of the Bao-Wierzbicki 

(BW) model in this effort.
32

Figure 28. Local Damage Criterion for Tensile Ductile Fracture Analyses

As implemented, the BW model is a basic form of a ductile fracture criterion [29]. It assumes 

that failure at a material location occurs when the damage within a surrounding characteristic 

volume (VMIC) exceeds a critical value. The damage development and failure criterion can be 

written in the form

( ) ∫ = = 1

c mean eq

p

eq d

D

ε σ σ

ε

over VMIC (8)

where D is the normalized damage parameter; p

eq dε is an increment in equivalent plastic strain; 

and ( ) c σ mean σ eq ε is the critical failure strain as a function of the stress triaxiality. The 

characteristic volume (VMIC) in this application is the element size which was maintained with a 

characteristic element length of approximately 0.040 in (1 mm) in the fracture zone. Damage 

accumulation occurs with plastic deformations, and the damage is tracked locally in each 

element in the model. When the damage level in any element exceeds the failure criterion 

(D=1), the local failure is propagated in the model by element erosion.

The critical strain function is that proposed in the BW criterion and contains multiple branches 

depending on the range of stress state as shown in Figure 29. The critical strains in each branch 

are governed by the equation
33

( )

( )

( ) ( )

[( )] ( )

( ) ( ) 





















≤

− + ≤ ≤

− ≤ ≤

+

∞ ≤ −

=

mean eq

mean eq

mean eq mean eq

mean eq

mean eq

mean eq

c mean eq

B

B A A

A

σ σ

σ σ

σ σ σ σ

σ σ

σ σ

σ σ

ε σ σ

3

1

3

3

1 9( ) 0

0

3

1

1 3

3

1

2

(9)

And the parameters A and B can be determined by a series of tests under different stress 

conditions, including notched tensile tests with specimens of varying notch radii [40] and tensileshear tests with different ratios of tension to shear stress. 

Figure 29. Bao-Wierzbicki Failure Surface and Tests Used for Model Calibration

2.4 Material Characterization Testing and Analyses

A wide variety of material characterization tests were performed to calibrate and validate the 

material constitutive and failure models. These included material tests such as standard tensile 

testing to assess the material stress-strain behavior and testing under various stress states 

(notched tensile or tensile-shear tests) to obtain the characteristics of the failure surface. 

Subsequent tests under more general loading conditions, such as the punch test configuration, are 

used to validate the models. The approach applied here is to perform detailed analyses of all the 
34

material testing conditions to assess the accuracy and validity of the models. The comparisons 

for the different testing conditions are provided in the following sections of this report. 

2.4.1 Tensile Tests and Analyses

Standard tensile test methods were employed in accordance with ASTM E8 [15]. The thick 

TC128B allowed fabrication of a round tensile specimen (diameter of 0.505 inch). For all other 

materials a flat specimen, as shown in Figure 30, was utilized. The specimen had a gauge length 

of 2 in. No machining was performed in the thickness direction and it was tested as received. 

Photographs of the TC128B round bar specimens that were tested are provided in Figure 31. An 

extensometer with a 2-inch gauge length was mounted on the specimen during testing. In one 

case, the thickest TC128B condition, strain gauges were also mounted (2 gauges, oriented 

opposite of each other) on the specimen gauge length. Due to the excellent agreement between 

the strain gauge and extensometer results, strain gauges were omitted in all subsequent testing.

Figure 30. Dimensions of the Specimen Used in Tensile Testing

Figure 31. Necking Behavior Observed in the TC128B Round Bar Specimens

All tests were performed in constant-rate displacement control. Two rates were used, either 

0.035 or 0.050 in/min. Due to the large elongation observed in all of the steel materials, typical 
35

test times ranged from 15–30 minutes (min) under the constant displacement testing. The data 

acquisition system was configured to record data at 3 Hz.

To confirm that the tensile test data reduction and material constitutive parameter extraction 

process was performed correctly, a model of the tensile specimen was generated and the tensile 

test was simulated using the constitutive model. The load and displacements were extracted 

from the analysis using methodologies consistent with the test. A comparison of the measured 

and calculated engineering stress-strain behaviors for TC128B is shown in Figure 32. The 

comparison shows that the model accurately reproduces the stress-strain behavior and captures 

the initialization of the necking response. 

Figure 32. Validation of the Tensile Test Behavior for TC128B

2.4.2 Notched Round Bar Tensile Tests and Analyses

The notched round bar tensile tests were used to assess the performance of the BW failure model 

in the high stress triaxiality regime. The tests were performed using round bars with various 

notch radii [17] to achieve different levels of confinement at the notch root and thus different 

stress triaxiality levels. Models were created for the different notched round bar specimens and 

the tests were simulated. 

Material was provided from the two full-scale tank shell test articles (Tests 1 and 2) in the form 

of 12x12-inch plates. These plates were taken from near the impact site and were fabricated 

from normalized TC128B with a thickness of 0.777 in. Specimens were extracted from these 

plates for mechanical testing. All specimens were oriented in the transverse direction relative to 

the original plate rolling direction. The transverse orientation of the plate used to fabricate a tank 

car ring segment corresponds to the axial direction of the tank.
36

The notched tensile testing was performed in accordance with the procedures of the conventional 

tensile test standard, ASTM E8. The inner net diameter of the notched specimen is 0.25 in and 

the gross outer diameter is 0.5 in. The three different notch geometries, with radii of 0.25, 0.10

and 0.05 in, were all gripped in smooth clamping friction grips. A photograph of the test setup is 

shown in Figure 33. 

Figure 33. Test Setup for the TC128B Notched Round Bar Specimens

A comparison of the calculated and measured stress-strain behavior across the notch for the three 

different radii specimens is shown in Figure 34. The comparison shows that the constitutive and 

damage model were capable of reproducing both the increase in stress level and reduction in 

ductility that occur as the notch radius is reduced. The BW failure parameters used result in 

good agreement between the calculated and observed failure levels of the specimens. 
37

Figure 34. Validation of the Notched Round Bar Test Behavior for TC128B

2.4.3 Tensile-Shear Tests and Analyses

The combined tensile-shear tests were used to assess the performance of the BW failure model in 

the low stress triaxiality regime (stress triaxiality between 0 and 1⁄3). The tests were performed 

using a modified Arcan specimen [41] to achieve different ratios of tensile and shear by rotating 

the orientation of the gauge section relative to the loading axis, as shown in Figure 35. A 

photograph of the test setup is shown in Figure 36. Instrumentation includes clip gauges across 

both of the slots separating the upper and lower specimen sections, a string potentiometer to 

measure the displacement along the load path, the load ram LVDT, and the load cell. The tests 

were performed in a displacement control mode at a rate of 0.002 in per second (s) and data was 

collected at 5 Hz. 

Simulations of the specimen geometry were initially performed to confirm that a relatively 

uniform stress state could be achieved in the specimen gauge section, as shown in Figure 37. 

Models were then created for each of the specimens with different gauge section orientations and 

the tests were simulated. A comparison of the calculated and measured load-displacement 

behaviors are shown in Figure 38. The comparison shows that the constitutive and damage 

model were capable of reproducing both the decrease in load level and increase in displacement 

that occur as the orientation is rotated from pure tension to pure shear. The BW failure 

parameters used result in good agreement between the calculated and observed failure levels of 

the specimens. 
38

Figure 35. Specimen Geometries for the Combined Tensile Shear Tests

Figure 36. Photograph of the Combined Tensile Shear Test Configuration
39

Figure 37. Analysis of the Specimen Behavior in the Pure Shear Orientation

Figure 38. Validation of the Combined Tensile Shear Test Behavior for TC128B
40

2.4.4 Punch Tests and Analyses

The above notched round bar and tensile shear tests provide a good set of data by which to 

validate the BW failure model’s ability to predict the damage development and failure of the 

TC128B material for a wide range of stress states. However, these tests were used to assess only 

the failure parameters A and B in Equation 9. Therefore, an independent punch test was 

developed and applied to validate that the model could predict the failure of the material under a 

more general loading condition.

The specialized puncture fixture was developed for the NGRTC program at the SwRI Materials 

Test Lab and installed in a 220-kip test machine, as shown in Figure 39. The punch test fixtures 

are shown with the 1.5-inch diameter punch and the 3-inch diameter receiving hole bore (socalled manhole cover). The fixture was designed so that different punch sizes and different 

manhole cover diameters could be used. 

The punches were fabricated from hardened bar stock material. The punch contact face was flat 

with a 0.30-inch radius around the perimeter. Punches were fabricated with diameters of 1.0, 

1.5, 2.0 and 3.0 in. Manhole covers were fabricated with hole diameters of 2.0, 2.5, 3.0, 3.5, 4.5, 

and 5.5 in. As a result, the punch test fixture was applicable for evaluating the behavior of 

multiple materials and structural components [20–22]. 

Figure 39. Simulation of the Punch Test on the Thin TC128B Plate Material

During testing, the actuator (the punch frame) displacement was measured with a remote LVDT 

mounted on the actuator. Three string pots were attached to the backside (opposite the punch) 

surface of the test specimen. These three string pots were all in a line with the middle location in 

the center of the punch and the two outer locations at the circumferential periphery of the punch. 

This placement allowed for additional measurements of the backside deformation opposite the 

punch on the front of the panel. Load was also measured from the load cell on the servohydraulic test frame. Tests were performed in displacement control at an applied rate of 1 
41

in/min. The multiple data channels were recorded with a custom data acquisition system 

operating at 10 Hz. This typically provided total data files of anywhere from 500–2000 points.

The tests used for the validation of the TC128B constitutive and failure model were performed 

on 0.488-inch-thick plate specimens with various combinations of ram and manhole diameters 

[20]. The three tests performed used the 1.0, 1.5, and 2.0-inchch diameter punches in 

combination with the 2.5, 3.0, and 3.5-inch diameter manhole covers, respectively. Photographs 

of the specimen failure behavior in these punch tests are shown in Figure 40. In all cases, the 

punch test sheared out a plug of material with a diameter approximately equal to the punch 

diameter. 

An example of a model and simulation of a punch test on a 0.488-inch-thick TC128B plate is 

shown in Figure 41. The corresponding comparison of measured and calculated punch forcedisplacement curves for a series of three different tests on the TC128B plate is provided in 

Figure 42. In addition to the comparison of the calculated and measured force-deflection curve,

the final profile of the plate specimens after the punch tests were digitized and compared with the 

analyses. A representative profile comparison is shown in Figure 43. 

Figure 40. Punch Test Failure Mode for the Thin TC128B Plate Material
42

(a) Cross section of punch test geometry

(b) Punch test response

Figure 41. Simulation of the Punch Test on the Thin TC128B Plate Material

Figure 42. Force-Deflection Curves for Three Punch Test Configurations on TC128B
43

Figure 43. Comparison of the Calculated and Measured Punch Test Plate Profile

The agreement of the measured and calculated behaviors for this punch test provides additional 

validation that the BW failure model is appropriate for predicting puncture of the tank cars. The 

application of the failure model for assessing puncture energies for different tank geometries and 

impact conditions is provided in the following section of this report. 
44

3 Analysis of Different Size and Shape Impactors

3.1 Introduction and Background

In this section, the detailed BW failure model described in Section 2 is applied to assess various 

tank and head puncture conditions. The analyses in this section are focused on the two primary 

impact configurations studied in the NGRTC program: a normal side impact centered on the 

tank and an offset head impact with the impact point offset approximately 29 in vertically 

downward from the center of the head. However, in this section we expand the range of 

impactors used in these scenarios to include a wide range of different sizes and shapes. 

3.1.1 Puncture Analysis Methodologies

The baseline failure models use a fine mesh of solid brick elements in the impact zone with an 

element dimension of approximately 0.040 in (1 mm). The mesh transitions to shell elements 

with increasing mesh coarseness. The model of the commodity tank and BW impact zone mesh 

used in the tank shell puncture analyses is shown in Figure 44. An algorithm in LS-DYNA is 

used to tie the edge of the shell elements to the solid elements around the edge of the impact 

zone. 

As a result of the very fine mesh in the impact zone, the puncture models were significantly 

larger and have correspondingly longer run times. To allow for the evaluation of a wide range of 

impact conditions and tank geometries, some simplifications in the tank model were 

implemented. 

The first simplification was the use of symmetry planes. For the majority of side impact 

analyses described in this section, two symmetry planes were used to reduce the model to onequarter of the full tank (a half model was used for the offset head impacts). This modification 

had a small effect since some tank car structural details could not be included in the quarter 

model (e.g. manway and bolsters). The primary effect of this approximation is that a side impact 

centered on the tank will have a slightly reduced stiffness for large dent sizes since the manway 

and surrounding structures are stiffer than the bare commodity tank. 

The head puncture modeling approach was identical to that of the tank side impact puncture 

analyses. The head impacts analyzed matched the NGRTC Test 1 impact condition (impact 

point offset below the tank head center). As a result, the problem had only one symmetry plane 

running vertically through the test specimen. This symmetry plane was used in most of the head 

impact simulations to reduce the model size to one half of the full head model. A model of the

tank head and BW impact zone mesh used in the head puncture analyses is shown in Figure 45. 
45

Figure 44. Tank Model and Impact Zone Mesh Used for Side Impact Puncture Analyses

Another simplification in the tank puncture model was in the modeling approach used for the 

fluid lading. In the preliminary analyses, an explicit model was used for the lading. However, 

this explicit model required a significant increase in the model size and also was not compatible 

with a quarter symmetry model. An alternate modeling approach was to evenly distribute the 

weight of the lading uniformly onto the commodity tank wall (smeared lading model). A 

comparison of the full tank car impact response using the two different lading modeling 

methodologies is shown in Figure 46. The comparison shows that the simplification of the 

smeared lading approach did not have a significant influence on the impact behavior. Therefore, 

this approximation was applied for the majority of analyses in this study. 
46

Figure 45. Tank Head Model and Impact Zone Mesh Used for the Head Puncture Analyses

Figure 46. Calculated Tank Car Impact Behavior Using Two Different Lading Models
47

The final geometric simplification of the impact modeling was that the ram car was not used in 

the analyses. Instead, a rigid model of the ram head was used with the mass of the entire ram 

car. This was a reasonable simplification since the measurements of ram car acceleration at 

distributed measurement locations were all in good agreement. 

Analysis of Tank Pressure Effects

The constant internal pressure modeling approximation used in the majority of the NGRTC 

analyses was found to introduce significant errors for larger impactor sizes. In the NGRTC 

chlorine tank car analyses the internal pressure was a constant 100 psi. However, with the 

formation of the dent in the tank during impact there was an increasing hydrostatic internal 

pressure level. For the 6-inch impactor this increase in pressure was relatively small (10–15

percent). However, the larger dents produced by the larger impactor sizes resulted in a larger 

internal pressure increase. 

To demonstrate the influence of the variable internal pressure during the impact, a series of 

analyses were performed. In these analyses, a control volume was established for the tank and 

the change in volume was used to calculate a corresponding change in pressure. The assumption 

in these analyses was that the tank had a 10.6 percent outage and the gas in the outage followed

an ideal constant temperature compression behavior during impact. The resulting relationship 

between the relative volume and pressure in the tank is shown in Figure 47. 

Figure 47. Pressure-Volume Relationship Used for the Tank Control Volume (10.6 percent

outage)
48

The force-deflection curves with both constant and variable internal pressure for the 500-pound

chlorine tanks and the three different impactor sizes are shown in Figure 48. For the updated 

analyses with the variable pressure, the impact velocities were also reduced by 5 mph to be 

closer to the expected puncture threshold velocity. Adding variable pressure to the model 

resulted in a stiffening of the later portions of the force-deflection curves in Figure 48 and a 

reduction in the ram displacements prior to the tank puncture. The reductions were more 

significant for the larger ram sizes. This difference was expected because the larger rams have 

larger displacements prior to the puncture with a larger associated pressure change inside the 

tank. The comparisons showed that the variable internal pressure does not have a significant 

influence on the puncture forces but does reduce the puncture energies by approximately 25–30

percent in the analyses with the 9x9- and 12x12-inch impactors. 

Figure 48. Effect of Variable Internal Pressure on 500-Pound Tank Impact Response

The control volume pressure histories for the three 500-pound chlorine tank impact analyses are 

plotted as a function of the ram displacement in Figure 49. In the 6x6-inch impactor analysis the 

pressure change is less than 10 percent and the previous approximation of a constant 100 psi 

internal pressure is a reasonable simplification for the analyses. For the 9x9- and 12x12-inch

impactors, the internal pressures increase to approximately 120 psi and 140 psi, respectively, at 

the point of the puncture initiation. These pressure increases become large enough to influence 

the tank effective stiffness during the impact. 

The simulation of the NGRTC Test 2 impact conditions using the tank puncture model and 

variable internal pressure is shown in Figure 50. The model shown was reflected vertically about 

the symmetry plane (seen as a line in the figure) for improved visualization of the impact 
49

behavior. The impactor in this analysis was a rigid 6x6-inch ram with a 0.5-inch radius around 

the edges and a total weight of 286,000 lb. The small rectangular patch of elements under the 

impactor (already punctured in Figure 50) is the fracture zone where the BW failure model was 

applied. The remainder of the tank structure was again modeled with 4-node shell elements and 

a tied shell-to-solid constraint was used at the interface of the two model regions. 

Figure 49. Calculated Internal Pressure Variations in the 500-Pound Tank Impact 

Analyses
50

Figure 50. Simplified Tank Model Analysis with Bao-Wierzbicki Failure Assessment

The comparison of the measured and calculated force-deflection behavior for Test 2 with the 

tank puncture model is provided in Figure 51. The comparison shows overall good agreement 

between the calculation and test. The peak load at which the tank was punctured was very 

accurately captured by the model. The primary discrepancy of the test and model was a slightly 

more compliant behavior in the model at large displacements. This difference in compliance 

could primarily be attributed to the removal of the manway from the tank model. 
51

Figure 51. Comparison of the Calculated and Measured Test 2 Impact and Puncture 

Behavior
52

3.2 Side Impact Analysis of Different Size and Shape Impactors

The tank puncture model was used to assess the puncture energies for a wide range of impactor 

sizes and shapes. The tank design used in these analyses is the 105J600 chlorine tank car. The 

TC128B tank shell is 100 in in diameter and 472 in long with 2:1 ellipsoidal heads. The tank is 

covered by a 0.119-inch-thick A1011 jacket with a 4-inch standoff from the tank. 

A sample puncture response is shown in Figure 52. The analysis shown corresponds to the 600-

pound chlorine tank geometry (note: the 600-pound tank designation is used in the industry and 

refers to a tank with a 600 psi test pressure). The ram head model, at an updated weight of 

295,000 lb, was modified in these analyses to include the tapered geometry used in the full-scale 

testing. The tapered geometry included a 6x6-inch contact face, but flared out to duplicate the 

ram geometry in the impact tests of the NGRTC program. Although the ram head was tapered in 

the analyses, the contact patch remained the 6x6-inch face until the protective layers and/or tank 

were punctured. As a result, the tapered geometry did not play a significant role in the prediction 

of the puncture energies reported in this report. 

The progression of the fracture behavior in the BW failure patch is shown in Figure 53. The 

fracture started near the corners of the impactor and propagated along the side of the impactor 

face. The crack subsequently ran along the top and bottom of the ram face. 

The energy balance for the 600-pound chlorine car impact is shown in Figure 54. The initial 

impact energy is approximately 4 million foot-pound (ft-lb) (all in the kinetic energy). As the 

impact progresses, the ram is decelerated and the kinetic energy drops off. The energy transfer is 

from the kinetic energy of the ram to the internal energy of the tank (plastic deformations of the 

tank material) and the pressure-volume work caused by the indentation reducing the total tank 

volume. The internal energy of the tank at rupture is approximately one million ft-lb and the 

pressure volume work is between 500,000 and 600,000 ft-lb. The hourglass energy and sliding 

energy in the calculation are both negligible, indicating that the calculation is stable and does not 

have any numerical energy losses. 
53

Figure 52. Detailed Impact and Puncture Sequence for a 600-Pound Chlorine Car
54

Figure 53. Calculated Puncture Initiation and Fracture Progression

Figure 54. Calculated Energy Balance for the 600-Pound Chlorine Tank Car Impact 

(R10F)
55

3.2.1 Effects of Impactor Size and Shape

A potential concern is that the selection of the 6x6-inch ram, as the primary threat used in the 

NGRTC program, will not identify the protection concept that provides the greatest benefit for 

impacts with a wide range of impactor types. To evaluate the effects of the ram impactor size 

and shape, analyses were performed on the 600-pound chlorine tank car being impacted by a 

range of impactors. 

The first set of analyses used 3x3, 3x6, 6x6, 9x9, 12x12, 3x12, 12x3 rectangular impactors, all 

with a 0.50-inch radius around the edges. The models for the tank were similar but with changes 

in the BW impact zone to match the corresponding impactor face shape and size. The model of 

the commodity tank and BW impact zone mesh used in the 12x12-inch impactor analyses is 

shown in Figure 55. Again, the refined zone is maintained along the perimeter of the impactor 

face with a characteristic element dimension of approximately 0.040 in (1 mm). 

Figure 55. Tank Model and Impact Zone Mesh Used for the 12x12 Inch Impactor

The initial set of shell puncture analyses was performed with the square impactors. The models 

for the square impactors are shown in Figure 56. The comparison of the force-deflection 

behaviors and puncture energies with the 3x3-, 6x6-, 9x9-, and 12x12-inch square impactors is 

shown in Figure 57 (the puncture energy is obtained by integrating the force-deflection curve of 

the impact up to the point of the tank puncture). Note that higher impact speeds are used in the 

calculations as the impactor size is increased to achieve the higher puncture energies required. 

Since the impact behavior is relatively insensitive to impact speed (within a limited range), the 

impact velocities were not considered to be a significant factor in the comparison. 
56

 

(a) 3x3 impactor (b) 6x6 impactor

 

(c) 9x9 impactor (d) 12x12 impactor

Figure 56. Models of the Different Size Square Impactors

The calculated puncture behaviors in Figure 57 show progressively increasing puncture forces 

and puncture energies with increasing impactor size. In Figure 58, the calculated puncture forces

for these square impactor analyses are plotted against the impactor perimeter length. The 

puncture forces show a nearly linear correlation with the ram perimeter length which is 

consistent with the punch shear failure mechanisms described in Section 1.3. The failure 

behavior can also be seen by the puncture of the ram through the tank shell BW impact zone as 

shown for the 3x3- and 12x12-inch impactors in Figure 59. Similar failure behaviors were seen 

for the 6x6- and 9x9-inch impactors. All of the impactors punch out a section of the tank wall 

approximately equal in size and shape to the impactor face. 

The second set of tank impact analyses performed used rectangular impactor face profiles to 

investigate the effects of the impactor aspect ratio. The additional impactors used were a 3x6, 

3x12, and 12x3 impactors as shown in Figure 60. The results from these impact analyses are 

added to the puncture force versus ram perimeter length graph reproduced in Figure 61. The 3x6 

impactor agrees well with the original linear correlation for the square impactors. However, the 

3x12 and 12x3 impactors both puncture at a force level that is 100–200 kips below the linear 

correlation. 
57

Figure 57. Updated 600-Pound Tank Impact Analysis with Different Size Impactors

Figure 58. Puncture Forces for the 600-Pound Tank Impacts with Different Size Impactors
58

Figure 59. Calculated Puncture Behaviors (3x3- and 12x12-Inch Impactors)

(a) 3x3 impactor (b) 3x6 impactor

(c) 3x12 impactor (d) 12x3 impactor

Figure 60. Models of the Different Size Rectangular Iimpactors
59

Figure 61. Puncture Forces for the 600-Pound Tank Impacts with Different Size Impactors

The calculated damage development in the tank wall prior to puncture is shown for the 3x3-, 

3x6-, 3x12-, and 12x3-inch impactors in Figure 62. An examination of the damage profiles 

explains the reduction of the puncture force levels for the 12x3 and 3x12 impactors relative to 

the linear correlation. All the rectangular impactors develop stress concentrations and increased 

damage at the corners. However, for the larger aspect ratio impactors, the discrepancy is much 

larger between the maximum loading and damage at the corners and at the minimum locations 

along the middle of the long edges of the impact face. Thus the long edges of the impactor do 

not effectively contribute to the puncture force resistance and the high aspect ratio impactors 

behave as if they were smaller. 

The third set of tank impact analyses performed used round impactor face profiles to investigate 

the effects of the impactor shape. The additional impactors used were 5.73-, 7.64-, 9.55-, 11.46-, 

and 13.37-inch diameter impactors (ram face perimeter lengths of 18, 24, 30, 36, and 42 in, 

respectively), as shown in Figure 63. The results from these impact analyses are added to the 

puncture force versus ram perimeter length graph reproduced in Figure 64. All of the round 

impactor analyses predict puncture at a force level that is approximately 200 kips above the 

linear correlation. 
60

(a) 3x3 impactor (b) 3x6 impactor

(c) 3x12 impactor (d) 12x3 impactor

Figure 62. Calculated Puncture Behaviors (3x3- and 12x12-Inch Impactors)

The calculated damage development in the tank wall prior to puncture is shown for the 5.73- and 

13.37-inch-diameter impactors in Figure 65. An examination of the damage profiles explains the 

increase for the puncture force levels for the round impactors relative to the linear correlation. 

The round impactor analyses have very uniform loads and damage development around the 

impact face perimeter with no significant stress concentrations. Thus, the round shape of the 

impactors maximizes the contribution of the entire perimeter to the puncture force resistance. 
61

(a) 5.73-inch-diameter impactor (b) 7.64-inch-diameter impactor (c) 9.55-inch-diameter impactor

(d) 11.46-inch-diameter impactor (e) 13.37-inch-diameter impactor

Figure 63. Models of the Different Size Round Impactors

Figure 64. Puncture Forces for the 600-Pound Tank Impact Analyses with Different Size 

and Shape Impactors
62

(a) 5.73-inch-diameter impactor (b) 13.37-inch-diameter impactor

Figure 65. Calculated Puncture Behaviors for Different Size Round Impactors

3.2.2 Definition of the Impactor Characteristic Size

A summary of the above analyses of side impact puncture behaviors for various size and shape 

impactors is provided in Table 2. The analyses show that the puncture force is strongly tied to 

the size of the impactor and the impactor shape is of secondary influence. The round impactors 

avoid any stress and strain concentrations that might occur at the corners of the rectangular 

impactors and therefore require a higher force to puncture the wall for an equivalent impactor 

face perimeter length. Compared to the square impactors, the higher aspect ratio of rectangular 

impactors accentuates the stress concentration effects and further reduces the puncture force. 

These secondary effects of the impactor shape suggest that there could potentially be an 

improved measure for the impactor effective size—one better able to capture these secondary 

shape effects. The parameter developed that best captures these effects involves defining the 

impactor “characteristic size” as the square root of the area of the impactor face. For a square 

impactor, the characteristic size is equal to the length along the edge of the impact face (i.e., the 

6x6-inch impactor has a 6-inch characteristic size). For round impactors, the characteristic size 

is approximately 11 percent smaller than the diameter. For high aspect ratio impactors, the 

characteristic size is smaller than the average length of the perimeter sides. For example, the 

3x12 impactor has a perimeter length that is 25 percent larger than that of the 6x6-inch impactor. 

However, the 6x6-inch impactor and the 3x12 impactor both have the same characteristic size of 

6 in. 
63

Table 2. Summary of the Baseline Side Impact Analyses for the 105J600 Tank Car

Calculation Tank 

Type

Tank 

Shell

Shell 

Jacket 

Impact 

Conditions

Internal 

Pressure

(psi)

Puncture 

Force (lb)

Puncture 

Energy

(ft-lb)

R15D 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

15 mph

6”x6” ram 100 psi 1.167E+06 1.500E+06

R15E 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 100 psi 2.160E+06 5.800E+06

R15F 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

20 mph

9”x9” ram 100 psi 1.690E+06 3.940E+06

R11G 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

10 mph

3”x3” ram 100 psi 5.760E+05 4.050E+05

R11H 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

3”x12” ram 100 psi 1.235E+06 1.950E+06

R11I 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x3” ram 100 psi 1.280E+06 2.360E+06

R11M 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

5.73 in. dia. 100 psi 1.044E+06 1.000E+06

R11N 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

13.37 in. dia. 100 psi 2.203E+06 6.040E+06

R11O 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. 100 psi 1.567E+06 3.000E+06

R11Q 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

15 mph

5.73 in. dia. 100 psi 1.025E+06 1.300E+06

R11T 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

15 mph

3”x6” ram 100 psi 8.505E+05 8.350E+05

R11U 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

20 mph

7.64 in. dia. 100 psi 1.343E+06 2.180E+06

R11V 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

11.46 in. dia. 100 psi 1.894E+06 3.950E+06

The summary of the puncture forces for the various impactors shown in Figure 65 is regenerated 

in Figure 66 using the impactor characteristic size. The figure shows that the impactor 

characteristic size parameter provides a much closer correlation for all the impactor sizes and 

shapes analyzed. Overall, there is a strong linear correlation between the puncture force and the 

characteristic size of the impactor. 

A similar summary of the puncture energies for the various impactors is shown in Figure 67. 

The figure shows that the impactor characteristic size parameter also correlates well to the 

puncture energies. There is more scatter in the correlation of the puncture energies, but that is 

expected since various factors such as the impact speed and BCs have been shown to introduce 

variations in the calculated impact energy. The impact energies in Figure 67 show that the 

correlation is roughly with the square of the characteristic size of the impactor. This is a result of 

the linear increase in the puncture force combined with a similar increase in the displacements 

required to reach the impact force. 
64

Figure 66. Correlation of the Puncture Forces with Ram Characteristic Size

Figure 67. Correlation of the Puncture Energies with Ram Characteristic Size
65

3.2.3 Analysis of Impactor Edge Sharpness

The impactor models used in the above analyses all had a 0.5-inch-radius edge around the face of 

the impactor. This value was originally selected to match the edge conditions on the 6x6-inch

impactor used in the NGRTC testing and analyses [1]. The edge radius was a simplification that 

would eliminate effects such as the edge deformation and wear for repeated use of the impactor 

in testing and was expected to produce more repeatable impact behaviors. In this section, the 

effect of the edge radius was analyzed to quantify the importance of the impactor edge sharpness. 

The analyses performed used the 3x3-, 3x12-, and 12x12-inch impactors. These were selected to 

include the smallest, largest, and highest aspect ratio of the impactors studied—with the 

assumption that these would be the cases where the edge radius might be the most significant. 

The analyses were performed for all three impactors with the original 0.5-inch edge radius, as 

well as with a much sharper 0.1-inch edge radius. In addition, an analysis using the 12x12-inch

impactor with a large 1.0-inch edge radius was performed. 

A summary of the results for these side impact analyses with different impactor face edge radii is 

provided in Table 3. The corresponding force deflection curves for all of the analyses are shown 

in Figure 68. The comparisons show that the edge radius has a small effect on the overall 

response and calculated puncture forces and energies. The largest discrepancy was for the 

puncture energies with the 3x12 impactor where the 0.1-inch edge radius resulted in a 10 percent 

reduction in the puncture energy compared to the baseline 0.5-inch edge radius. However, this 

difference was probably influenced by the fact that the puncture occurred in a very flat region of 

the force-deflection response for this impact scenario. The comparison of the corresponding 

puncture forces for these two 3x12 impactor analyses shows that they agree to within 

approximately 1 percent. 

Table 3. Summary of the Analyses to Assess the Impactor Face Edge Radius

Impact 

Calc.

Tank 

Type

Tank 

Shell

Tank 

Jacket 

Impact 

Conditions

Impactor 

Edge 

Radius

Internal 

Pressure

(psi)

Puncture 

Force (lb)

Puncture 

Energy

(ft-lb)

R11G 600 lb 

Cl

0.981 in

TC128B

0.119 in

A1011

10 mph

3”x3” ram 0.50 in 100 psi 576,000 405,000

R11J 600 lb 

Cl

0.981 in

TC128B

0.119 in

A1011

10 mph

3”x3” ram

0.10 in 100 psi 590,000 375,000

R11H 600 lb 

Cl

0.981 in

TC128B

0.119 in

A1011

25 mph

3”x12” ram 0.50 in 100 psi 1,235,000 1,950,000

R11K 600 lb 

Cl

0.981 in

TC128B

0.119 in

A1011

25 mph

3”x12” ram 0.10 in 100 psi 1,227,000 1,750,000

R15E 600 lb 

Cl

0.981 in

TC128B

0.119 in

A1011

35 mph

12”x12” ram 0.50 in 100 psi 2,160,000 5,800,000

R11P 600 lb 

Cl

0.981 in

TC128B

0.119 in

A1011

35 mph

12”x12” ram 0.10 in 100 psi 2,006,000 5,700,000

R12V 600 lb 

Cl

0.981 in

TC128B

0.119 in

A1011

35 mph

12”x12” ram 1.00 in 100 psi 2,206,000 5,780,000
66

The calculated puncture response for the two analyses with the 3x12-inch impactors is shown in 

Figure 69. The calculated response is shown at times of 80 and 100 ms after impact—

corresponding to points after the fracture initiation and full penetration of the impactor through 

the tank wall. The comparison shows that the 0.1-inch-impactor puncture development is further 

along at a time of 80 ms and results in a slightly cleaner fracture surface around the final plug 

formation at 100 ms. However, these differences were considered to be minor and the 

dominating punch-shear failure mechanism is seen for all of the analyses. As a result, the edge 

radius is considered to be a secondary effect for the puncture of the pressure tank cars. 

Figure 68. Calculated Force-Deflection Behaviors for the Impactor Edge Radii Evaluations

3.2.4 Analysis of Complex Impactor Shapes

The above analyses of the effects of impactor sizes and shapes considered only idealized 

rectangular and round impactors. However, in more general derailment and impact conditions, 

the impactors may have a much more complex geometry or impact condition. In this section, we 

analyze the impact behavior for some of these complex impactor scenarios. 

Rail Section Impactor

One significant impactor threat that has been observed in derailments is a section of broken or 

displaced rail. To evaluate this threat, a rail section impactor was created and used to calculate 

the puncture behavior. The impactor model created is shown in Figure 70. The impactor is a

section of 141-pound rail with a flat end impactor face. The geometry used to generate the rail 

section impactor is shown in Figure 71. 
67

(a) 0.5-inch radius (t=80 ms) (b) 0.5-inch radius (t=100 ms)

(c) 0.1-inch radius (t=80 ms) (d) 0.1-inch radius (t=100 ms)

Figure 69. Calculated Puncture Behavior for the 3x12 Impactor with 0.5 and 0.1 in Edge 

Radii

Figure 70. Model for the Rail Section Impactor
68

(a) Cross section geometry

(b) Cross section and bounding area definition

Figure 71. Geometry for the Rail Section Impactor
69

To compare the rail section impactor puncture behavior with the puncture behavior of other 

impactor shapes, we need to evaluate its characteristic size. However, for this impactor with a 

mix of concave and convex curves around the perimeter of the impact face, the impactor area can 

be defined by different methodologies. The first is to use the cross sectional area of the rail as 

shown in Figure 71(a). This cross sectional area is 13.8 square inches (in2) which corresponds to 

an impactor characteristic size of 3.7 in. The second methodology would be to use the bounding 

impact area defined in Figure 71(b). This bounding impact area is 33.4 in2 and corresponds to an 

impactor characteristic size of 5.8 in. 

The calculated side impact puncture behavior for the rail section impactor is shown in Figure 72. 

The damage is greatest at the stress concentrations at the corners of the head and base of the rail,

and the puncture initiates at these sites. The puncture then progresses to the point where a rail 

shaped plug of material is removed from the tank wall. 

(a) Before puncture (b) Puncture initiation

(c) Complete puncture (d) Tank puncture mode

Figure 72. Calculated Side Impact Puncture Behavior for the Rail Section Impactor
70

In Figure 73, the side impact puncture force for the rail impactor is compared to the puncture 

force for other impactors. The rail puncture force is shown using both the 3.7 and 5.8 in initial 

estimates for the impactor characteristic size. The comparison in Figure 73 shows that these 

estimates for the characteristic size bound the correlation for the other simple impactor 

geometries. If we use the fit from the previous analyses, the rail impactor puncture force 

corresponds to an impactor with a 5-inch characteristic size. 

Figure 73. Puncture Forces for the 600-Pound Tank Impact Analyses with the Rail 

Impactor

Coupler Impactor

A second significant impactor threat that has been observed in derailments is a coupler. To 

evaluate this threat, a coupler impactor model was created and used to calculate the puncture 

behavior. The impactor model created is shown in Figure 74. It is a rigid model of the coupler 

head and shank with a complex impactor face geometry. 

As a result of the complex impactor face profile of the coupler, it was not possible to estimate the 

characteristic size in advance. Therefore, the impact and puncture analyses were performed and 

the calculated puncture behaviors were used to back calculate the equivalent characteristic size 

of the impactor. 

The initial coupler impact analysis was performed using a normal side impact scenario with an 

initial impact velocity of 25 mph and an impactor weight of 295,000 lb. The calculated coupler 

impact damage development and puncture behavior is shown in Figure 75. The calculated 

damage profile shows that the damage development is nonuniform over the impact face of the 
71

coupler—the largest concentration of damage appears around the protruding interlocking lug on 

the wing, and secondary damage concentrations appear around the knuckle. These load 

concentrations are significant since the damage under the interlocking lug initiates a crack 

through the tank shell significantly earlier than the load at which the entire coupler head 

punctures the tank. 

Figure 74. Model for the Coupler Head Impactor

The calculated force-deflection behavior for the coupler normal side impact is compared to that 

of the 12x12 impactor in Figure 76. The comparison shows that the force deflection behaviors 

for the complete puncture are very similar with a peak force of approximately 3 million lb and a 

maximum ram displacement of 55–60 in. However, the fracture initiation under the interlocking 

lug occurs at a load of approximately 1.7 million lb and a ram displacement of 40 in. Thus, the 

point at which the commodity release would occur is significantly earlier for the coupler normal 

impact than for the 12x12-inch impactor. 

The nonuniformity of the loading and damage suggests that the coupler impact and puncture 

behavior may be sensitive to the orientation of the coupler head relative to the tank wall. To 

investigate this effect, two additional calculations were performed where the coupler head 

orientation was rotated laterally in each direction by 15 degrees. The motion of the rotated 

impactors was still in a direction normal to the tank wall. 

The calculated impact damage and force deflection for the first rotated coupler impact are shown 

in Figure 77 and Figure 78, respectively. The rotation for this case results in a more 

concentrated load on the coupler interlocking lug, and the tank wall is initially breached at a 

force of approximately 1 million lb and an impact energy of 800,000 ft-lb. 
72

(a) Before puncture (t=60 ms)

(b) Puncture initiation (t=120 ms)

(c) Complete puncture (t=220 ms)

Figure 75. Calculated Puncture Behavior for the Coupler Head Normal Impact
73

Figure 76. Calculated Force-Deflection Behavior for the Coupler Head Normal Impact
74

(a) Before puncture (t=20 ms)

(b) Puncture initiation (t=40 ms)

(c) Puncture growth (t=100 ms)

Figure 77. Calculated Puncture Behavior for the Coupler Head 15-Degree Rotation 

Impact
75

Figure 78. Calculated Force-Deflection Behavior for the Coupler 15-Degree Rotation 

Impact

The calculated impact damage and force deflection for the second rotated coupler impact 

configuration are shown in Figure 79 and Figure 80, respectively. The rotation for this case 

produces a more distributed load across the coupler face. The tank wall is not breached until 

reaching a force of approximately 2.3 million lb and an impact energy of 5.7 million ft-lb. 

The forces for which the tank wall is breached in the three coupler impact scenarios are added as 

the horizontal dashed lines in Figure 81. Using the correlation between puncture force and 

impactor characteristic size developed in the previous analyses with the idealized impactors, we 

can calculate the effective size of the coupler in these three impact analyses. This methodology 

shows that in the unfavorable orientation, the coupler head has the puncture potential of a 5-inch

characteristic size impactor (a 5x5-inch impactor). However, at a more favorable orientation, the 

coupler head has a similar puncture potential to the 12x12-inch impactor (12-inch characteristic 

size). 
76

(a) Before puncture (t=120 ms)

(b) Puncture initiation (t=180 ms)

(c) Puncture growth (t=200 ms)

Figure 79. Calculated Puncture Behavior for the Coupler 15-Degree Rotation Impact
77

Figure 80. Calculated Force-Deflection Behavior for the Coupler 15-Degree Rotation 

Impact

Figure 81. Puncture Forces for the 600-Pound Tank Impact Analyses with the Coupler 

Head Impactor
78

3.2.5 Analysis of Impactor Orientation Effects

The above analysis of the coupler head impacts at various orientations shows that the orientation 

of an impactor can play a significant role in the puncture response. To quantify this effect, the 

12x12-inch impactor with a 0.1-inch edge radius was used in a series of analyses where the 

orientation was varied. The orientation included various combinations of yaw and pitch rotation 

of the impactor head. Examples of the impact scenarios for various impactor yaw rotations are 

shown in Figure 82. The impact condition for all of the analyses was still a normal velocity 

trajectory with a 25-mph impact speed and a total impactor weight of 295,000 lb. 

The calculated force-displacement curves and integrated puncture energies for the analyses with 

various levels of yaw rotation are shown in Figure 83. The figure shows that all of the analyses 

are following along a roughly equivalent characteristic force-deflection curve for the tank and 

impact conditions. However, as the yaw rotation increases, the concentration of impact load and 

damage along the leading edge of the impactor increases and the point at which the impactor 

punctures the tank is earlier (lower force levels). 

(a) 15-degree yaw rotation (b) 30-degree yaw rotation (c) 45-degree yaw rotation

Figure 82. Example Impactor Orientation Analyses Performed for Side Impacts
79

Figure 83. Calculated Force-Deflection Behaviors for the 12x12-Inch Impactor and 

Various Levels of Yaw Rotations

A summary of all of the analyses performed to quantify the impactor orientation effects is 

provided in Table 4. The puncture forces for all of the analyses are plotted against the impactor 

rotation angles in Figure 84. The effects for the pitch rotation are similar to those for the yaw 

rotation, but with a slight increase in the puncture forces—resulting from the relative stiffness of 

the tank when bending in the longitudinal and radial directions in the impact zone. The analyses 

where the yaw rotation was maintained at 45 degrees, then various levels of pitch rotation were 

added, further concentrates the load and damage at the corner of the impactor. The damage 

profiles for the edge and corner impacts produced by the extreme rotation combinations analyzed 

are shown in Figure 85. 
80

Table 4. Summary of the Analyses to Assess the Impactor Orientation Effects

Side Impact 

Calculation

Tank 

Type

Tank 

Shell

Tank

Jacket 

Impact 

Conditions

Ram 

Yaw 

Angle 

(deg.)

Ram 

Pitch 

Angle 

(deg.)

Puncture 

Force (lb)

Puncture 

Energy

(ft-lb)

R11P 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 0.0 0.0 2.154E+06 5.650E+06

R12H 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 5.0 0.0 1.910E+06 3.950E+06

R12I 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 10.0 0.0 1.576E+06 3.100E+06

R12J 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 15.0 0.0 1.348E+06 2.250E+06

R12K 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 20.0 0.0 1.130E+06 1.150E+06

R12L 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 45.0 0.0 8.380E+05 5.850E+05

R12O 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 45.0 5.0 8.160E+05 5.400E+05

R12P 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 45.0 10.0 7.850E+05 4.800E+05

R12Q 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 45.0 15.0 7.400E+05 4.250E+05

R12R 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 45.0 20.0 6.510E+05 3.300E+05

R12S 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 45.0 45.0 9.096E+05 7.000E+05

R13C 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 0.0 5.0 2.020E+06 5.400E+06

R13D 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 0.0 10.0 1.830E+06 3.900E+06

R13E 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 0.0 15.0 1.613E+06 3.400E+06

R13F 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 0.0 20.0 1.423E+06 2.900E+06

R13G 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 0.0 45.0 1.090E+06 1.150E+06
81

Figure 84. Puncture Forces for the 12x12-Inch Impactor at Various Orientations

For comparison, the puncture forces calculated for the rotated 12x12-inch impactor were 

converted to obtain the impactor characteristic size which is shown on the right axis of Figure 

84. The plot shows that the characteristic size of the impactor decreases rapidly as the rotation 

increases from 0 to approximately 30 degrees then levels out beyond that point where the contact 

is primarily with only the edge or corner of the impactor. The characteristic size of the 12x12 

impactor drops from 12 in in the normal impact to approximately 4.5–5 in in an edge impact. 

The characteristic size is further reduced to approximately 3 in for the corner impact. These 

results show that impacting objects with corners and edges can have the penetration potential of 

a much smaller object if the orientation of the impactor concentrates the loading to the edge or 

corner. 
82

(a) Normal impact (no rotation) (b) 45-deg yaw and 0-deg pitch

(c) 0-deg yaw and 45-deg pitch (d) 45-deg yaw and 45-deg pitch

Figure 85. Puncture Behavior for the 12x12-Inch Impactor with Face, Edge, and Corner 

Impacts
83

3.3 Head Impact Analysis of Different Size and Shape Impactors

The above sections describe the effects of different size and shape impactors on the side impact 

behavior and puncture response. A similar set of analyses was performed for the head impact on 

the 600-pound tank car. The head impact analyses were performed using a configuration similar 

to the head impact tests in the NGRTC program [1]. The head and a short length of the tank 

shell are used and the boundary condition is a rigid restraint at the trailing edge of the shell. This 

boundary condition is representative of the head impact test frame used in the NGRTC program.

The heads were impacted by various size impactors. In the analyses, the impactor is given an 

initial velocity and constrained to move in the longitudinal direction only. The target impact 

point was offset approximately 29 in vertically downward from the center of the head. The 

weight of the impactor is 295,000 lb which matches the final impactor test sled weight used in 

the NGRTC tests. The primary difference from the NGRTC head test series is that the heads 

were pressurized to 100 psi in the analyses performed in this section. For these preliminary 

analyses a constant internal pressure level is used. The constant pressure assumption is more 

appropriate for the head impacts where the structural stiffness of the head geometry is larger 

(thus pressure effects play a smaller role). In addition, the dent shape for head impacts is a 

smaller fraction of the tank volume than the side impact dent shape and the pressure change is 

smaller. 

3.3.1 Effects of Impactor Size and Shape

An example of the calculated impact and puncture behavior for the 600 lb tank head is shown in 

Figure 86. The specific example shown is for the 11 mph impact with the 6x6-inch impactor. 

The response mechanisms include a dent formation under the impactor for both the tank head 

and head shield, buckling of the jacket supporting the head shield, and eventually the puncture of 

the head and shield. The puncture initiates at the top edge of the impactor and opens a flap of 

material under the impact face. 

A summary of results from the baseline head impact analyses is provided in Table 5. All of the

analyses in the table are for the 600-pound tank geometry with a 0.5-inch-thick A572-50 head 

shield and 100 psi internal pressure. The impactors all have the baseline 0.5-inch edge radius. 

The calculated force-deflection behaviors and puncture energies for the 3x3-, 6x6-, 9x9-, and 

12x12-inch impactors are shown in Figure 87. The highly constrained head structures result in a 

behavior where the impact force is roughly linearly proportional to the impactor displacement 

(dent depth). 

The calculated head impact puncture forces are plotted against the impactor characteristic size in 

Figure 88. The puncture forces again show a trend of a linear correlation with the impactor 

characteristic size, with slightly more scatter in the correlation. It is believed that this is a result 

of the offset impact condition that produces uneven loading at the upper and lower edges of the 

impactor. As a result, the results are more sensitive to the shape of the impactor. 
84

(a) Impact configuration (b) Puncture behavior

Figure 86. Analysis of the Tank Head Puncture Behavior for the 6x6-Inch Impactor

Table 5. Summary of the Baseline Head Impact Analyses

Head Impact 

Calculation

Tank 

Type

Tank 

Head

Jacket 

or Head 

Shield

Impact 

Conditions

Impactor 

Edge 

Radius

Internal 

Pressure

(psi)

Puncture 

Force (lb)

Puncture 

Energy

(ft-lb)

R10K 600 lb Cl 1.1360 

A516-70

0.500” 

A572-50

14 mph

6”x6” ram 0.50 in 100 psi 1,206,000 1,121,000

R10N 600 lb Cl 1.1360 

A516-70

0.500” 

A572-50

11 mph

6”x6” ram 0.50 in 100 psi 1,229,000 1,110,000

R10V 600 lb Cl 1.1360 

A516-70

0.500” 

A572-50

20 mph

9”x9” ram 0.50 in 100 psi 1,868,000 2,450,000

R11F 600 lb Cl 1.1360 

TC128B

0.500” 

A572-50

25 mph

12”x12” ram 0.50 in 100 psi 2,334,000 3,672,000

R11L 600 lb Cl 1.1360 

TC128B

0.500” 

A572-50

10 mph

3”x3” ram 0.50 in 100 psi 774,000 400,000

R11M 600 lb Cl 1.1360 

TC128B

0.500” 

A572-50

18 mph

3”x12” ram 0.50 in 100 psi 1,298,000 1,035,000

R11N 600 lb Cl 1.1360 

TC128B

0.500” 

A572-50

18 mph

12”x3” ram 0.50 in 100 psi 1,660,000 1,830,000

R11O 600 lb Cl 1.1360 

TC128B

0.500” 

A572-50

12 mph

5.73” Dia. 0.50 in 100 psi 1,176,000 915,000

R11P 600 lb Cl 1.1360 

TC128B

0.500” 

A572-50

18 mph

9.55” Dia. 0.50 in 100 psi 1,753,000 2,000,000

R11R 600 lb Cl 1.1360 

TC128B

0.500” 

A572-50

15 mph

7.64” Dia. 0.50 in 100 psi 1,562,000 1,520,000

R11S 600 lb Cl 1.1360 

TC128B

0.500” 

A572-50

21 mph

11.46” Dia. 0.50 in 100 psi 2,236,000 3,500,000
85

Figure 87. Calculated Head Impact Force-Deflection Behaviors for the Square Impactors

Figure 88. Calculated Head Impact Puncture Forces for Various Impactors
86

The largest discrepancy from the linear puncture force correlation was for the 12x3-inch

impactor that has a puncture force significantly larger than the fit to the data. The damage 

development and puncture behavior for the 12x3- and 3x12- inch impactors are shown in Figure 

89. The comparison shows that the load is distributed over a much wider region for the 12x3 

impactor and as a result it acts like a larger impactor compared to the 3x12 impactor for this 

scenario. Therefore the 12x3 impactor orientation had a small sensitivity to the offset impact 

effects and the 3x12 impactor had a large sensitivity to the offset impact geometry.

(a) 3x12 impactor (t=60 ms) (b) 3x12 impactor (t=80 ms)

(c) 12x3 impactor (t=80 ms) (d) 12x3 impactor (t=100 ms)

Figure 89. Calculated Head Puncture Behaviors for the 3x12 and 12x3 Impactors

The calculated head impact puncture forces and energies are compared to the corresponding side 

impact values in Figure 90 and Figure 91, respectively. The head puncture forces are on average 

approximately 10 percent greater than the side impact puncture forces. The difference is a 

combination of two competing factors. First, the combined head and head shield thickness is 

almost 50 percent thicker than the combined thickness of the tank shell and jacket. However, 

this thickness increase is partially negated by the offset head impact scenario producing larger 

stress and strain concentrations at the top edge of the impactor that reduce the puncture forces. 
87

Figure 90. Comparison of the Calculated Head and Side Impact Puncture Forces

Figure 91. Comparison of the Calculated Head and Sside impact puncture energies.
88

The comparison of the side and head puncture energies in Figure 91 show that again the head 

impacts have a similar fit to the square of the ram characteristic size but the puncture energies 

are 30% to 35% lower for the head than for the shell. The difference is primarily that the head 

and rigidly constrained impact scenario are much stiffer than for the shell side impacts. As a 

result, the puncture forces are reached at significantly lower ram displacements resulting in the 

reduction of puncture energies. 

3.3.2 Analysis of Complex Impactor Shapes

The above analyses of the effects of impactor sizes and shapes considered only idealized 

rectangular and round impactors. However, in more general derailment and impact conditions, 

the impactors may have a much more complex geometry or impact condition. In this section, we 

analyze the head impact behavior for complex impactor scenarios. 

Rail Impactor

The calculated head deformations for an 11 mph impact with the rail section impactor are shown 

in Figure 92. The impactor forms a dent in the head shield and head at the impact location and 

the rail punctures the head. The section of the 11 gauge jacket supporting the head shield 

buckles as a result of the offset impact loads. The corresponding puncture behavior in the 

detailed impact patch for the rail section impactor is shown in Figure 93. As a result of the offset 

impact the damage is greatest at the stress concentrations at the corners of the rail head and the 

puncture initiates at these sites. The puncture then progresses to the point that a rail shaped flap

of material is punched in the tank head. 

The calculated force-deflection behavior for the rail section impact analyses is compared to those 

of the 3x3- and 6x6-inch impactors in Figure 94. The comparison shows that the rail impact 

more closely corresponds to the behavior of a 6-inch impactor. We can evaluate the 

characteristic size of the rail impactor by comparing the calculated head impact puncture force to 

the other impactors, as shown in Figure 95. The rail puncture force is shown using both the 3.7 

and 5.8 inch initial estimates for the rail impactor characteristic size (defined previously in 

Section 3.2.4). The comparison in Figure 95 indicates that the upper range 5.8 inch 

characteristic size estimate correlates best with the linear fit generated from the other simple 

impactor geometries. 

An additional head impact analyses was performed using the rail impactor in an upside down 

orientation. In this impact scenario, the wider bottom flange of the rail is the primary contact 

zone against the head. The calculated puncture behavior in the impact zone for the upside down 

rail impactor is shown in Figure 96. A comparison of the corresponding force-deflection curves 

for the rail impactor in the two orientations is shown in Figure 97. The comparison shows that 

the orientation does not have a big effect on the puncture force. The puncture energy is 

increased by approximately 20% for the upside down orientation impact. 
89

(a) Impact configuration (b) Impact behavior

Figure 92. Analysis of the 11 mph Rail Section Impact Behavior on the Constrained Head

(a) Before puncture (b) Puncture mode

Figure 93. Calculated Head Impact Puncture Behavior for the Rail Section Impactor
90

Figure 94. Calculated Head Puncture Impact Response for the Rail Section Impactor

Figure 95. Calculated Head Impact Puncture Forces for Various Impactors
91

(a) Before puncture (b) Puncture mode

Figure 96. Calculated Head Puncture Behavior for the Upside Down Rail Impactor

Figure 97. Calculated Head Impact Response for the Rail Section Impactors
92

Coupler Impactor

A significant impactor threat for the tank head is a coupler. To evaluate this threat, the coupler

impactor model, shown previously in Figure 74, was used to calculate the head impact puncture 

behavior. The initial impact analysis was performed with the constrained tank head impact 

configuration and an impact speed of 18 mph. The calculated head deformations for the 18 mph 

coupler impact are shown in Figure 98. The coupler impact forms a dent in the head shield and 

head at the impact location. The section of the 11 gauge jacket supporting the head shield 

buckles as a result of the offset impact loads. 

(a) Impact configuration (b) Impact behavior

Figure 98. Analysis of the 18 mph Coupler Impact Behavior on the Constrained Head

The corresponding damage on the inside surface of the tank head is shown in Figure 99. This 

damage profile shown in Figure 99 corresponds to the end of the analysis where the ram has 

rebounded and the contact force between the tank head and coupler are zero. The coupler impact 

was not sufficient to fully penetrate the tank head but the damage under the location of the

greatest load concentration formed an incipient through crack in the head that would result in a 

release. The crack develops at a time close to the maximum ram displacement of approximately 

31 in. 

A second coupler head impact analysis was performed where the impact speed was increased 

from 18 to 25 mph. At this impact speed, the coupler has sufficient impact energy to fully 

penetrate the tank head for this scenario. The puncture response is shown in Figure 100. The 

damage is shown at two times corresponding to a 32-inch ram displacement where a through 

crack in the head is fully developed and after the coupler has fully penetrated the tank head and 

the impact loads have significantly dropped (approximately 46 in of ram displacement). 
93

 

Figure 99. Calculated Damage for the 18 mph Coupler Impact on the Constrained Head

The calculated force-deflection behaviors for the two coupler impact analyses are compared to 

those of the 9x9- and 12x12-inch impactors in Figure 101. The force-deflection behaviors were 

very similar for the two coupler impact analyses up to the maximum displacement of the 18 mph 

impact. At the higher impact speed the forces continue to rise until the coupler fully punctures 

and penetrates the tank head. The comparison to the idealized impactors in Figure 101 shows 

that the coupler impact more closely corresponds to the behavior of the 12-inch impactor. 

However, the point at which a through crack penetrates the tank head corresponds to a puncture 

energy of 3.15 million ft-lb which is between that of the 9-inch and 12-inch impactors. 

We can evaluate the characteristic size of the coupler impactor by comparing the calculated head 

impact puncture force to the other impactors, as shown in Figure 102. The coupler puncture 

force shown in Figure 102 is the force at which the through crack is formed in the tank head (at 

approximately 32 in of ram displacement). The comparison in Figure 102 indicates that the 

coupler impactor has a characteristic size of approximately 10.8 in based on the linear fit 

generated from the other simple impactor geometries. 
94

 

(a) Initial head puncture (32-inch ram displacement)

 (a) Full head penetration (46-inch ram displacement)

Figure 100. Calculated Damage for the 25 mph Coupler Impact on the Constrained Head
95

Figure 101. Calculated Head Puncture Impact Response for the Rigid Coupler Impactor

Figure 102. Calculated Head Impact Puncture Forces for Various Impactors
96

3.3.3 Analysis of Offset Head Impact Location Effects

The above analyses all used the baseline offset head impact configuration. A parameter of

interest is the impact location on the head. In this idealized impact scenario, the sill is not 

modeled so the distance from the tank head center should be similar in any direction. As a result, 

a set of analyses was performed using the half head model with one symmetry plane and 

different offset distances for the impact point. The offsets used are 0.0 in (center impact), 15.0

in, 28.5 in, and 40.0 in. The head impact models for the offset impact scenarios are shown in 

Figure 103. 

(a) Center impact (b) 15-inch offset

(c) 28.5-inch offset (d) 40-inch offset

Figure 103. Impact Scenarios Used in the Vertical Offset Impact Analyses
97

A comparison of the calculated force-deflection curves for the four different offset head impacts 

is shown in Figure 104. As expected, the center head impact has the highest puncture force and 

puncture energy. At the center impact location the behavior is nearly axisymmetric and the load 

around the perimeter of the impactor is more uniform, resulting in a higher puncture force. As 

the impact location moves further from the head, the angle between the normal vectors of tank 

head impact position and the impactor face becomes greater and the corresponding puncture 

force drops. 

Figure 104. Calculated Force-Deflection Behaviors for Variable Offset Head Impacts

3.4 Analysis of Impact Speed Effects

For the analyses described in this report, the selection of the impact speed is primarily based on 

engineering judgment with the objective of picking an impact speed that will have a high 

probability of puncturing the tank but not have too large of a residual kinetic energy. The 

assumption is that the puncture energy for this impact speed is a good approximation of the 

threshold puncture energy for the tank. This methodology was used previously in the NGRTC 

program [1]. In that study, some analyses were performed at different impact speeds to 

investigate the magnitude of the effects. In this section, we revisit the impactor speed effects for 

the 600-pound chlorine tank car design and the updated impact analysis methodologies used in 

this study. 

3.4.1 Analysis of Impact Speed for Side Impacts

For this side impact comparison, a set of the normal side impacts summarized in Table 2 was 

repeated at higher impact velocities. The comparison of the original force-deflection curves for 
98

the 3-, 6-, 9-, and 12-inch square impactors and the corresponding behavior for the higher speed 

impacts is provided in Figure 105. In this comparison, the impact speed was increased by 5 mph 

for each of the impact scenarios. For many impacts the effects of the impact are relatively small 

with slightly higher forces produced by increased inertial resistance and corresponding small 

reductions in the ram displacement required to puncture the tank. 

Figure 105. Comparison of Side Impact Behaviors at Different Impact Speeds

For the larger impactors, the impact speed has a slightly larger effect on the impact behavior. 

For the 9- and 12-inch impactors the higher speed impact results in a puncture near the end stage 

of the initial loading response of the force-deflection curve. By increasing the impact speed, 

some of the late time tank impact kinematics and interaction with the reaction wall are 

eliminated (some of these boundary condition effects are discussed below as well as in Section 

4.3.1 of this report). As a result, the calculated puncture energy will be reduced at the higher 

impact velocity. 

The comparison of the puncture forces and puncture energies for the baseline and higher speed 

impacts are provided in Figure 106 and Figure 107, respectively. Overall, there is little 

difference in the puncture forces with a 4 percent reduction in the slope of the linear fit to the 

higher speed impacts. The effect of the impact speed on the puncture energies is slightly larger 

than on the puncture forces but still relatively small with on average an approximately 9 percent 

reduction in the puncture energies for the cases analyzed. 
99

Figure 106. Comparison of Side Impact Puncture Forces at Different Impact Speeds

Figure 107. Comparison of Side Impact Puncture Energies at Different Impact Speeds
100

An alternative evaluation of the speed effects was performed by running the 9.55-inch-diameter 

impactor at impact speeds of 10, 15, 20, and 25 mph. A comparison of the force-deflection 

behaviors is shown in Figure 108. All of the curves have similar behaviors in the initial phase of 

the impact loading. However, the effects of the unloading and interaction with the wall appear 

much earlier in the force-deflection behavior for the lower speed impacts. Note that the 20 and 

25 mph impacts puncture the tank but the 15 and 10 mph impacts are below the puncture 

threshold for this tank and impactor. 

Figure 108. Comparison of the Tank Side Loading Response at Different Speeds

An alternative comparison for the different speed impacts, shown in Figure 108, is to plot the 

force-time histories, as shown in Figure 109. In this comparison we see that the timing for the 

initial unloading is similar and initiates at around 150 ms. However, the point at which the wall 

interaction and reloading of the tank occurs is earlier for the higher speed impacts. This is a 

result of both the ram and tank moving at a higher speed in the unloading for the higher speed 

impact scenarios. 
101

Figure 109. Comparison of the Tank Side Loading Response at Different Speeds

The lower bound of side impact speeds was analyzed for the 9.55-inch-diameter round impactor. 

An analysis was performed using a steady rate displacement control boundary condition at a 

loading rate sufficiently slow to minimize dynamic impact effects (quasi-static). The calculated 

force-deflection behavior for this analysis is compared to the 25 mph impact in Figure 110. The 

comparison shows that the puncture forces again are similar but the loading rate can significantly 

change the force-deflection behavior for this side loading scenario. These effects, and their 

interaction with different tank BCs, will be explored further in Chapter 4. 
102

Figure 110. Comparison of the Tank Side Loading Response at Different Speeds

3.4.2 Analysis of Impact Speed for Head Impacts

A set of analyses was performed to evaluate the effects of the impact speed for the baseline 

constrained tank head impact condition. The head was pressurized to 100 psi and the 6x6-inch

square impactor was used. Impact analyses were performed at 11 and 14 mph. In addition, a 

quasi-static loading was applied where the ram was given a steady rate displacement control 

boundary condition at a rate sufficiently slow to minimize dynamic impact effects. 

The calculated head force-deflection characteristics for the three loading rates are compared in 

Figure 111. The comparison shows that there is little difference in the calculated deformation or 

puncture behavior. Thus, the behavior of the constrained tank head is mostly independent of the 

impact speed. The corresponding effects for a head impact on an unconstrained tank will be 

explored further in Chapter 4. 
103

Figure 111. Comparison of Head Impact Behaviors at Different Impact Speeds
104

3.5 Analysis of Tank and Lading Temperature Effects

An important assumption used in the above impact analyses is that the tank and lading are at a 

nominal temperature of approximately 78 o

F. From the chart of chlorine physical properties in 

Figure 112, this temperature produces an internal vapor pressure for the tank of 100 psi. The 

corresponding outage volume for a tank loaded to the specified limit would be 10.6 percent. In 

this section, we investigate the effects that the lading will have on the impact and puncture 

response if the temperature is significantly different. 

Figure 112. Physical Properties of Chlorine as a Function of Temperature

From the physical properties shown in Figure 112, we see that the vapor pressure increases and 

the liquid density decreases as the temperature rises. A decrease in the liquid density will 

produce an increase in the liquid volume with a corresponding reduction in the outage volume. 

Increasing the pressure and reducing the outage can reduce the puncture resistance of a tank car. 

As a result, a higher temperature for the tank and lading are expected to lower the tank puncture 

energies in impacts. 

The condition analyzed in this section is a 105J600W chlorine tank car at an equilibrium 

temperature of 105 o

F. This temperature increases the internal vapor pressure for the tank to 155 

psi and lowers the corresponding outage volume for a tank loaded to the specified limit to 7.5

percent. The resulting pressure-volume relationships for the chlorine tank at 78 oF and 105 oF

are compared in Figure 113. The comparison shows that the higher temperature results in 

significantly higher pressures at the initial condition and the pressures rise more rapidly as a 

result of volume changes produced by dent formations. 
105

Figure 113. Pressure-Volume Relationships for the Chlorine Tank Car at 78 o

F and 105 oF

The calculated puncture forces and energies in normal side impacts for the chlorine tank car at 

the two temperature conditions are compared in Figure 114 and Figure 115. The comparison 

shows that the temperature has little effect on the puncture forces. This result was expected 

since the puncture force for a given impact geometry is primarily a function of tank shell 

thickness and strength which are unchanged in these scenarios. However, the corresponding 

puncture energies are reduced on average approximately 25 percent. 

In addition to the normal side impacts, a set of 45-degree oblique impacts was also performed for 

the 105J600W chlorine tank car at an equilibrium temperature of 105 o

F. A summary of results 

for all of the normal and oblique impacts for the tank at higher temperature is given in Figure 

116. In the figure, the calculated puncture energies at 105 o

F are normalized by the puncture 

energies at 78 oF for the corresponding impact conditions. In addition, an average value line is 

added to the graph. We see that on average, the increase in temperature dropped the puncture 

energies by 20 percent. However, the puncture energies for smaller impactor sizes are more 

similar at the two temperatures. This is because the impact response for small impactors is 

dominated more by the structural stiffness. The internal pressure (and pressure increase) plays a 

smaller roll for the small dent sizes prior to puncture with the small impactor sizes. 
106

Figure 114. Comparison of Side Impact Puncture Forces at 78 o

F and 105 oF

Figure 115. Comparison of the Side Impact Puncture Energies at 78 o

F and 105 oF
107

Figure 116. Normalized Side Impact Puncture Energies at 105 o

F
108

4 Analysis of General Impact Conditions

4.1 Introduction

In this section, the detailed BW failure model described in Section 2 is applied to assess various 

tank and head puncture conditions. The analyses in this section are focused on expanding the

impact scenarios to understand the tank response when exposed to more general impact 

conditions. 

4.2 Oblique Impacts

An initial set of oblique impact analyses was performed using the 12x12 in square impactor at an 

impact speed of 25 mph. The obliquity angles were 15, 30, and 45 degrees as shown in Figure 

117. These oblique impact analyses are significantly different than the rotated impactor 

analyses, previously described in Section 3.2.4, because the impactor trajectory is now rotated 

relative to the tank axis. In the rotated impactor analyses the orientation of the impactor was 

rotated but the impact trajectory was still normal to the tank. The force deflection curves for 

these oblique impacts are compared to each other and to the normal impact in Figure 118. 

(a) 15-degree obliquity (b) 30-degree obliquity (c) 45-degree obliquity

Figure 117. Various Oblique Impact Conditions Investigated for Side Impacts

The force deflection characteristics for the oblique impacts show a few specific trends. First, the 

force level at which the tank punctures is reduced for higher obliquity angles. This trend is 

expected since the impact face is now rotated relative to the tank wall producing stress 

concentrations at the edges and corners of the impact face (as seen in the rotated impactor 

analyses described in Section 3.2.4). 
109

Figure 118. The Effects of Impact Obliquity on the Tank Impact and Puncture Response

One significant difference seen in the oblique impacts compared to the normal impact with a 

rotated impactor is the puncture initiation behavior. A sequence of the impact damage and 

failure of the tank wall for the 45-degree oblique impact is shown in Figure 119. The sliding 

contact with the oblique impact results in large concentrations of damage at the corners of the 

impactor. These concentrations result in cracks that penetrate the tank wall significantly earlier 

than the time at which the entire impact face punctures the tank wall. Thus, with this type of 

oblique impact scenario, it is possible to have conditions that produce small cracks through the 

tank wall but do not produce a large puncture hole. 

A second unique feature of the force-deflection curves in Figure 118 is that the slope of the 

force-displacement curve is reduced as the impact obliquity increases. However, this can be 

attributed to the reference displacement in the plot being the ram displacement which is no 

longer normal to the tank axis. If we modify the plot to use only the component of 

displacements normal to the tank axis, the slopes of the curves are much more consistent, as seen 

in Figure 120. This suggests that the force buildup is a function of the component of the ram 

displacement normal to the tank axis. 
110

(a) Initial impact

(b) Fracture at impactor corners

(c) Full tank puncture

Figure 119. Oblique Impact Damage Development and Puncture Behavior for Side 

Impacts
111

Figure 120. The Effects of Impact Obliquity on the Tank Impact Response and Puncture

Further insight into the oblique impact behavior can be obtained by comparing the oblique 

impact with the normal impact where the impactor face is rotated by the same angle. Here, we 

will compare the 45-degree rotated impactor and 45-degree oblique impact configurations shown 

in Figure 121. The comparison of the corresponding force-displacement curves for these two 

impact scenarios is shown in Figure 122 (using the tank normal displacement). By correcting for 

the tank normal displacement the two curves have a similar slope. In addition, by using the 

rotated impactor, the puncture forces and puncture energies are relatively similar. 

In addition to the above oblique analyses with the 12x12 in square impactor, a full set of analyses 

was performed with the full range of impactor sizes and shapes at a 15, 30, and 45-degree 

oblique impact angle. Comparisons of the normal and oblique impact puncture forces and 

energies are provided in Figure 123 and Figure 124, respectively. The puncture forces are 

reduced with increasing obliquity angles and at the 45-degree oblique impacts the puncture 

forces are more than 50 percent lower than the normal impacts for the largest impactor. 

However, as the impactor size is reduced, the differences in puncture force are also reduced. At 

a 6-inch characteristic size, the 45-degree oblique impact puncture force is only reduced by 40

percent compared the normal impact. Finally, for the 3x3-inch impactor there is very little 

difference between the normal and oblique impact puncture forces. As a result, a linear fit to the 

oblique puncture force data would not intercept the origin of the graph as used in the normal 

impact data. The fits shown for the oblique impacts correlate the puncture forces to the square 

root of the impactor characteristic size. 
112

(a) 45-degree impactor rotation (b) 45-degree oblique impact

Figure 121. Effect of Impactor Angle on Oblique Impact Response for Side Impacts

Figure 122. The Effects of Impact Obliquity on the Tank Impact Response and Puncture
113

Figure 123. Comparison of Puncture Forces for Normal and Oblique Impacts

Figure 124. Comparison of Puncture Energies for Normal and Oblique Impacts
114

The puncture energies for the oblique impact show similar trends to the puncture forces. The 

puncture energies for the largest impactors are reduced by roughly 70 percent. Again, as the 

impactor size is reduced the differences in puncture energies are also reduced. At a 6 inch 

characteristic size the oblique impact puncture energy is only reduced by 50 percent compared 

with the normal impact. Finally, for the 3x3-inch impactor there is very little difference between 

the normal and oblique impact puncture energies. For the oblique impact puncture energies a 

linear fit of the data was used. 

4.3 Impact Boundary Condition Effects

4.3.1 Side Impact Constraint Effects 

A series of analyses were performed to investigate the effects of the constraint level on the tank 

response. The initial analyses are for the side impact of the 600-pound chlorine tank car. The 

impactor selected for these analyses was the 9.55-inch-diameter round impactor. Three different 

levels of constraint were considered, as shown in Figure 125. The highly constrained boundary 

condition is the tank shown in Figure 125(a) backed by the rigid impact wall that has been used 

for the majority of the side impact analyses in this report (as well as the NGRTC analyses in 

Reference 1). The unconstrained boundary condition is a single tank that is free to translate, 

shown in Figure 125(b). The moderately constrained boundary condition is two deformable 

tanks sitting side-by-side, shown in Figure 125(c). 

One of the issues in evaluating the effects of the BCs is that for many impact conditions the 

constraint on the back of the tank is not significant. If the impact speed is sufficiently high for a 

given size impactor, the tank will be punctured before there is sufficient time for the tank to 

move. For example, the force-deflection curves for the 25 mph impact of the 9.55-inch-diameter 

impactor for the 600-pound chlorine tank car with the impact wall and free BCs are compared 

with the red and blue curves in Figure 126. The comparison shows that the curves are nearly 

identical and the constraint conditions behind the tank are not significant for this impact 

scenario. With a fully loaded tank and relatively fast impact speed, the inertial constraint of the 

tank is the dominant factor. This example demonstrates that the scenario selected for the 

assessment of the BCs is important. It must have a sufficiently large impactor moving 

sufficiently slowly to allow for the constraint conditions behind the tank to be significant. 

To further demonstrate the importance of the inertial constraint on this impact scenario, the two 

25 mph impacts using the 9.55-inch-diameter impactor (wall and free) were repeated but the 

target tank models were modified to have the weight of an “empty” tank (the lading pressure 

effects were maintained). The comparison of the behaviors for the baseline and lighter “empty” 

tanks is shown with the black and green curves in Figure 126. The comparison shows that the 

lighter tanks develop forces more slowly since the ram motion does not need to accelerate as 

much mass. Similarly the effects of the tank dynamic response and BCs are seen much earlier 

since the lighter tank has higher natural response frequencies. For these analyses the boundary 

constraint plays a large role. The tank constrained by the impact wall provides a reaction force 

where the impactor loads recover and eventually puncture the tank. The free tank is pushed 

away from the impactor and is not punctured.
115

(a) Highly-constrained tank (reaction wall) (b) Unconstrained tank (free)

(c) Moderately-constrained tank (side-by-side tanks)

Figure 125. Various Tank Motion Constraint BCs for Side Impacts

To investigate the boundary constraint effects, a modification was made to the impactor BCs. In 

the majority of analyses performed in this study, the impactor was designed to represent the ram 

car from the NGRTC program [1]. As such, the impactor model was given a 295,000 lb weight 

with an initial impact velocity and was constrained to 1D motion along the initial trajectory. The 

impactor was free to decelerate and even reverse direction as it interacted with the target tank. 
116

Figure 126. The Effects of Constraint Conditions for a 25 mph Impact and 9.55-inchDiameter Impactor with Differing Tank Weights

For many of the analyses in this section, the impactor was prescribed to have a constant velocity 

impact condition. This is more representative of the loading for an impactor that is attached to a 

longer section of train in a derailment where the very large mass results in small changes in 

impactor velocity over the duration of any individual impact event. A comparison of the forcedeflection characteristics for the side impact response with the three different constraint 

conditions (wall, tank, free) is shown in Figure 127. For reference, a corresponding forcedeflection curve for the impact scenario of a 25 mph impact with the 295,000 lb impactor is also 

shown on the graph. 

The comparison shows that the initial portion of the force-deflection curves for all three 15 mph 

impacts are identical (up to approximately 30 in of ram displacement). All three impacts reach 

an initial peak force that is very close to the failure level before the dynamic response of the tank 

results in a temporary drop in the impact force (at approximately 40 in displacement). Beyond 

this time, the tank constraint BCs begin to play a large role in the behavior. With the highly 

constrained impact wall scenario the impact force quickly recovers and the tank is punctured at 

approximately 48 in of ram displacement. With the moderately constrained side-by-side tank 

scenario the impact force more slowly recovers and the tank is punctured at approximately 56 in 

of ram displacement. Finally, with the unrestrained tank the impact force never fully recovers to 

the puncture force level and the tank does not puncture. 
117

Figure 127. The Effects of Constraint Conditions for the 15 mph Constant Velocity 

Impacts

To further remove the effects of the tank dynamics from the impact behavior, an additional 

analysis was performed using a constant velocity of the ram of approximately 0.5 mph. This 

slow impact speed eliminates most of the tank dynamic effects and approximates a quasi-static 

loading of the tank between the ram and the wall. The force deflection for this quasi-static 

analysis is compared to those of the 25 mph initial velocity and 15 mph constant velocity impacts 

in Figure 128. Without the dynamic effects, the initial portion of the force-deflection curve is 

lower for the quasi-static analysis. However, as the tank is compressed and the internal pressure 

increases, the slope of the force-deflection curve rises and the tank punctures at approximately 

40 in of displacement. The internal pressure rises from 100 psi initially to over 130 psi at the 

point of puncture for this analysis. 

The wall provides a relatively high level of constraint against the tank translation in side impacts. 

However, it still allows for motion of the tank center of gravity (CG) away from the direction of 

impact. An idealized impact scenario that does not allow for any translation of the tank CG is to 

add the third symmetry plane to the tank normal to the direction of the impact. This is equivalent 

to a tank being impacted symmetrically between impactors on either side of the tank. An 

example of the model and impact response for this symmetric impact condition is shown in 

Figure 129. 
118

Figure 128. The Effects of Impact Speed on the Highly Constrained Side Impacts

Two analyses were performed for the symmetric impact condition with the 105J600 chlorine 

tank car. Both analyses used the 9.55-inch-diameter impactor. The difference is that the first 

analysis used a constant velocity 15 mph impact speed and the second analysis was performed at 

a much slower quasi-static loading condition. The calculated force deflection behaviors for these 

two analyses are shown in Figure 130. For comparison, the force deflection curve for the quasistatic loading of the tank against the wall is included in the figure. 

The comparison of the behaviors using the symmetric BC helps to develop an improved 

understanding of the tank response. The first observation is that the gross behaviors of the quasistatic and 15 mph analyses are similar and both fail at nearly identical displacements and forces. 

The primary difference is that the 15 mph impact behavior has some effects of the tank dynamic 

vibrations superimposed on the quasi-static force deflection path. 

The other interesting comparison is between the quasi-static loading for the symmetric BC and 

the quasi-static loading against the wall. Both cases have relatively linear force deflection curves 

and both fail at roughly equivalent puncture forces. However, the symmetric loading fails at a 

ram displacement of approximately 30 in and the loading against the wall fails at a ram 

displacement of approximately 40 in. However, the symmetric condition assumes that the tank is 

between two moving rams. Thus, the total compaction of the tank between the two ram faces is 

approximately 60 in. 
119

(a) Initial condition (b) Early impact

(c) Before tank puncture (d) After tank puncture

Figure 129. Calculated Response for the Symmetric Tank Side Impact Scenario

The comparison can be further used to estimate the stiffness of the tank compressed against the 

wall. If we use the symmetric analyses to determine that the dent depth around the impactor is 

30 in at the time of puncture, then the compression of the far side of the tank against the wall has 

a 10-inch depth. We would expect this depth to be much smaller than the ram dent depth since 

the loaded area is very large but the total wall reaction force is equal to that on the ram face. To 

investigate the wall reaction stiffness, an additional analysis was performed where the tank was 

quasi-statically compressed between two reaction walls (symmetric analysis with a moving 

wall). The calculated force-deflection for the symmetric wall loading is compared to the other 

quasi-static load cases in Figure 131. The comparison shows that the 1.5 million lb reaction load 

develops over a displacement of approximately 10 in (after the initial 4-inch standoff distance of 

the jacket from the tank is crushed). 
120

Figure 130. The Effects of Constraint BCs on the Side Impact Response

Figure 131. The Effects of Constraint BCs on the Side Impact Response
121

4.3.2 Head Impact Constraint Effects 

A similar set of analyses was performed to investigate the effects of the constraint BCs on the 

head impact response. The baseline head impact conditions, adapted from the NGRTC program, 

were for a highly-constrained tank head mounted on a test frame that does not allow for any 

motion at the specimen support. The head impact specimen included the tank head and head 

shield, supported by a short length of the tank shell and jacket, which were welded to a rigid test 

frame. A model for these highly-constrained head impact conditions is shown in Figure 132(a). 

In the model, the nodes at the back of the shell and jacket section are fixed and do not allow for 

any displacement or rotations. 

(a) Highly-constrained head motion (fixed BC)

(b) Unconstrained tank motion (head impact)

Figure 132. Various Tank Motion Constraint BCs for Side Impacts
122

To investigate the constraint effects in head impacts, an unconstrained tank model was developed 

as shown in Figure 132(b). The model includes the entire tank which is free to translate. Gravity 

was included in the analyses to develop appropriate vertical forces and motions in the offset 

impact scenario. Without the test frame support, a model of the ground was needed to resist the 

gravitational free-fall motions of the tank. The tank is free to slide along the ground as a result 

of the impact. 

One factor of the head impact response that was unknown is how the lading couples to the tank 

motions. To determine the bounds on the effect, an initial pair of analyses was performed where, 

in the first analyses, none of the weight of the lading was added to the tank, and in the second 

analysis, all of the lading mass was smeared into the tank. The force deflection curves for these 

two analyses are compared to that of the fully constrained tank head impact analysis in Figure 

133. The analyses are for an 18 mph impact of the 9.55-inch-diameter round impactor at 18 

mph. 

Figure 133. The Effects of BC Restraint on Head Impact Response

(18 mph Impacts)

The force-deflection curve for the highly constrained tank head has a roughly linear relationship 

between the ram displacement and impactor force up to a puncture force of approximately 1.8 

million lb at a ram displacement of approximately 25 in. The force-displacement curves for the 

two unconstrained tank models start along the same force deflection curve. However, the force 

curves for both begin to fall below that of the constrained head force curve. The rate at which 

the force curve diverges is much more rapid for the light tank than the heavy tank. This is 

because the impact forces can push the light tank away from the impactor more rapidly than the 

heavy tank. 
123

A similar set of analyses was performed on the tank and tank head using the coupler impactor 

model and an impact speed of 25 mph. The analyses again included the bounds of the empty and 

fully laded tank weights. The force deflection curves for these two analyses are compared to that 

of the fully constrained tank head impact analysis in Figure 134. The trends are very similar to 

those of the 18 mph impact. These results will be discussed further in the development of a 

simplified head impact analysis algorithm, described in Section 6.2 of this report. 

Figure 134. The Effects of BC Restraint on Head Impact Response

(25 mph Coupler Impacts)
124

4.4 Lading Response Effects

4.4.1 Lading Effects for Side Impacts

A set of preliminary analyses was used to assess the effects of the lading in the side impact 

response during the NGRTC program [1]. The impact conditions for this analysis were the Test 

1 side impact conditions from the NGRTC project on April 26, 2007, at the Transportation

Technology Center, Inc. (TTCI) in Pueblo, CO [77]. This test involved a side impact of a 

23x17-inch impactor with 1-inch-radius edges and corners into the side of a 105J500 chlorine 

tank car backed by a rigid impact wall. The ram car impact speed was measured optically at 13.9 

mph using speed trap reflectors placed within 6 ft of the impact point.

Additional parameters for Test 1 were as follows:

• Tank Car Weight (estimated) 265,000 lb

• Tank Shell: 0.777-inch-thick normalized TC128B

• Jacket: 11 gauge A1011 steel at 4-inch standoff distance

• Slurry Density 11.6 lb/gallon

• Outage 10.4 percent

• Capacity 17,391 gallons

• Internal Pressure 100 psi

• Ram Car Weight: 285,600 lb

• Ram Car Energy (derived): 1.86 million ft-lb

A tank car model was developed and used to predict the Test 1 impact response. The model of 

the 105J500 chlorine tank car is shown in Figure 135. The model includes the commodity tank, 

jacket and jacket standoffs, sill and bolsters, trucks, and outriggers attached to the draft gear to 

prevent a post-test rollover of the target tank caused by the rebound off the reaction wall. 

There are many different modeling approaches that can be used to include the dynamic effects of 

the fluid lading. The different modeling methodologies have tradeoffs in terms of accuracy, 

efficiency, and utility. Some of these methodologies have been investigated in studies for side 

impacts of tank cars [1, 80-82]. An example is the simplified explicit model of the lading 

included in the tank car model in the NGRTC program, shown in Figure 136 [1]. The lading 

model consisted of a low strength viscoelastic material that fills the same volume as the slurry 

added to the test tank. The sloshing of the lading model can be seen in the cutaway view of the 

predicted impact response. This lading modeling approach was established to capture some of 

the momentum transfer of the coupled fluid-structure response but to minimize effects such as 

sloshing at the fluid free surface that can cause numerical stability problems. 
125

(a) Complete tank car model

(b) Tank car mesh

Figure 135. Updated Model Generated for a 105J500W Pressure Tank Car

The comparison of the predicted and measured force-deflection curves is shown in Figure 137. 

The comparison of the force-deflection behaviors shows good agreement between the calculation 

and the test. The comparison of the pretest prediction and impact test serves as a validation of 

the model for the tank collision dynamics and impact deformation behavior. The responses 

include the initial impact, the reaction of the impact loads against the wall, and the post-impact 

rebound from the wall. Additional details of the impact behavior captured in the model included 

the target tank roll motion and lifting forces on the ram car caused by the lateral support of the 

target tank truck on the stub rail sections and the action of the outriggers resisting a post-test 

rollover behavior. 

In this study, an additional series of calculations were performed for this impact condition to

evaluate the effects of various approximations to the lading models and BCs used in the analyses

of side impacts. The three different BCs analyzed are shown in Figure 138. The first boundary 

condition, shown in Figure 138(a), is the idealized case where the tank is assumed to have 

vertical symmetry and no vertical gravitational loads are imposed. This is the simplest 

approximation and was used for the majority of analyses in this study. However, with symmetry

and without gravity, this model is not suitable for explicit modeling of the effects of the lading 

sloshing behavior. The second boundary condition, shown in Figure 138(b), adds the effects of 

vertical gravitational loads and a rigid flat model of the ground to resist the vertical tank motions. 

The third boundary condition, shown in Figure 138(c), adds the effects of vertical gravitational 

loads and models of the bolsters and trucks to support the tank and resist vertical tank motions. 

As a simplification of this condition the motions of the wheels were fixed. 
126

 

(a) Before impact (t=0.1 s) (b) Near max. displacement (t=0.25 s)

Figure 136. Calculated Test 1 Impact Response with Cutaway Showing Lading

Figure 137. Comparison of the Measured and Predicted Test 1 Force-Deflection Curves
127

(a) Tank model with vertical symmetry (b) Tank supported on ground

(c) Tank supported on trucks

Figure 138. Various Model Support BCs for a 105J500W Pressure Tank Car

The calculated tank impact force histories with the smeared lading model and the three different 

support BCs are compared to the measured impact force history in Figure 139. The response for 

the models with the vertical symmetry and the tank supported on the ground are very similar to 

each other and agree well with the peak force levels for both the initial loading and secondary 

loading to the maximum force for this test. The model supported on the trucks also agrees well 

with the initial loading and first force peak. However, the model with trucks unloads more 

slowly and does not accurately capture the reloading to the secondary peak force level. The 

reason for this discrepancy was not determined. However, it is possible that approximations 

such as the constrained motions of the wheels and the constrained vertical motion of the 

impactor resist the rotational movement of the tank for this scenario and modify the impact 

dynamics. 
128

Figure 139. Calculated Tank Car Impact Behavior Using Three Different Support BCs

A second analysis was performed on the model with the truck support BCs to reassess the effects 

of the modeling approximations for the lading. In the analysis, an alternative mesh-free 

Smoothed Particle Hydrodynamics (SPH) approach is used to model the lading. This has the 

advantage of being able to capture the fluid sloshing without mesh distortion effects and possible 

numerical instability of classical Lagrangian analyses. The SPH methodology is also compatible 

with the traditional Lagrangian analysis methodologies being used to evaluate the tank response. 

As a result, it is more computationally efficient than the Arbitrary Lagrangian Eulerian (ALE) 

methodologies that have been used for the fluid-structure interaction in tank car impacts [80-82]. 

The calculated Test 1 side impact tank and lading deformations at various times during the 

impact are shown in Figure 140. The corresponding force-time histories for the analyses with 

the smeared and SPH lading models are compared to the measured behavior in Figure 141. With 

the SPH lading model, the initial unloading occurs earlier and the reloading to a second peak 

force is more accurately reproduced. The timing of the initial and secondary force peaks are in 

good agreement with the experiment. The primary differences from the measured behavior is 

that the drop in load after the initial force peak is not as rapid or as large as measured and some 

of the higher frequency response characteristics are dampened by the SPH lading model. 
129

(a) Before impact (time=0.0 s) (b) Near first load peak (time=0.10 s)

(c) Near second load peak (time=0.25 s) (d) After unloading (time=0.50 s)

Figure 140. Calculated Side Impact Response with SPH Lading Model
130

Figure 141. Calculated Tank Car Impact Behavior Using Two Different Lading Models

The above analyses of the Test 1 impact conditions with different lading models and tank BCs 

illustrate the complexities of this test configuration. The late time response will be influenced to 

varying degrees by the constraints on the lateral, vertical, and rotational motions as well as the 

modeling of the lading. However, all of the modeling approximations agree well with the initial 

loading response which is the most important portion of the impact response (punctures often 

occur during this initial loading). In addition, the various modeling methodologies all give 

reasonable estimates for the duration and amplitude of the impact force pulse. 

4.4.2 Lading Effects for Head Impacts

A similar head impact analysis in an unconstrained tank was performed using an 18 mph impact 

with the 9.55-inch-diameter impactor. Again the impact was analyzed with the SPH lading 

model. The calculated tank and lading deformations at various times during the impact are 

shown in Figure 142. The corresponding force-displacement curve is compared with the 

analyses with the similar impact condition for the empty and loaded weight models in Figure 

143. The comparison shows that the force-deflection curve for the SPH model is closer to that of 

the empty tank weight than the smeared mass model of the fully loaded tank. This suggests that 

only a fraction of the lading mass couples to the motions of the unconstrained tank in head 

impacts. This effect is confirmed by including fringes of longitudinal velocity in the lading as 

shown in Figure 144. The time shown is well past peak load half way through unloading. 

However, the bulk of the lading is still stationary (blue fringes in the figure). Only the regions of 

the fluid very near to the tank wall or directly behind the impacted tank head are moving. 
131

(a) Before impact (time=0.1 s)

(b) Near load peak (time=0.16 s)

(c) After unloading (time=0.22 s)

Figure 142. Calculated Head Impact Response with SPH Lading Model

To investigate the effective weight of the fluid lading contributing to the motion in the head 

impact, we applied the impact response algorithm, described in Section 6.2.1, to run analyses at 

different tank weights and iterate on an approximate equivalent weight of the tank. The value 

that matched the analysis best was a tank weight of 130 percent of the empty weight. To confirm 

this result, we performed an additional finite element impact scenario where the weight of the 

tank was equal to 130 percent of the empty weight using a smeared mass approach (increasing 

the density of the commodity tank material). The comparison of this analysis with the 130

percent tank weight with the empty tank model, the full weight model (smeared mass) and full 

model with SPH lading is shown in Figure 145. The agreement of the SPH model with the 130

percent tank weight model is quite good. Note that the 130 percent weight model increases the 

tank from an empty weight of 61,300 lb to a weight of 79,690 lb. The full weight of the tank is 

263,000 lb which is the empty tank plus approximately 200,000 lb for the lading. As a result, 

these analyses show that less than 10 percent of the lading is coupled to the motion of the tank 

for this head impact scenario. 
132

Figure 143. Calculated Tank Car Head Impact Behavior Using Different Lading Models

(a) Full tank profile (time=0.18 s)

(b) Impact zone (time=0.18 s)

Figure 144. Calculated Longitudinal Velocity Distribution in the SPH Lading
133

Figure 145. Calculated Tank Car Head Impact Behavior Using Different Lading Models
134

4.5 Head Impact Test Configuration

One of the important tank head protection requirements is to provide for the puncture resistance 

of a coupler impact at a relative impact speed of 18 mph. This head impact condition is designed 

to verify the integrity of new or untried tank head puncture protection systems and to test for 

system survivability after coupler-to-tank-head impacts. We have already analyzed many 

aspects of this head impact scenario including the effects of a coupler impacting the constrained 

tank head in Section 3.3.2, the effects of the BC constraints in Section 4.3.2, and the effects of 

the BC constraints in Section 4.4.2. In this section we extend these analyses to further analyze 

the head impact test configuration. The details of the head impact testing requirements are 

provided in Appendix A of this report. 

The head impact condition uses a rigid 263,000-pound ram car equipped with a coupler, and a 

draft sill including the draft yoke and draft gear. The coupler protrudes from the end of the ram 

car so that it is the leading location of perpendicular contact with the impacted test car. The 

impacted test car is loaded and pressurized to 100 psi. In addition, the target tank car is coupled 

to a 200,000-pound rigid backup car (trailing mass) for a combined target total weight of 

486,000 lb. The overall model configuration for a head impact analysis is shown in Figure 146. 

The analysis was conducted with the coupler impacting on the lateral centerline of the tank car at 

a height of 21 in above the top of the sill. 

Trailing Mass Tank Impactor

Figure 146. Tank Head Impact Analysis Model Geometry

4.5.1 Draft Gear Effects for the Impactor

There are several features of this head impact test configuration that add complexity. The first is 

the complex geometry of the impactor face with a coupler head impactor. This has already been 

analyzed for both side and head impacts and is discussed in Sections 3.2.4 and 3.3.2. The 

regulations of the testing configuration (49 CFR § 179.16) do not specify the specific coupler 

type or manufacturer. As a result, variations may exist in the impact face geometry that could 

influence the puncture potential. 

A second effect that complicates this test configuration is the use of the coupler impactor “sled” 

with a sill and draft gear. To investigate this effect, a model of a coupler impact sled was 

developed and used in an impact analysis. The model for the coupler impactor sled is shown in 

Figure 147. It consists of a large rigid sled with a mass of 263,000 lb. This value was selected to 

conform to the regulatory coupler head impact test specification. A rigid sill was attached to the 

mass and a model of the coupler and draft gear was included in the sill. The model of the draft 

gear is shown in Figure 147(b). It includes an energy absorbing draft gear model, a realistic 
135

geometry of a draft gear yoke, and a draft gear design that applies a retaining key to holds the 

assembly together. Identical draft gear models were used in both the tank car and the rigid 

impactor block. The energy absorbing draft block allows for 3.2 in of travel before the draft gear 

follower plate seats against the friction draft gear case and the gear creates a direct load path 

from the coupler to the lugs. 

(a) Full coupler impact sled model

(b) Coupler and draft gear model

Figure 147. Model of the 263,000 Coupler Impactor Sled

The force-deflection characteristics of the draft gear were obtained using a nonlinear spring with 

the specified properties shown in Figure 148. The draft gear develops a force of approximately 

500,000 lb after one half inch of displacement that steadily increases to approximately 900,000 

lb at approximately 3 in of displacement. After the 3 in of travel the loads increase rapidly. 

During unloading the force deflection behavior follows the same curve and there is no hysteresis 

to dissipate energy in the draft gear. This is a conservative assumption in that the draft gear 

loads will remain at elevated levels and more of the energy dissipation will occur in the tank 

head deformations. 

A comparison of the 25 mph impact behaviors of the restrained tank head using the initial rigid 

coupler impactor model and the new coupler impact sled model are shown in Figure 149. The 

higher 25 mph impact speed was used in these analyses to increase the impact severity to a 

condition that would puncture the tank head. Overall, the force deflection characteristics of the 

two impact analyses are similar. The slight reductions in impact force are probably a result of 

the compaction of the draft gear allowing for a slight increase in the sled displacement compared 

to that of the coupler face. The larger discrepancy is in the point of failure initiation through the 

tank head. The impactor sled allows for small rotations of the coupler within the sill and this 

effect could allow for some redistribution of the contact loads across the coupler face. With the 
136

sled, the puncture force is increased by approximately 8 percent. However, with the additional 

compliance of the draft gear and the slope of the force-deflection curves, this results in a 27

percent increase in the puncture energy. 

Figure 148. Force-Deflection Characteristics Used for the Energy Absorbing Raft Gear
137

Figure 149. Comparison of 25 mph Coupler Impact and Puncture Behaviors

4.5.2 Trailing Mass Effects for the Impactor

The head impact tests conditions specify that the impacted test car must be coupled to one or 

more “backup” cars to achieve a total weight of 217,724 kg (480,000 lb) with hand brakes 

applied on the last “backup” car. To investigate the effects of the reaction forces from the 

backup car, a model for a 200,000 lb rigid trailing mass was generated and coupled to the test 

tank car. In the initial analyses, the tank was modeled at 130 percent of the empty tank weight 

using the smeared lading model approximation (1.3X). This provided the approximate inertial 

effects of the liquid lading in a head impact as shown in Section 4.4.2. 

The transfer of momentum in the impact analysis is shown in Figure 150. In the figure, blue is 

stationary and red is the initial velocity of the impactor mass of 18 mph. The times shown are 

before impact and at 40 ms intervals after impact. The corresponding velocity histories for the 

impact mass, the trailing mass, and the commodity tank are shown in Figure 151. The impact 

mass decelerates from the 18 mph initial velocity to less than 6 mph after impact. Similarly, the 

tank and trailing mass is accelerated to a velocity of greater than 10 mph after the impact. 

The corresponding impact forces for the tank and the transmitted forces to the trailing mass are 

shown in Figure 152. For comparison, an identical impact analysis was performed without the 

trailing mass coupled to the tank. The comparison shows that the trailing mass has only a 

modest influence on the peak impact force (approximately a 20 percent increase in the peak 

force). This modest increase in impact severity does not justify the significant increase in the 

complexity of the test conditions and collision dynamics. 
138

One of the modeling approximations used in this analysis of the head impact test condition is the 

1.3X lading model. As described in Section 4.4.2, this model couples less than 10 percent of the 

lading to the motion of the tank for this head impact scenario. This is probably appropriate for 

the early time motion of the tank including the peak impact force. However, at some later time 

the lading inertial effects will interact with the tank motions. To evaluate the bounds of the 

effects, an additional set of analyses was performed using the modeling approximation where all 

of the lading mass was smeared into the tank model. 

The calculated velocity histories for the impact mass, the trailing mass, and the commodity tank 

for the smeared full lading model are shown in Figure 153. The impact mass decelerates from 

the 18 mph initial velocity to approximately 4 mph after impact. Similarly, the tank and trailing 

mass is accelerated to an average velocity of approximately 8 mph after the impact. 

The corresponding impact forces for the tank and the transmitted forces to the trailing mass are 

compared to those of the 1.3X model in Figure 154. The comparison shows that the lading 

inertial approximation has a much larger effect than that of the trailing mass. In addition, with 

the smeared full lading model, the trailing mass has only a small influence on the peak impact 

force (approximately a 10 percent increase in the peak force). 
139

Figure 150. Momentum Transfer for the Tank Car Head Impact Analysis
140

Figure 151. Velocity Histories for the 1.3X Lading Head Impact Analysis

Figure 152. Calculated Impact Behavior Using the 1.3X Lading Model
141

Figure 153. Velocity Histories for the Smeared Full Lading Head Impact Analysis

Figure 154. Calculated Head Impact Behavior Using the Smeared Full Lading Models
142

4.5.3 Summary of the Head Impact Test Evaluation

The above analyses, supported by analyses in other sections of this report, allow for observations 

to be made about the head impact test requirement. The first observation is that the details of the 

test are not tightly controlled. This includes aspects of the coupler and draft gear geometry and 

energy absorbing characteristics, tolerances of the coupler and striker clearances that will allow 

for rotation of the coupler impactor face against the tank head, and the geometry of the impactor 

and trailing masses. Many features of the test could be changed to increase or reduce the 

severity of the impact and the test conditions would still fall within the bounds of the testing 

specifications. 

An example of this test uncertainty is that the test requirements allow for one or more backup 

cars to be used to provide the inertial resistance to the impact. However, the analyses performed 

in this study illustrate that a single rigid mass coupled to the target tank car can provide only a 

modest level of inertial resistance to the initial impact forces. If this coupled mass was replaced 

by several lighter masses coupled together, each subsequent mass would contribute to a lesser 

extent and with a delayed effect. As a result, the inertial restraint of the backup cars could be 

minimized and still be within the allowable testing configuration. 

A second general observation is that the test is very complex both for the performance of an 

experiment and even more so for analysis of the test condition. To accurately model the test 

condition requires the modeling of the lading sloshing effects, the interaction of the target tank 

car and coupled “backup” cars, and the modeling of the impactor with a complex coupler 

impactor face and draft gear behavior. With all of these effects, there are many potential 

modeling assumptions and approximations that could be applied by different analysts that would 

introduce large errors in the calculated impact forces and puncture resistance. 

Ideally, the head impact test condition should be replaced with one where the head is attached to 

a rigid mass with a well-defined attachment BC. The impactor should also effectively be a rigid 

mass with a well-defined impactor face geometry. The motions of the two bodies should be 

controlled to a one-dimensional translation. With these approximations, the test will provide 

much more repeatable and reproducible results and the analyses will be greatly simplified,

reducing the potential errors from different modeling methodologies. 
143

4.6 Analysis of Offset Side Impact Effects

4.6.1 Analysis of Vertical Offset Side Impacts

For the idealized side impact analyses discussed in Chapter 3, the impact point was always at the 

center of the tank both along the length and at the vertical mid-height (belt line). In this section, 

we explore the effects of offsetting the impact position both vertically and longitudinally. 

The initial series of offset side impact analyses were performed on the side impact condition 

where the impact point was offset vertically by different magnitudes. This offset effect is similar 

to that of the analyses of the head impacts that have typically included the effects of an impact 

that was offset from the center of the tank head. The offset impact was found to influence the 

damage development of the tank head under the impactor and reduce the load at the puncture 

initiation. 

The vertical offset side impact analyses were performed using the 9.55-inch-diameter round 

impactor. In the idealized side impact analyses, described in Section 3.2, the models contained 

longitudinal and vertical symmetry planes to model one-quarter of the tank. That model 

reflected about the symmetry plane is shown in Figure 155(a). For the offset analyses, the 

vertical symmetry plane can no longer be used. As a result, BCs to control the vertical motions 

of the tank were needed. The methodology used was to apply gravity to the tank and to add a 

rigid ground model that supports the tank. The corresponding models for the center impact and 

impact points offset 15 and 25 in below the centerline are shown in Figure 155(b–d). 

The calculated force-deflection histories for the four models shown in Figure 155 are compared 

in Figure 156. The idealized impact conditions with symmetry (Figure 155a) and the center 

impact analyses with ground and gravity added (Figure 155b) fail at roughly equivalent puncture 

forces and energies. There are slight differences introduced by the more complex BCs but the 

overall behavior is similar and the puncture energies are within 10 percent. However, as the 

impact point is offset, the puncture forces and energies are significantly reduced. 

The calculated puncture mode for the 25-inch vertical offset side impact analyses is shown in 

Figure 157. The puncture behavior looks very similar to the behavior of an offset head impact

where the damage is concentrated near the top of the impactor and the puncture forms as a flap 

that initiates at this top edge. We see for this 25-inch offset that the failure initiates while only 

the top half of the impactor is significantly interacting with the tank wall. As a result, the forces 

are concentrated at the upper edge and the total force required to initiate the puncture is reduced. 
144

(a) Idealized impact (b) Center impact

(c) 15-inch offset (d) 25-inch offset

Figure 155. Impact Scenarios Used in the Vertical Offset Impact Analyses

A summary of the calculated puncture response for all of the vertical offset side impact analyses 

is provided in Table 6. The corresponding puncture forces and puncture energies are plotted 

against the vertical offset distance in Figure 158 and Figure 159, respectively. The comparison 

shows that a small vertical offset (10 in or less) has little effect on the puncture force. However, 

as the offset increases, the puncture force drops significantly and a 25-inch offset reduces the 

puncture force by approximately 35 percent. The trends are similar for puncture energies, but 

are more pronounced. The 25-inch offset reduces the puncture energy by approximately 60

percent. This is because the puncture force reduction is compounded by a corresponding 

reduction in the ram displacement required to develop that force. 
145

Figure 156. Comparison of the Calculated Side Impact Behavior with Vertical Offsets

(a) Before puncture (b) Puncture initiation

Figure 157. Calculated Puncture Behavior for the 25-inch Vertical Offset Side Impact
146

Table 6. Summary of the Vertical Offset Side Impact Analyses

Head Impact 

Calculation

Tank 

Type

Tank 

Shell Jacket Impact Conditions

Vertical 

Offset 

(in)

Internal 

Pressure

(psi)

Puncture 

Force (lb)

Puncture 

Energy

(ft-lb)

R13X 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. 0.0 100 psi 1,569,000 2,520,000

R13Y 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -15.0 100 psi 1.287,000 1,400,000

R13Z 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -25.0 100 psi 990,000 1,000,000

R14A 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -5.0 100 psi 1,576,000 2,450,000

R14B 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -10.0 100 psi 1,467,000 2,060,000

R14C 600 lb Cl 0.981 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -20.0 100 psi 1,116,000 1,180,000

Figure 158. Calculated Puncture Forces for the Various Vertical Offset Side Impacts
147

Figure 159. Calculated Puncture Energies for the Various Vertical Offset Side Impacts

4.6.2 Analysis of Longitudinal Offset Side Impacts

A corresponding set of analyses was performed to investigate the effects of a longitudinal offset 

to the impact point on side impacts. As the impact point move further from the tank center of 

gravity (CG) the tank motions will include more rotation away from the impact as opposed to the 

pure translation when the impact is aligned with the tank CG (center impact). 

The three primary impact conditions analyzed are shown in Figure 160. In addition to the 

reference condition of the center impact, the impact locations with longitudinal offsets of 80 and 

160 in were also considered. All of the analyses used a vertical symmetry plane to constrain the 

motions of the tank in a two dimensional plane. 

The initial three analyses used a 15 mph constant velocity impact condition on an unconstrained 

tank. The force-deflection curves for these three analyses are compared in Figure 161. None of 

the tanks are punctured by these impact conditions. However, the larger the longitudinal offset, 

the more easily the tank is pushed out of the way from the path of the impactor. As a result, the 

effect of the longitudinal offset is very similar to the effects of reducing the tank weight. Since 

the tank can be more easily pushed away from the path of the impacting object, the probability of 

a given impactor puncturing the tank will be reduced as the impact point moves further from the 

tank CG. 
148

(a) Center hit (b) 80-inch offset (c) 160-inch offset

Figure 160. Various Impact Locations Investigated for Unconstrained Side Impacts

The above effects of the offset impact will be reduced as the motions of the tank are more highly 

constrained. A set of additional impact analyses was performed with a longitudinal offset impact 

condition and an impact wall behind the tank to constrain the tank motions. The models for the 

80- and 160-inch offset impacts are shown in Figure 162. Note that the impact wall position is 

also offset by the same distance to remain aligned with the impactor. 

The initial offset impact analyses on the constrained tanks used the 15 mph constant velocity 

impact condition. The comparison of the force-deflection curves for the center, 80-inch offset, 

and 160-inch-offset impact conditions is shown in Figure 163. Overall, the differences in these 

force-deflection curves are relatively small. However, the larger offset distances introduce 

changes to the tank kinematics, and small asymmetry to the impact behavior that results in 

failures at slightly less displacement levels and reduced puncture energies. 
149

Figure 161. The Effects of Longitudinal Offsets on Unconstrained Side Impact Behavior

An additional set of offset impact analyses was performed on the constrained tanks using a 25 

mph impact initial condition with the 295,000 lb impactor. The comparison of the forcedeflection curves for the center, 80-inch offset and 160-inch-offset impact conditions is shown in 

Figure 164. Again, the differences in these force-deflection curves are relatively small. 

However, for the higher impact speed, the response is dominated more by the inertial constraint. 

As the offset distance increases, the tank more rapidly moves away from the impact and more of 

the kinematics and interaction with the BC come into play. As a result, the larger offsets cause 

failures at slightly larger displacement levels and increased puncture energies. This is the 

opposite of the trend produced at the slower 15 mph impacts. 
150

(b) 80-inch offset (c) 160-inch offset

Figure 162. Longitudinal Offset Impact Locations Investigated for Constrained Side 

Impacts
151

Figure 163. Offset Impact Effects on a Constrained Tank, Constant 15 mph Impact

Figure 164. Offset Impact Effects on a Constrained Tank, 25 mph Initial 

Velocity Impact
152

5 Impact Analyses on Other Tank Car Designs

5.1 Introduction and Background

One of the significant factors in the puncture resistance of various pressure tank car designs are 

the effects of the commodities that they carry. The vapor pressure and liquid density of EO, AA, 

and chlorine are plotted as a function of temperature in Figure 165. The comparison shows that 

for a given temperature, AA has a vapor pressure that is approximately 25 percent higher than 

chlorine, and EO has a much lower vapor pressure. However, EO is different from these other 

commodities because nitrogen padding is used for safety considerations. As a result, the typical 

pressure in an EO tank car during transit is approximately 50 psi and results primarily from the 

nitrogen padding applied to the tank for safety considerations. 

Figure 165. Comparison of Physical Properties of Common Pressure Tank Car 

Commodities

The resulting pressure-volume relationships used for tank car impact analyses with the three 

commodities are compared in Figure 166. These assume the tank and lading are at a temperature 

of approximately 75 o

F and that the associated outage volume is 10.6 percent. As a result, the 

internal tank pressure for all three commodities rapidly increases as the tank relative volume 

approaches a shell full condition (relative volume of 0.896). 
153

Figure 166. Tank Pressure-Volume Relationships for Various Commodities (10.6 Percent

Outage)

5.2 DOT 105J500 Chlorine Tank Cars

The tank design used in the analyses in Chapters 3 and 4 of this report is the 105J600 chlorine 

tank car required under the interim rule. The TC128B tank shell is 100 in in diameter and 472 in 

long with 2:1 ellipsoidal heads. The tank is covered by a 0.119-inch-thick A1011 jacket with a 

4-inch standoff from the tank. In this section, we analyze the puncture performance of the 

105J500 chlorine tank car which was the standard prior to the interim rule. The difference 

between these two designs is that the 0.981-inch-thick tank shell used in the 105J600 is reduced 

to a 0.777-inch thickness for the 105J500 tank car.

A series of analyses were performed with the 105J500 chlorine tank car including different size 

and shape impactors (summarized in Table 7), vertically offset impacts (summarized in Table 8), 

and 45-degree oblique impacts (summarized in Table 9). The objective of these analyses was to 

compare the relative puncture performance of the 105J600 chlorine tank car to that of the 

105J500 tank car. 
154

Table 7. Summary of the Baseline Side Impact Analyses on the 105J500 Tank Car

Calculation Tank Type Tank Shell Shell 

Jacket 

Impact 

Conditions

Internal 

Pressure

(psi)

Puncture 

Force (lb)

Puncture 

Energy

(ft-lb)

R18A 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

15 mph

6”x6” ram 100 psi 8.860E+05 1.050E+06

R18B 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 100 psi 1.561E+06 3.560E+06

R18C 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

20 mph

9”x9” ram 100 psi 1.289E+06 2.280E+06

R18D 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

10 mph

3”x3” ram 100 psi 4.670E+05 3.220E+05

R18E 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

15 mph

3”x6” ram 100 psi 6.770E+05 6.910E+05

R18F 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

3”x12” ram 100 psi 1.036E+06 1.330E+06

R18G 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

15 mph

5.73 in. dia. 100 psi 7.960E+05 9.040E+05

R18H 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

20 mph

7.64 in. dia. 100 psi 1.040E+06 1.610E+06

R18I 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. 100 psi 1.209E+06 2.220E+06

R18J 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

11.46 in. dia. 100 psi 1.452E+06 2.930E+06

R18K 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

13.37 in. dia. 100 psi 1.629E+06 3.660E+06

Table 8. Summary of the Vertical Offset Side Impact Analyses on the 105J500 Tank Car

Head Impact 

Calculation

Tank 

Type

Tank 

Shell Jacket Impact 

Conditions

Vertical 

Offset 

(in)

Internal 

Pressure

(psi)

Puncture 

Force (lb)

Puncture 

Energy

(ft-lb)

R18L 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. 0.0 100 psi 1.224E+06 2.190E+06

R18M 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -15.0 100 psi 9.950E+05 1.000E+06

R18N 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -25.0 100 psi 7.590E+05 7.000E+05

R18O 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -5.0 100 psi 1.273E+06 2.020E+06

R18P 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -10.0 100 psi 1.144E+06 1.350E+06

R18Q 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. -20.0 100 psi 8.510E+05 7.960E+05
155

Table 9. Summary of the 45-Degree Oblique Side Impact Analyses on the 105J500 Tank 

Car

Calculation Tank 

Type

Tank 

Shell

Shell 

Jacket 

Impact 

Conditions

Internal 

Pressure

(psi)

Puncture 

Initiation 

Force (lb)

Puncture 

Initiation 

Energy (ft-lb)

R18R 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

18 mph

6”x6” ram 100 psi 4.430E+05 3.850E+05

R18S 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

12”x12” ram 100 psi 6.710E+05 6.830E+05

R18T 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9”x9” ram 100 psi 5.680E+05 4.570E+05

R18U 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

10 mph

3”x3” ram 100 psi 3.500E+05 2.350E+05

R18V 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

15 mph

5.73 in. dia. 100 psi 5.070E+05 4.140E+05

R18W 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

20 mph

7.64 in. dia. 100 psi 6.320E+05 7.120E+05

R18X 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

9.55 in. dia. 100 psi 7.320E+05 8.820E+05

R18Y 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

11.46 in. dia. 100 psi 8.250E+05 1.200E+06

R18Z 500 lb Cl 0.777 in

TC128B

0.119 in

A1011

25 mph

13.37 in. dia. 100 psi 9.660E+05 1.610E+06

The normal side impact puncture forces and energies for the 105J500 tank car are compared to 

those of the 105J600 lb tank car for various size and shape impactors in Figure 167 and Figure 

168, respectively. The puncture force comparison shows that the puncture forces for the 

105J600 tank cars are approximately 30 percent greater than for the 105J500 tank cars. This 

difference is slightly greater than expected since the 0.981-inch tank shell is 26 percent thicker

than the 0.777-inch tank shell and both have identical 0.119-inch A1011 jackets. The puncture 

energy comparison, shown in Figure 168, indicates that the 105J600 tank car has a roughly 40–

50 percent increase in puncture energy over the 105J500 tank car for the baseline side impacts. 

The offset and 45-degree oblique side impact puncture energies for the 105J500 tank car are 

compared to those of the 105J600 lb tank car in Figure 169 and Figure 170, respectively. The 

vertical offset impact comparison shows that the puncture energies for the 105J600 tank cars 

range between 15–53 percent greater than for the 105J500 tank cars. The puncture energy 

comparison for the 45-degree oblique impacts, shown in Figure 170, indicates that on average 

the 105J600 tank car has a roughly 20-percent increase in puncture energy over the 105J500 tank 

car. 
156

Figure 167. Puncture Force Comparisons for the 105J500 and 105J600 Tank Cars

Figure 168. Puncture Energy Comparisons for the 105J500 and 105J600 Tank Cars
157

Figure 169. Comparison of the Offset Impact Puncture Energies 

for the 105J500 and 105J600 Tank Cars

Figure 170. Comparison of the 45-Degree Oblique Impact Puncture Energies 

for the 105J500 and 105J600 Tank Cars
158

A summary of the relative side impact puncture energy of the 105J500 and 105J600 tank cars is 

shown in Figure 171. The summary includes all of the baseline, offset, and oblique impact 

conditions summarized in Figure 168, Figure 169, and Figure 170. Each point on Figure 171

represents the calculated puncture energy for the 105J600 tank car normalized by the 

corresponding puncture energy for the 105J500 tank car under identical impact conditions. The 

individual scenarios result in a range of normalized puncture energies from a minimum of 1.15 to 

a maximum of 1.85 (15–85 percent higher puncture energies). However, the wide range of 

impact scenarios considered results in an average increase in puncture energy of 39 percent for 

the 105J600 over the 105J500 chlorine tank car. 

Figure 171. Normalized Puncture Energy Summary for the 105J500 and 105J600 Tank 

Cars

5.3 Ethylene Oxide Tank Cars

The baseline EO tank car design analyzed was the 300-pound EO tank car which is the most 

common existing design used for EO shipments. Analyses were also performed to evaluate 

variations on this design that include a proposed increase to a 400-pound design and the 500-

pound design specified under the FRA interim rule. A summary of the tank parameters for these 

analyses is provided in Table 10. 
159

Table 10. Summary of the Ethylene Oxide Tank Car Design Parameters

Tank Designation Tank Shell Tank Jacket Combined 

Thickness 

Tank 

Diameter

Jacket 

Standoff

Baseline 105J300W 0.5625” TC-128B 0.119” A1011 0.6815 in 111.0 in 1.0 in

Baseline 105J400W 0.7350” TC-128B 0.119” A1011 0.8540 in 111.0 in 1.0 in

Interim 105J500W 0.9180” TC-128B 0.119” A1011 1.0370 in 111.0 in 1.0 in

Three sets of analyses were performed for each of the tank designs. These include: (1) normal 

side impacts with a variety of different size and shape impactors, (2) vertical offset impacts, and 

(3) oblique side impacts with a variety of different size and shape impactors. The analyses of 

normal side impacts include 3x3, 6x6, 9x9, 12x12, 3x6, and 3x12 rectangular impactors, all with 

a 0.50-inch radius around the edges. Additional impact analyses were performed using 5.73, 

7.64, 9.55, 11.46, and 13.37 in diameter round impactors (ram face perimeter lengths of 18, 24, 

30, 36, and 42 in, respectively). These impactors (shown previously in Figure 56, Figure 60, and 

Figure 63) provide a significant amount of variation in impactor size and shape. 

5.3.1 Normal side Impacts of EO Tank Cars

A summary of the normal side impact puncture forces and puncture energies for the baseline 

300, 400, and 500-pound EO tank cars are provided in Figure 172 and Figure 173, respectively. 

The values for the puncture forces and energies are plotted against the ram face characteristic 

size (defined as the square root of the area of the impactor face). The comparison of the baseline 

EO tank car designs show that the puncture forces for the 400 and 500-pound EO tank cars are 

on average 32 percent and 68 percent greater, respectively, than for the baseline 300-pound EO 

tank. Similarly the puncture energies for the 400- and 500-pound EO tank cars are on average 35

percent and 98 percent greater, respectively, than for the baseline 300-pound EO tank. As 

expected, increasing the thickness of the commodity tank is an effective method for increasing 

the puncture resistance of a given tank design.
160

Figure 172. Calculated Baseline EO Tank Puncture Forces for Various Size and Shape 

Impactors

Figure 173. Calculated Baseline EO Tank Puncture Energies for Various Size and Shape 

Impactors
161

5.3.2 Offset Impacts of EO Tank Cars

The second series of analyses performed for each of the EO tank car designs are the vertical 

offset impacts. The analyses were performed using conditions identical to those for the chlorine 

tank car described in Section 0. The vertical offset side impact analyses were performed using 

the 9.55-inch-diameter round impactor. 

A summary of the puncture forces and puncture energies for the various EO tank car designs are 

plotted against the vertical offset distance in Figure 158 and Figure 159, respectively. The 

comparison shows that a small vertical offset (10 in or less) has little effect on the puncture 

force. However, as the offset increases the puncture force drops significantly and a 25-inch

offset reduces the puncture force by approximately 25 percent. The trends are similar for 

puncture energies, but are more pronounced. The 25-inch offset reduces the puncture energy by 

approximately 60 percent. This is because the puncture force reduction is compounded by a 

corresponding reduction in the ram displacement required to develop that force. 

Figure 174. Calculated Puncture Forces for the Various Vertical Offset Side Impacts
162

Figure 175. Calculated Puncture Energies for the Various Vertical Offset Side Impacts

5.3.3 Oblique Impacts of EO Tank Cars

In addition to the above normal and offset side impact analyses, a set of analyses was performed 

with the full range of impactor sizes and shapes at a 45-degree oblique impact angle. The impact 

scenario is shown in Figure 1176. 

Comparisons of the normal and oblique impact puncture forces and energies are provided in 

Figure 123 and Figure 124 for the baseline 300-pound, 400-pound, and 500-pound EO tank cars. 

The oblique puncture forces are approximately 50 percent of the normal puncture forces for the 

largest impactors. However, as the impactor size is reduced the differences in puncture force are 

also reduced. At the smallest 3x3-inch impactor there is very little difference between the 

normal and oblique impact puncture forces. As a result, a linear fit to the oblique puncture force 

data would not intercept the origin of the graph as used in the normal impact data. 

The puncture energies for the oblique impact show similar trends to the puncture forces. The 

puncture energies for the largest impactors are reduced by approximately 70 percent. Again, as 

the impactor size is reduced the differences in puncture energies are also reduced. For the 3x3-

inch impactor there is much less difference between the normal and oblique impact puncture 

energies. 
163

Figure 176. Impact Scenario for the 45-Degree Oblique Side Impact Analyses

Figure 177. Comparison of Puncture Forces for Normal and Oblique Impacts
164

Figure 178. Comparison of Puncture Energies for Normal and Oblique Impacts

5.3.4 Summary of EO Tank Car Puncture Performance

The full sets of normal, offset, and oblique impact analyses were performed for all three of the 

EO tank designs listed in Table 10. Thus, we have 26 different impact conditions analyzed for 

each of the EO tank designs. In this section, we summarize the relative puncture performance 

for the various designs. 

To assess the relative puncture performance of different designs, we compare the puncture 

energy for each design under the same impact conditions. In this comparison, we normalize the 

puncture performance of each of the various designs to the baseline 300-pound EO tank car. 

Using this approach, the relative performance of the baseline 400-pound and 500-pound EO tank 

cars is summarized in Figure 179. Each of the symbols in Figure 179 represents the calculated 

puncture energy from one of the 26 impact scenarios divided by the corresponding puncture 

energy from the baseline 300-pound EO tank car for the same impact scenario. In addition to the 

puncture energy data from each of the calculations, an average value line for all 26 impact 

scenarios is added to the graph for each design. The comparison shows that the 400-pound tank 

car has on average a 34 percent higher puncture energy than the 300-pound EO tank car for the 

set of impact conditions analyzed. Similarly, the puncture energies for the 500-pound EO tank 

car are approximately double those of the 300-pound EO car for these impacts. 
165

Figure 179. Comparison of Relative Puncture Performance of the Baseline EO Tank 

Designs

An alternative was to compare the performance of the EO tank designs with the chlorine tank 

designs. For this comparison, the results of the normal and 45-degree oblique side impact 

analyses were used (20 analyses for each design). The puncture energy of each of the EO tank 

designs was normalized to the puncture energy for the 105J500 chlorine tank car. These 

normalized puncture energies are shown in Figure 180. For comparison the normalized puncture 

energies for the 105J600 chlorine tank car are added to the graph. In this comparison, the 

puncture energies for the 105J500W EO tank car design are considerably higher than those of the 

105J600W chlorine tank car. The EO tanks have relatively high puncture energies as a result of 

the lower tank pressures and larger diameter tanks. The 105J500W, 105J400W, and 105J300W 

EO tank cars have puncture energies on average 82 percent higher, 17 percent higher, and 12

percent lower, respectively, than the 105J500W chlorine tank car. The corresponding puncture 

energies for the 105J600W chlorine tank car were on average 37 percent higher than the 

105J500W chlorine tank car. 
166

Figure 180. Comparison of Relative Puncture Performance of EO and Chlorine Tank 

Designs

5.4 Anhydrous Ammonia Tank Cars 

The baseline AA tank car designs analyzed was the 340-pound AA tank car which is a common 

existing design used for AA shipments. Analyses were also performed to evaluate the 500-

pound design specified by the FRA interim rule. A summary of the tank parameters for these 

analyses are provided in Table 11. 

Table 11. Summary of the Anhydrous Ammonia Tank Car Design Parameters

Tank Designation Tank Shell Tank Jacket Combined 

Thickness 

Tank 

Diameter

Jacket 

Standoff

Baseline 112J340W 0.6250” TC-128B 0.119” A1011 0.7440 in 111.0 in 1.0 in

Interim 112J500W 0.9180” TC-128B 0.119” A1011 1.0370 in 111.0 in 1.0 in

Two sets of analyses were performed for each of the tank designs. These include the normal side 

impacts and the 45-degree oblique side impacts with a variety of different size and shape 

impactors. The impactors include the 3x3, 6x6, 9x9, 12x12, 3x6, and 3x12 rectangular impactors 

and the 5.73-, 7.64-, 9.55-, 11.46-, and 13.37-inch-diameter round impactors. These impactors 

(shown previously in Figure 56, Figure 60, and Figure 63) provide a significant amount of 

variation in impactor size and shape. 
167

5.4.1 Normal side Impacts of AA Tank Cars

A summary of the normal side impact puncture forces and puncture energies for the baseline 

340-pound and 500-pound AA tank cars are provided in Figure 181 and Figure 182, respectively. 

The values for the puncture forces and energies are plotted against the ram face characteristic 

size defined as the square root of the area of the impactor face. The comparison of the baseline 

AA tank car designs show that the puncture forces for the 500-pound AA tank cars are on 

average approximately 40 percent greater than for the baseline 340-pound AA tank. Similarly,

the puncture energies for the 500-pound AA tank cars are on average 85 percent greater than for 

the baseline 340-pound AA tank. As expected, increasing the thickness of the commodity tank is 

an effective method for increasing the puncture resistance of the tank design.

Figure 181. Calculated Baseline AA Tank Puncture Forces for Various Size and Shape 

Impactors
168

Figure 182. Calculated Baseline AA Tank Puncture Energies for Various Size and Shape 

Impactors

5.4.2 Oblique Impacts of AA Tank Cars

In addition to the above normal side impact analyses, a set of analyses was performed with the 

full range of impactor sizes and shapes at a 45-degree oblique impact angle. The impact scenario 

is the same as that used for the EO tank cars, shown previously in Figure 117. Comparisons of 

the normal and oblique impact puncture forces and energies are provided in Figure 183 and

Figure 184 for the baseline 340-pound and 500-pound AA tank cars. The oblique puncture 

forces are approximately 50 percent of the normal puncture forces for the largest impactors. 

However, as the impactor size is reduced the differences in puncture force are also reduced. At 

the smallest 3x3-inch impactor there is very little difference between the normal and oblique 

impact puncture forces. As a result, a linear fit to the oblique puncture force data would not 

intercept the origin of the graph as used in the normal impact data. 

The puncture energies for the oblique impact show similar trends to the puncture forces. The 

puncture energies for the largest impactors are reduced by approximately 60 percent. Again, as 

the impactor size is reduced the differences in puncture energies are also reduced. For the 3x3-

inch impactor there is much less difference between the normal and oblique impact puncture 

energies. 
169

Figure 183. Comparison of Puncture Forces for Normal and Oblique Impacts

Figure 184. Comparison of Puncture Energies for Normal and Oblique Impacts
170

5.4.3 Summary of AA Tank Car Puncture Performance

The full sets of normal and oblique impact analyses were performed for both of the AA tank 

designs listed in Table 11. Thus, we have 20 different impact conditions analyzed for both of the 

AA tank designs. In this section, we summarize the relative puncture performance for the 

various designs. 

The performance of the AA tank designs is compared to the chlorine tank designs in Figure 185. 

For this comparison, the results of the normal and 45-degree oblique side impact analyses were 

used (20 analyses for each design). The puncture energy of each of the AA tank designs was 

normalized to the puncture energy for the 105J500W chlorine tank car. For comparison the 

normalized puncture energies for the 105J600W chlorine tank car are added to the graph. The 

112J500W and 112J340W AA tank cars are on average 10 percent above and 39 percent below 

the 105J500W chlorine tank car, respectively. The puncture energies for the 105J600W chlorine 

tank car were on average 37 percent higher than the 105J500W chlorine tank car. 

Figure 185. Comparison of Relative Puncture Performance of AA and Chlorine Tank 

Designs
171

5.5 Comparison of the Various Pressure tank Car designs

The full set of normal and 45-degree oblique side impacts was performed for all of the chlorine, 

EO, and AA tank car designs considered. A comparison of the puncture energies for the normal 

impacts of the various tank cars is provided in Figure 186. The designs include 500-pound and 

600-pound chlorine tank cars, 340-pound and 500-pound AA tank cars, and 300-pound, 400-

pound, and 500-pound EO tank cars. The 112J340W AA tank car has the lowest puncture 

energies. The 105J300W EO tank car has the second lowest puncture energies. However, the 

puncture energies for the 105J300W EO tank car are on average approximately 50 percent higher 

than the 112J340W AA tank car and only 15 percent lower than the 105J500W chlorine tank car. 

The puncture energies for the 105J400W EO tank car are on average 20 percent greater than the 

105J500W chlorine tank car and 10 percent higher than the 112J500W AA tank car. The 

puncture energies for the 105J500W EO tank car are the highest for any of the designs analyzed 

and on average 10 percent greater than the 105J600W chlorine tank car. 

For a further comparison of the various designs, we added the results of the oblique impacts to 

the normal impacts and normalized all of the various designs to the puncture energies of the 

105J500W chlorine tank car. The comparison for these normalized results is provided in Figure 

187. In this comparison, the puncture energies for the 105J500W EO tank car are considerably 

higher than for any of the other tank car designs. The 105J400W EO tank car puncture 

performance is above the 112J500W AA tank car and below 105J600W chlorine tank car. 

Figure 186. Comparison of Relative Puncture Performance of Various Tank Cars
172

Figure 187. Comparison of Relative Puncture Performance of Various Tank Designs

5.6 DOT Class 111 tank cars

There have been ongoing activities in the tank car community to address safety of general 

purpose tank cars. These activities were summarized in the FRA October 2011 regulatory 

update [75]. The background information from that update is summarized below.

On March 9, 2011, the Association of American Railroads (AAR), on behalf of its members and 

the Tank Car Committee (TCC), jointly petitioned the Pipeline and Hazardous Materials Safety 

Administration (PHMSA) and Transport Canada (TC) to establish new standards for DOT Class 

111 tank cars used to transport hazardous materials in packing groups I and II. The petition (P1577), which was an outgrowth of a TCC executive working group, proposed new construction 

standards and specifically recommended no modification for existing tank cars. The AAR 

agreed to forward the petition to PHMSA on behalf of the TCC as a result of a unanimous 

decision by the Committee.

On May 10, 2011, FRA met with the Railway Supply Institute’s (RSI) Tank Car Safety 

Committee to discuss improvements to tank cars used for the transportation of crude oil in unit 

trains. FRA requested this meeting to discuss improving tank car safety specific to crude oil tank 

cars given the recent increase in demand for these cars. The intent of the meeting was to spur 

discussion about innovative solutions that improve tank car safety for future changes in the 

hazardous materials transportation supply chain. The meeting resulted in the RSI members 

offering to develop an industry standard (non-regulatory) in collaboration with the AAR, the 

Renewable Fuels Association (RFA), Growth Energy, and the American Petroleum Institute 

(API). This effort is being conducted through a TCC Task Force led by FRA.
173

On June 15, 2011, an Industry Consortium consisting of RSI, AAR, API, Growth Energy and the 

RFA submitted an action plan for the continuous reduction of risk associated with rail 

transportation of Crude Oil classified as PG I and II and Ethanol. The objectives of the action 

plan are to: (1) make recommendations on derailment risk reduction actions that can be quickly 

implemented, and (2) develop a new specification for tank cars transporting the aforementioned 

commodities and allowance for new cars for these services to be constructed to the standard 

proposed in P-1577. The Industry Consortium met with FRA on July 12, 2011, to review the 

plan. The FRA concurred with the objectives and supported the proposed approach.

On July 20, 2011, at the summer AAR Tank Car Committee meeting, docket T87.6 was created 

with a dual charge to develop an industry standard for tank cars used to transport crude oil, 

denatured alcohol, and ethanol/gasoline mixtures; and to consider operating requirements to 

reduce the risk of derailment of tank cars carrying Crude Oil classified as PG I and II, and 

Ethanol. The task force has been organized into two separate working groups; the first referred 

to as the design working group, and the second referred to as the operations working group. The 

35 member design working group has met three times, August 17, September 9, and September 

23 and has made significant progress. 

The overarching objective of the working group is to maximize benefits, in this case safety, 

while minimizing cost. The working group is evaluating numerous design features intended to 

improve the survivability in accidents of tank cars transporting the referenced commodities. 

These features will include the new AAR standards outlined in CPC-1230 and petition P-1577, 

which is currently under review with PHMSA. The additional features will be considered that 

are based on the findings of forensic evaluations of recent derailments involving tank cars built 

for ethanol service. The segments of the industry represented in the working group all define 

cost differently. The tank car builders/owners define cost in terms of manufacturability, 

utilization (limited number of commodities), and suitability of design (retrofit requirements to 

comply with changing regulations). The railroads define cost in terms of imposed operating 

requirements. The shippers define cost in terms of loss of capacity and compatibility with 

existing facility and railroad infrastructure.

The analyses described in this section of the report are in support of these T87.6 activities. The 

objective is to assess the relative puncture performance of existing and proposed designs. The 

properties of the specific designs analyzed are summarized in Table 12. The initial three designs 

analyzed were: (1) a baseline 111A100W1 tank car with a 7/

15-inch A516-70 tank shell, (2) a 

CPC-1230 and P-1577 proposed design with a 0.5-inch TC128B tank shell, and (3) a proposed 2-

layer concept that had a 3⁄8-inch TC128B Tank shell with a 1/

4-inch jacket. However, for 

comparison, jacketed versions of the first two designs were added and a final design that 

considered the 3⁄8-inch shell and 1/

4-inch jacket combined into a single monolithic 5/6-inch

TC128B tank shell. 
174

Table 12. Summary of the General Purpose Tank Car Design Parameters

Tank Designation Tank Shell Tank Jacket Combined 

Thickness 

Tank 

Diameter

Jacket 

Standoff

111A100W1 7/16” A516-70 N/A 0.4375 in 111.0 in 1.0 in

111A100W3 7/16” A516-70 0.119 in A1011 0.5565 in 111.0 in 1.0 in

P1577/CPC1230 0.5 in TC-128B N/A 0.5000 in 111.0 in 1.0 in

P1577/CPC1230(1) 0.5 in TC-128B 0.119 in A1011 0.6190 in 111.0 in 1.0 in

Concept 1 (2-Layer)(2) 3/8” TC-128B 1/4” TC-128B 0.6250 in 111.0 in 1.0 in

Concept 2 (Monolithic) 5/8” TC-128B N/A 0.6250 in 111.0 in 1.0 in

Notes: (1) Note that the CPC-1230/P-1577 proposed design allows for a reduced 7/16-inch TC128B tank shell 

when a jacket is used. However, for these analyses the full 0.5-inch tank thickness was maintained to 

achieve a combined thickness that is roughly equivalent to the concept 1 and 2 designs. 

(2) The 3⁄8-inch tank thickness is less than the minimum allowable under current regulations (7/

16-inch). 

However, it was included to generate a hypothetical 2-layer design with a total combined thickness close 

to other designs. 

5.6.1 Effects of Outage Volume

The general purpose tank cars carry commodities in an unpressurized or low pressure condition. 

However, with many of the commodities they carry they can typically operate with relatively 

low outage volumes. As a result, significant pressures can develop as an impactor dents the tank 

car and reduces the tank volume. A series of analyses were performed on a general purpose car 

to analyze the effects of this outage volume and it was found to be a significant factor for the 

impact response [76]. The results of these analyses are summarized in this section. 

The outage volume effects analyses were performed on an unpressurized DOT-111A100W1 tank 

car (no jacket). The specific geometry modeled is a 24,000 gallon tank shown in Figure 188. 

The tank is 111-inch in diameter with a 44-foot, 7-inch long cylindrical shell and 2:1-ellypsoidal 

heads. The tank is constructed with a 0.4375-inch-thick A516-70 steel tank shell. The tanks are 

impacted by the standard 6x6-inch impactor (286,000 lb) at a speed of 16.2 mph. 
175

(a) Quarter-symmetry model of tank, ram, and reaction wall

(b) Mesh resolution of the tank and impact patch

Figure 188. Model of a 23,000 Gallon DOT-111A100W Tank for Analysis of Outage 

Volume Effects

The tanks in the analyses were modeled as initially unpressurized with a control volume 

algorithm used to include the pressure-volume effects. Control volume curves were generated

representative of a tank filled with an incompressible liquid to various levels up to as much as 99

percent of the tank capacity (1 percent outage). The control volume pressure curves (gauge 

pressure) for outage volumes between 1 percent and 18 percent are shown in Figure 189 and are 

generated assuming the outage volume contains an ideal gas initially at one atmosphere (absolute 

pressure). 
176

Figure 189. Control Volume Pressure Curves for Various Outages between 1 and 18 

Percent

A comparison of the impact deformations at the point of the tank shell penetration (puncture) for 

the 1 percent, 3 percent, and 9 percent outage volumes are shown in Figure 190. The comparison 

clearly shows that the larger outage volumes allow for a larger ram displacement before the tank 

is punctured. The comparison of the corresponding force-deflection behaviors and puncture 

energies with the different outage volumes is shown in Figure 191. A summary of the results 

from all of the calculations is provided in 

Table 13. The comparison shows that tanks with outage volumes between 1 percent and 18 

percent are punctured at similar force levels (392,000 to 467,000 lb) but at significantly different 

displacements (16 to 65 in) resulting in puncture energies between 256,000 and 1,370,000 ft-lb. 
177

 

(a) Deformation at puncture for 1 percent outage

 

(b) Deformation at puncture for 3 percent outage

 

(c) Deformation at puncture for 9 percent outage

Figure 190. Calculated Impact and Puncture Behaviors for Different Outage Volumes
178

Figure 191. Force-Deflection Curves and Puncture Energies for Different Outage Volumes

Table 13. Summary of Impact Analyses to Assess Outage Volume Effects

Outage 

Volume Tank Shell Impact 

Conditions

Ram Puncture 

Displacement

Puncture 

Force (lb)

Puncture 

Energy

(ft-lb)

Pressure at 

Puncture

1 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 16 in 467,000 256,000 178 psi

2 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 25 in 464,000 474,000 89 psi

3 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 28 in 452,000 537,000 53 psi

6 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 36 in 439,000 715,000 29 psi

9 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 42 in 428,000 825,000 22 psi

12 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 47 in 415,000 935,000 18 psi

15 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 53 in 410,000 1,075,000 17 psi

18 % 0.4375 in

A516-70

16.2 mph

6”x6” ram 65 in 392,000 1,370,000 21 psi

100 % 0.4375 in

A516-70

16.2 mph

6”x6” ram >110 in n/a >1,800,000 n/a
179

The calculated control volume pressures in the various analyses are compared in Figure 192 and 

the corresponding pressures at the time of tank puncture are included in 

Table 13. As expected, the displacement required to develop an internal pressure increase is 

significantly larger for the larger outage volumes. Another interesting finding is that the 

calculated pressure levels at the point of the tank puncture is significantly reduced for the larger 

outage volumes. Thus, the fraction of the impact force resulting from the impact deformations is 

larger as the puncture deformation is increased and the effects of increasing the outage volume 

would be expected to have a diminishing return. 

Figure 192. Control Volume Pressures for Impacts with Different Outage Volumes

The calculated puncture energies are plotted against the outage volume in Figure 193. Also 

included in the figure is an approximate fit to the calculated energies. The functional form of the 

fit is a puncture energy that is proportional to the square root of the outage volume. Thus, the 

effect of an incremental increase of the outage volume results in a corresponding smaller 

increase in the puncture energy as the outage volume grows larger. 

The calculated puncture energies have some natural variability about the functional fit. This 

variability can be seen by considering the impact behavior of an empty tank as shown in Figure 

194. In the empty tank analysis the impactor dents the side of the tank and the dent continues to 

grow until the impactor eventually impacts the far side of the tank and impact wall (greater than 

110-inch dent depth). As the side of the tank collapses the resistance of the tank dent oscillates 

between 150,000 and 300,000 lb as the dent grows. The timing of the puncture for the different 

outage levels would be influenced by these natural variations in the impact resistance and as a 

result the calculated puncture energies do not fall directly on the smooth functional fit. 
180

Figure 193. Effect of the Outage Volume on the Puncture Energy in Side Impacts

Figure 194. Force-Deflection Curve and Impact Energy Dissipation for an Empty Tank
181

An inspection of the puncture results in Table 13 indicates a trend of modest reduction in the 

puncture force as the outage volume is increased. The mechanism believed responsible for this 

is the uniformity of the stresses around the edge of the impact face. The profile of the impact 

damage during the indentation process for both the 1 percent and 18 percent outage calculations 

is shown in Figure 195. When the tank has a 1 percent outage volume the damage development 

is relatively uniform around the perimeter of the contact patch other than the slight 

concentrations of damage at the corners of the impact face. However, for the 18 percent outage 

the damage along the top and bottom of the impact face is greater than that along the sides of the 

impactor. In addition, the larger dent depths would allow for more plastic bending around the 

edges and corners of the impact face which could result in a less uniform stress state and damage 

development through the thickness of the tank wall. 

(a) Damage Profile for 1 percent outage (b) Damage Profile for 18 percent outage

Figure 195. Side Impact Damage Distribution for 1 Percent and 18 Percent Outage 

Volumes

5.6.2 Analyses of Different General Purpose Tank Designs

The various general purpose tank car designs, listed in Table 12, were analyzed with a suite of 

various size and shape impactors. The baseline analyses include the 3x3, 6x6, 9x9, 12x12, and 

3x12 rectangular impactors as well as the 5.73-, 7.64-, 9.55-, 11.46-, and 13.37-inch-diameter 

round impactors. The initial analyses used the 1 percent outage volume since it was considered 

to be the most critical tank condition. 

The summary of the puncture forces for the various tank designs is shown in Figure 196. There 

is an approximately 40 percent increase in the puncture forces for the strongest tank designs 

(Concepts 1 & 2 and jacketed CPC1230/P1577) compared to the weakest tank design 

(111A100W1). However, these strong tank car designs have approximately 40 percent more 

steel in the tank and jacket than the baseline 111A100W1 design. 
182

Figure 196. Correlation of the Side Impact Puncture Forces with the Impactor 

Characteristic Size

To eliminate the tank thickness effect, the puncture forces were normalized by dividing them by 

the combined tank and jacket thickness, shown in Figure 197. Although there is still some 

variation in the designs, the correlation of normalized puncture force and impactor size between 

designs is much closer. Some of the variation in the normalized puncture forces for the various 

designs comes from the difference between single and two layer (jacketed) systems. In the two 

layer systems the layers can puncture sequentially. If the sequential failures occur at 

significantly different levels of deformation, the puncture protection is not optimized and the 

normalized puncture force is lower than would be achieved by a similar single layer system. 

A summary of the puncture energies for the various general purpose tank designs is shown in 

Figure 198. The comparison shows that there is an approximately 70 percent increase in the 

puncture energies for the strongest tank designs (Concepts 1&2) compared to the weakest tank 

design (111A100W1). In addition, these improvements are greater than the 40 percent more 

steel in the Concept 1 & 2 tank designs compared to the baseline 111A100W1 design. The 

puncture energies for the jacketed CPC1230/P1577 design (with the 0.5-inch TC128B tank shell) 

are only about 10 percent lower than the Concept 2 design. 
183

Figure 197. Comparison of the Normalized Side Impact Puncture Forces

The puncture energies in Figure 198 show a correlation that is roughly linear with the 

characteristic size of the impactor. This is in contrast with the comparison of impact energies for 

the 600-pound chlorine tank car, shown previously in Figure 67, where the shape of the puncture 

energy correlation is more closely represented by the square of the characteristic size of the 

impactor. 

The differences in the puncture energy correlations of the 600-pound chlorine and general 

purpose tank cars can be seen in the comparison of the response measures. The force deflection 

curves for the 105J600 and 111A100W3 tank cars and the 3-, 6-, 9-, and 12-inch square 

impactors are compared in Figure 199. For the 105J600 tank car the ram displacement at 

puncture is approximately linearly proportional to the puncture forces (and therefore the 

impactor characteristic size). The 3-inch impactor punctures at approximately 18 in of ram 

displacement and the 12-inch impactor punctures at 55 in of displacement. However, for the 

general purpose tank car, the shape of the force deflection curves shows a response that becomes 

significantly steeper as the displacement increases and, as a result, the corresponding growth in 

the puncture displacements is reduced. The 3-inch impactor punctures at approximately 21 in of 

ram displacement and the 12-inch impactor punctures at 28 in of displacement with the 

111A100W3 general purpose tank car. 
184

Figure 198. Correlation of the Side Impact Puncture Energies with the Ram Face 

Characteristic Size

A major factor controlling these behaviors of the chlorine and general purpose tank cars is the 

initial pressure combined with the pressure buildup as the impactor dents the tank. The pressure 

displacement curves for the 105J600 and 111A100W3 tank cars and various rectangular 

impactors are compared in Figure 200. For the 105J600 tank car the initial pressure was 100 psi. 

The initial pressure helps to increase the initial stiffness of the tank. In addition, the pressure 

does not increase significantly until approximately 30–40 in of ram displacement where the 10.6

percent outage volume starts to be significantly reduced. Only the 9- and 12-inch impactors 

puncture at pressures that are well above the initial pressure (160 and 210 psi respectively for the 

9- and 12-inch impactors). 

The internal pressure effects are significantly different for the 111A100W3 tank cars. These 

general purpose tank cars were initially unpressurized resulting in a more compliant tank car. 

However, the pressure begins to build up significantly after approximately 15 in of ram 

displacement as a result of the much smaller 1 percent outage volume. All of the general 

purpose tank car analyses are influenced by this buildup of pressure within the tank. The 

pressure at burst is approximately 25 psi for the 3-inch impactor and increases steadily to 

approximately 180 psi for the 12-inch impactors. The effects of these pressures can be compared 

to the shape of the force-deflection curve for the empty general purpose tank car shown in Figure 

194, where the indentation force remains low. 
185

(a) 105J600 chlorine tank car

(b) 111A100W3 general purpose tank car

Figure 199. Calculated Force-Deflection Curves for the 105J600 and 111A100W3 Tank 

Cars
186

(a) 105J600 chlorine tank car

(b) 111A100W3 general purpose tank car

Figure 200. Calculated Pressure-Deflection Curves for the 105J600 and 111A100W3 Tank 

Cars
187

The above analyses were all performed for the assumed worst-case scenario of a 1 percent 

outage volume. However, it is desirable to also compare the trends to see if the conclusions hold 

for a more typical outage volume. To investigate this effect, an additional set of analyses was 

performed with the outage volume increased to 3 percent. The analyses were performed for the 

jacketed DOT11A100W3 tank car, the P1577/CPC1230 tank car (both with and without a 

jacket), and the Concept 1 tank car. The comparison of the puncture forces for various size 

impactors, provided in Figure 201, shows that the outage volume has very little effect on the 

puncture forces. However, the corresponding comparison of the puncture energies for the 

various impactors, provided in Figure 202, shows that the larger outage volumes result in 

significantly increased puncture energies. 

Figure 201. Comparison of Calculated Puncture Forces for 1 Percent and 3 Percent

Outage

An example of the corresponding force deflection curves for the 3-, 6-, 9-, and 12-inch square 

impactors for the 1 percent and 3 percent outage are shown in Figure 203. The comparison 

shows that the force deflection characteristics are similar with the exception that the 

displacement level, where the forces begin to rapidly increase, are significantly larger for the 3

percent outage. This can be seen also in the comparison of the tank pressure histories for various 

impact conditions, shown in Figure 204. The larger outage volume allows for larger 

displacements up to the point where the compression of the gases in the outage volume develops 

internal pressure levels that are significant. 

The relative puncture energy performance for the various tank car designs, summarized in Figure 

202, is mostly consistent between the 1 percent and 3 percent outage calculations. The one 

notable discrepancy is the Concept 1 design which had the best performance at the 1 percent 

outage level but was equivalent to the jacketed P1577/CPC1230 car at the 3percent outage. This 
188

illustrates a potential issue associated with multi-layer tank car protection systems. The multiple 

layers have the potential for protection improvements over an equivalent single layer system 

when optimized for a given scenario. However, when impacted in alternative non-optimal 

conditions, the layers can be defeated sequentially and the performance is degraded below that of 

the single layer. 

Figure 202. Comparison of Calculated Puncture Energies for 1 Percent and 3 Percent

Outage
189

Figure 203. Comparison of Force-Deflection Characteristics for 1Percent and 3 Percent

Outage

Figure 204. Comparison of Calculated Tank Pressures for Analyses with 1 Percent and 3

Percent Outage
190

5.6.3 Offset Impact Analyses

In addition to the investigation of various impactor sizes and shapes for the general purpose tank 

cars, a series of analyses were performed to investigate the effects of a vertically offset impact 

point. The analyses and BCs were identical to those used for the 600-pound chlorine tank car 

described in Section 4.6.1. The puncture forces and puncture energies for the various general 

purpose tank car designs and offset impact conditions are shown in Figure 205 and Figure 206, 

respectively. It is interesting to note that the 25-inch offset impacts result in an approximately 25

percent reduction in the puncture energies for the various general purpose tank car designs. This 

is in contrast to the 60 percent drop in puncture energy for the 25-inch offset impact on the 

105J600 chlorine tank car. 

Again in the offset impact analyses, the Concept 1 and 2 designs provide the greatest level of 

protection. An interesting result of these offset impact analyses is that the performance of the 2-

layer Concept 1 design improves relative to the monolithic Concept 2 design as the impact offset 

increases. This suggests that the 2-layer design has the potential for increased puncture 

resistance in real-world impact conditions that would include primarily offset and oblique impact 

conditions. 

Figure 205. Calculated Puncture Forces for the Various Vertical Offset Side Impacts
191

Figure 206. Calculated Puncture Energies for the Various Vertical Offset Side Impacts

5.6.4 Summary of Analyses for General Purpose Tank Cars 

The analyses discussed in the previous sections of this report show that the various proposed 

designs for general purpose tank cars (improved material selection, increased thickness, and/or 

added jackets) all resulted in increases in the puncture energies compared to the baseline 

111A100W1 tank car. As a way to quantify the magnitude of the improvements, the puncture 

energy obtained from each calculation was normalized by the puncture energy of the 

111A100W1 tank car in the identical impact scenario. These normalized puncture energies, 

along with linear fits through the data, are summarized in Figure 207. 

The normalized puncture energies show that the baseline P1577/CPC 1230 tank car (without 

jacket) results in an approximately 20 percent increase in puncture energy across the full range of 

impactor sizes. Similarly, the monolithic 5⁄8-inch-thick TC128B tank car (concept 2) has greater 

than a 50 percent increase in the puncture energy. Adding a jacket to the baseline tank car 

(111A100W3) results in an approximately 20 percent increase in puncture energy. However, the 

improvements were less for small impactors and more for large impactors. This was similar to 

the addition of a jacket on the P1577/CPC 1230 tank car where the average performance was 

approximately 40 percent above the 111A100W1 tank car. Overall, the improvements were 

greatest for the largest impactors. 
192

Figure 207. Normalized Puncture Energies for the Various Vertical Offset Side Impacts

The normalized puncture energies for the analyses of tank cars with the 3 percent outage are 

summarized in Figure 208. The normalization for these analyses is still with reference to the

111A100W1 tank car at 1 percent outage. The trends are again similar where the multi-layer 

systems are seen to perform better for large impactors than for small impactors. The biggest 

difference is that the average puncture energy improvements range from approximately 90

percent to more than 130 percent compared to the 111A100W1 tank car at 1 percent outage. 
193

Figure 208. Normalized Puncture Energies for the Various Vertical Offset 

Side Impacts
194

6 Analytical Models for Tank Car Impacts

6.1 Introduction

The detailed FE impact analyses and BW failure have been extensively applied to assess various 

tank impact conditions as described in Chapters 3 through 5 of this report. The FE modeling 

approach is very useful for understanding the mechanics of tank impacts and punctures. 

However, at times, a simplified analysis methodology or impact algorithm is useful for the 

assessment of various factors on tank impact safety. As a result, other researchers have 

developed similar analytical approaches for tank impacts [e.g. 83-85]. However, these have 

typically been developed and applied to very limited sets of impact conditions. In this chapter, 

we describe the development of tank impact algorithms. 

When assessing appropriate analysis methodologies, we examined the response characteristics of 

both head and side impacts. We found that the behaviors for these two impact conditions are 

sufficiently unique that different analysis methodologies were appropriate for the head and side 

impacts. These will be described in separate sections of this chapter. 

6.2 Head Impact Analyses 

The head impact response has several characteristics that influenced the methodology applied for 

the simplified impact algorithm. The tank head is a stiffer structure under impact and the impact 

behavior for a constrained head is relatively independent of the impact speed (minimal dynamic 

effects – see Section 3.4). The most common head impact scenario is with the motions and 

orientations of the impacted and impacting cars nearly aligned with the original direction of 

travel. As a result, the motions can be assumed to be primarily one dimensional. In addition, the 

effects of the lading model assumptions are much more significant for head impacts on 

unconstrained tanks. In light of these factors, a unique analytical methodology was used to 

develop an algorithm for head impacts. 

6.2.1 Head Impact Analysis Algorithm

The initial methodology for the head impact response algorithm was developed and validated 

against the analyses of head impacts with different constraint conditions described previously in 

Section 4.3.2. The constraint effects in head impacts are bounded by analyses of the fully 

constrained tank head and an unconstrained tank. The unconstrained tank model includes the 

entire tank which is free to translate. To bound the lading effects on the unconstrained tank,

analyses were performed where, in the first analyses, none of the weight of the lading was added 

to the tank, and in the second analysis, all of the lading mass was smeared into the tank. 

The force-deflection curves for initial set of impact analyses used in the assessment of the 1D 

impact algorithm are shown in Figure 209. The analyses are for an 18 mph impact of the 9.55-

inch-diameter round impactor. The three analyses are the constrained tank head impact and the 

two unconstrained tank models at different tank weights. 

A simple 1D algorithm was developed for the head impact tank motions with different constraint 

conditions. The algorithm uses a known force-deflection curve of the fully constrained tank 

head as a characteristic property of the tank structure. The forces are then used to update the 

tank and impactor motions. The relative displacement of the impactor and tank are used to 

calculate an updated tank depth and corresponding change in impact force. 
195

Figure 209. The Effects of BC Restraint on Head Impact Response

The 1D head impact algorithm was developed as a set of equations that are solved for a given 

impact using a time stepping methodology. The equations governing the motion are:

Time Stepping: t t t i+1 = i + ∆ (5)

Impactor Displacement:

i

i

i

i

i Xi+1 = X + ∆t *V (6)

Tank Displacement: t

i

t

i

t Xi+1 = X + ∆t *V (7)

Relative Penetration Depth: t

i

i δ i+1 = Xi+1 − X +1 (8)

Updated Impactor Force: ( ) F δ i+1 (9)

Impactor Velocity: *[ ( ) ( )] 2 1

1

+1 + +

∆ = − i i

i

i

i

i F F

M

t V V δ δ (10)

Tank Velocity: *[ ( ) ( )] 2 1

2

+1 + +

∆ = + i i

t

i

t

i F F

M

t V V δ δ (11)

Where: M1 = impactor mass, M2 = tank mass, and ∆t = time step
196

The initial application of the algorithm uses the calculated force-deflection curve of the fully 

constrained tank head as a characteristic property of the tank structure. The forces are used by a 

tabular lookup to update the impact forces based on the current dent depth of the unconstrained 

tank. An approximate value, such as a linear stiffness, could also be used. 

The force-deflection behaviors predicted by this simple one dimensional (1D) algorithm for the 

two unconstrained tank impacts with the empty and full tank weights of 61,300 and 263,000 lb,

respectively, are compared to the detailed FE analyses in Figure 210. The comparison shows 

that the simple approach of an uncoupled force versus dent depth interaction and tank motions 

describe the majority of the impact behavior. The largest deficiency of the 1D algorithm is that 

the nonlinear unloading behavior was not included in the analyses. In the detailed FEA a 

residual dent is maintained in the unloading process as the tank separates from the impactor. In 

the preliminary development of the algorithm the dent displacement unloads along the original 

loading curve. 

Figure 210. Comparison of the 1D Model and FEA Predictions for Tank Impact Forces (18 

mph Impacts)

A modification was made to the model to include the unloading effects. The approach uses a 

linear unloading modulus when the relative motions between the tank and the ram are negative. 

To estimate the unloading modulus, the plots of force versus relative displacement for the 18 

mph impacts of the loaded and empty tanks are compared in Figure 211. The comparison shows 

that a linear unloading behavior is a reasonable approximation and the unloading modulus of 

approximately 2 million lb/in is a good average value for the 600 lb tank head. 

Using the modified model with unloading, the force-deflection behaviors predicted by the simple 

1D algorithm for the two unconstrained tank impacts with the empty and full tank weights are 
197

compared to the detailed FE analyses in Figure 212. The comparison shows that the simple 

algorithm accurately reproduces the force versus dent depth interaction and tank motions for the 

full impact and unloading behavior. 

Figure 211. Comparison of the FEA Analyses with Unloading Behaviors
198

Figure 212. Comparison of the 1D Model and FEA Predictions with Unloading

(18 mph Impacts)

To confirm the performance of the algorithm, we applied it to a similar set of analyses using the 

coupler impactor model and an impact speed of 25 mph. The force deflection curves for these 

analyses are compared in Figure 213. The comparison of the detailed FEA and the simplified 1D 

head impact algorithm are shown in Figure 214. The comparison shows again that the simplified 

1D algorithm does a good job of predicting the force-deflection curves for the head impacts on 

the tank. 
199

Figure 213. The Effects of BC Restraint on Head Impact Response

(25 mph Coupler Impacts)

One of the complexities of this approach is that the detailed force-deflection curve for a fixed 

tank head was obtained from a detailed FEA and applied in a tabular lookup to obtain the 

interaction forces. An alternative approach is to use a simplified linear stiffness for the forcedeflection behavior of the tank head. We can approximate the indentation stiffness of the 600-

pound chlorine tank head and head shield at 80,000 lb/in. A comparison of this constant stiffness 

approximation to the fixed head force-deflection curves is shown in Figure 215. Using this 

constant stiffness value in the 1D algorithm we can recalculate the force-deflection behaviors for 

the empty and full tanks for the 18 and 25 mph impacts. The comparison of the constant 

stiffness 1D algorithm approximation to the detailed FEA results is shown in Figure 216. Again 

the overall agreement is quite good. The largest discrepancies are for the late time impacts on 

the loaded tanks where the force reduction from the head shield damage is not captured by the 

constant stiffness approximation. 
200

Figure 214. Comparison of the 1D Model and FEA Predictions with Unloading 

(25 mph Coupler Impacts)

Figure 215. Comparison of the FEA and Constant Stiffness Approximation
201

Figure 216. Comparison of the 1D Model and FEA Predictions with Unloading 

(Fixed Head Stiffness – 18 and 25 mph Impacts)

6.3 Side Impact Analyses 

The side impact response has several characteristics that influenced the methodology applied for 

the simplified impact algorithm. The tank is a more compliant structure under side impacts and 

the impact behavior is not independent of the impact speed (dynamic effects – see Section 3.4). 

The impact scenarios under side impacts are also typically occurring in large scale lateral 

buckling behaviors of a derailment where the motions of the various cars are chaotic. Therefore, 

the side impacts will include a greater range of variability in impact location and orientation. As 

a result, the motions will be at least two dimensional. In light of these factors, a unique 

analytical methodology was used to develop an algorithm for side impacts. 

6.3.1 Supporting FE Tank Analyses

In the previous sections of the report, many of the possible behaviors of tank cars in various side 

impact conditions have been analyzed. This information will be used to assist in the 

development and validation of the side impact model. However, there are other aspects of the 

tank response that are difficult to extract from the complex impact analyses. Therefore, a series 

of idealized tank side loading analyses were performed to address some of the physics of tank 

behaviors. 

An example of the type of additional analyses performed to assist the development of the 

analytical model is an analysis of the effects of different BCs. A series of analyses were 

previously performed to assess different tank constraint conditions as described in Section 4.3.1

of this report. Initially, a series of side impact analyses were performed where the impacted tank 

was placed against a wall, against another tank, and free to translate. The effects of the BCs
202

could be detected but under the dynamic impact conditions the effects are seen only at late times 

in the response. 

To more clearly evaluate the effects of the boundary constraints, idealized impact scenarios were 

analyzed where the tank was loaded at slow rates and under symmetrical conditions between two 

rams or two walls. Under these loading conditions, the tank has relatively linear force deflection 

curves and both fail at roughly equivalent puncture forces, as shown in Figure 217. The quasistatic loading with a 9.55-inch-diameter rams of a tank against the wall fails at a force of 

approximately 1.5 million lb and a ram displacement of approximately 40 in. The symmetric 

loading between two 9.55-inch-diameter rams fails at a similar load level and a corresponding 

ram displacement of approximately 30 in. However, the symmetric condition assumes that the 

tank is between two moving rams. Thus, the total compaction of the tank between the two ram 

faces is approximately 60 in. The calculated force-deflection for the symmetric wall loading 

develops a 1.5 million lb reaction load over a displacement of approximately 10 in (after the 

initial 4-inch standoff distance of the jacket from the tank is crushed). 

The significant difference in the compliance of the tank against either an impactor or the reaction 

wall is a result of the load application over a much larger area with the wall. This suggests that 

the size of the wall would have a significant effect on the wall reaction forces and tank 

deformations against the wall. To investigate this effect, a series of analyses were performed 

where the tank is quasi-statically compressed between walls of different sizes (symmetric 

loading analyses). 

Figure 217. The Effects of Constraint BCs on the Side Impact Response

In the initial series of analyses, the length of the wall was varied. The height of the wall is 6 ft 

and centered on the tank height. This dimension is sufficiently large that it exceeded the height 

of the contact patch of the tank and jacket for all of the analyses. The baseline width of the wall 
203

was 25 ft to match the width of the impact wall at the transportation Technology Center Inc. 

(TTCI) test facilities where the NGRTC tests were performed [1]. Additional widths analyzed 

included 1, 4, 8, 16, and 32 ft. This ranges from a very narrow width that will behave as if the 

tank were resting against a structural column to a wide width that extends nearly the full length 

of the tank shell. The models for the 1-foot and 32-foot wall length analyses are shown in Figure 

218. 

The comparison of the force-deflection curves for the analyses with the different wall lengths is 

shown in Figure 219. The comparison shows that the wall length has a significant influence on 

the stiffness of the reaction forces. This effect is not too surprising since a longer section of the 

tank cylinder is being compressed with the longer wall. To quantify the effect, we plot the 

approximate steady state stiffness of the tank compression against the wall width as shown in 

Figure 220. The comparison shows a relatively linear increase in the tank stiffness as the width 

of the wall is increased. The non-zero intercept of the ordinate in Figure 220 is probably an 

indication of the magnitude of the edge effect for the tank denting outside the direct load 

application region against the wall. 

(a) 32-foot wall length

(b) 1-foot wall length

Figure 218. Comparison of Models Used to Investigate Reaction Wall Size Effects
204

Figure 219. The Effects of Constraint Wall Width on the Reaction Loads

Figure 220. The Effects of Wall Width on the Tank Compression Stiffness

These effects of the reaction wall width can be seen in an impact analysis where the tank 

dynamics and wall interaction are significant. A series of analyses were performed for a 15 mph 
205

impact of the 9.55-inch-diameter round impactor. This impact condition is below the puncture 

threshold for the 105J600W chlorine tank car. The three BCs analyzed were a free tank (no 

wall) and a tank against the 1-foot-wide and 25-foot-wide reaction walls. The forcedisplacement curves for these three analyses are shown in Figure 221. The initial loading 

behaviors for all three analyses are identical, but the tank dynamics (unloading and reloading) at 

the large displacement levels are significantly different. 

Figure 221. The Effects of Wall Width on the Tank Impact Behavior

The effects of the wall interaction can be seen more clearly in the force-time histories for the 

three impact analyses, shown in Figure 222. With no wall, the tank loads up against the impactor 

over the initial 150 ms followed by an unloading over the next 80 ms as the tank is pushed away 

from the impactor. With the 25-foot-wide wall, the motions of the tank interact with the stiff 

wall to resist the tank motions and the rebound off the wall and reloading process starts at a time 

of approximately 180 ms (approximately halfway through the unloading). The reloading 

behavior reaches a peak force that is approximately 10–15 percent higher than the peak force in 

the initial loading. 

The impact with the 1-foot-wide reaction wall allows for a much more compliant behavior of the 

tank against the wall. As a result, the wall reaction forces develop more slowly and the tank 

rebound off the wall and reloading process starts at a time of approximately 250 ms after the 

initial impact force has completely unloaded. As a result of the longer overall impact duration, 

there is less residual impact energy and the peak force in the reloading behavior is approximately 

5 percent lower than the peak force in the initial loading. 
206

Figure 222. The Effects of Wall Width on the Impact Force Histories

An additional series of analyses were performed to investigate the effects of the wall height. The 

32-foot-wide wall was used for these analyses. The 6-foot height is sufficiently large that it 

exceeded the height of the contact patch of the tank and jacket for all of the analyses. As a 

result, smaller heights of 1, 2, and 4 ft were also investigated. The comparison of the forcedeflection curves for the analyses with the different wall heights is shown in Figure 223. The 

comparison shows that the wall height has a small influence on the stiffness of the reaction 

forces. This suggests that the shape of the tank deformations against the wall do not vary 

significantly with much smaller wall heights. A comparison of the 1-foot and 6-foot wall height 

deformations is provided in Figure 224. There are differences in the deformations of the outer 

jacket but the deformations of the commodity tanks are very similar. 
207

Figure 223. The Effects of Constraint Wall Height on the Reaction Loads

(a) 6-foot wall height (b) 1-foot wall height

Figure 224. Comparison of Tank Deformations with Different Wall Heights

The baseline side impact algorithm development was performed for the 600-pound chlorine tank 

car (105J600W) at a 100 psi internal pressure. However, for the algorithm to have greater utility, 

it needs to be applicable to other tank car designs and pressure levels. One approach to 

extending the analysis to other tank cars or pressure conditions is to develop scale factors for the 

system stiffness based on the tank design parameters. To assess these potential scale factors, a 
208

series of quasi-static compression analyses were performed on a tank where the thickness, radius, 

and pressure were varied independently. 

The analyses were performed for the quasi-static symmetric compression loading of a tank 

between two 25-foot-wide walls. In the initial series of analyses, the diameter of the tank and the 

initial internal pressure were held constant and the thickness of the tank shell was varied. The 

thickness variations evaluated were one-half, two-thirds, and five-sixths of the original 600-

pound tank shell thickness. The calculated force deflection curves for these different thickness 

tanks are shown in Figure 225. The thickness has a moderate influence on the tank stiffness 

under the side loading. 

Figure 225. The Effects of Tank Thickness on Quasi-Static Compression Loads

To quantify the effect, we determined the relative stiffness of the various tanks between 8 and 12 

in of displacement. This is a relatively linear portion of the response after the initial jacket 

compaction is complete and before the variable pressure effects become large. A plot of this 

effective tank stiffness against the tank wall thickness is shown in Figure 226. A fit shows a 

relatively linear increase in the tank stiffness with changes to the tank shell thickness. 

In the second series of analyses, the tank shell thickness was fixed (0.981-inch-thick TC128B) 

and the initial internal pressure was held at 100 psi while the diameter of the tank was varied at 

80, 100, and 120 in. The calculated force deflection curves for these different pressure tanks are 

shown in Figure 227. The comparison shows that the tank diameter has a very small influence 

on the tank stiffness under the side compression loading. 
209

Figure 226. The Effects of Tank Thickness on Quasi-Static Compression Stiffness

Figure 227. The Effects of Tank Radius on Quasi-Static Compression Loads
210

In the final series of analyses, the tank design was fixed (600 lb Cl tank) and initial internal 

pressures of 0, 50, 100, and 150 psi were analyzed. The calculated force deflection curves for 

these different pressure tanks are shown in Figure 228. The pressure has a large influence on the 

tank stiffness under the side compression loading. This is seen clearly by the comparison to the 

force-deflection behavior of the unpressurized tank. Without the pressure the force deflection 

curve is very nonlinear with reductions in the compaction stiffness at increased deflection levels. 

Figure 228. The Effects of Tank Pressure on Quasi-Static Compression Loads

To quantify the effect of the internal pressure, we determined the relative stiffness of the various 

tanks between 8 and 10 inches of displacement. This is a portion of the response after the initial 

jacket compaction is complete and before the variable pressure effects become large. A plot of 

this effective tank stiffness against the tank pressure level is shown in Figure 229. A fit shows a 

relatively linear increase in the tank stiffness with the internal pressure levels. At 100 psi the 

compaction stiffness of the tank is nearly four times that of the unpressurized tank. 
211

Figure 229. The Effects of Tank Pressure on Quasi-Static Compression Stiffness

6.3.2 Side Impact Analysis Algorithm

The approach used to formulate a side impact analysis algorithm involves developing a springmass model for the tank that can replicate the force-deflection characteristics for side loading 

against various objects (e.g. impactor, reaction wall). These loads can then be applied with 

equations for the tank kinematics under the combined actions of the loads. 

The side impact algorithm was developed with Python coding language [88] using the NumPy 

scientific computing package [89]. The equations of motion were written in matrix form as a 

series of first-order differential equations and integrated with a fixed time step. The objective is 

to fit the mode across multiple trials (impact conditions) and develop optimized spring constants 

and tank mass distribution. Wherever possible, information about the tank’s known physical 

behaviors are used as constraints. 

A schematic of the spring-mass system used for the side impact algorithm is shown in Figure 

230. The tank is represented by a series of five symmetric masses connected by springs. The 

outer masses (M1) are small and represent a small region of the tank that is involved in the initial 

interaction with the impactor or reaction structures. The secondary masses (M2) represent the 

region of the tank in the deformation zone around the impactor or reaction structures that become 

significant as the deformation progresses. The central mass (M3) is the remainder of the tank 

mass. 
212

Figure 230. Idealized Schematic of the Side Impact Spring Mass Model

The impact is modeled using a rigid impactor mass (MI) and an external nonlinear spring (KI) 

between the impactor and the outer tank mass on the impactor side. The impactor mass can be 

given different BCs such as a constant velocity or be free to decelerate based on the interaction 

forces with the tank. The general characteristics of the external spring is a relatively low 

stiffness over the initial 4 in of travel (the initial engagement and crushing of the jacket standoff) 

followed by a high stiffness spring. This effectively produces a constraint where the motions of 

the impactor and the outer mass under the impactor have equivalent displacements as long as the 

interaction force is compressive. 

The approach used for the reaction on the back side of the tank is similar to the approach used on 

the front side of the tank. The reaction mass (MR) can be given various displacement BCs (e.g. 

fixed or free to translate). For a stiff object, such as the reaction wall, the spring interacting with 

the external tank mass (M1) will be similar to the external impactor spring. This will allow for a 

small amount of tank displacement at low interaction forces while the standoff distance from the 

tank to the jacket is crushed. After the standoff is eliminated, the high external spring stiffness 

will effectively result in a displacement constraint against the reaction for the external tank mass. 

A significant difference of the reaction model is the addition of a secondary spring between the 

reaction mass and the secondary tank mass (M2) on the reaction side. This additional spring was 

necessary to model the interaction of a much larger contact area (such as the reaction wall). The 

properties of this secondary spring will be a function of the reaction wall size and if the reaction 

is localized to a small contact area this secondary spring is eliminated. 

Another physical characteristic of the impact response that was added to the spring-mass model 

is the effect of nonlinear elastic-plastic unloading behavior. When the forces between the tank 

and impactor (or reaction wall) begin to unload, they do not follow the initial loading curve. 

This is a result of the plastic deformations of the tank shell around the impact zone. The springs 

were modified to be elastic-plastic springs where they load along an initial linear path with the 

spring displacements divided into elastic and plastic components. When the interaction begins to 

unload, the unloading occurs with the elastic components of the displacement only. The model 
213

uses a ratio of 70 percent plastic and 30 percent elastic deformations during the loading process. 

A comparison of the idealized elastic-plastic spring behavior with a calculated force-deflection 

curve for an impact response with unloading is shown in Figure 231. The comparison shows that 

the 70 percent plasticity approximation is reasonable for the tank impact response. 

Figure 231. Idealized Elastic-Plastic Spring Behavior and Calculated Unloading Response

The values used for the spring-mass model parameters were derived in a two-step fitting process. 

Initially, a series of Monte-Carlo analyses were performed where the parameters were allowed to 

vary randomly, within ranges determined by physical constraints. Results were compared to a 

series of FE impact analyses and the correlation for each set of parameters was determined. 

Subsequently, the parameters that provided the best fit to the impact data were optimized by 

finding the minimum error in the parameter space around the initial Monte Carlo parameter set. 

The values that were selected based on this methodology are summarized in Table 14. 

The resulting model was then applied to simulate a series of impact behaviors and the results 

were compared to the corresponding FE analyses. For example, a series of impacts with the 

9.55-inch-diameter impactor at different impact speeds are compared in Figure 232. The 

comparison shows that the spring-mass model does a good job of reproducing the variations in 

impact behaviors produced by different speed impacts. Note that the spring-mass model does 

not include puncture prediction so the comparison of the higher speed impacts are only 

appropriate up to the point of the calculated tank punctures in the FEA. 
214

Table 14. Parameter Values for the Spring-Mass Side Impact Algorithm

Component Subcomponent Value

105J600 Tank Mass 1 (M1) 39 lb

105J600 Tank Mass 2 (M2) 4.432x104 lb

105J600 Tank Mass 3 (M3) 1.745x105 lb

105J600 Tank Spring 1 (K1) 3.465x105 lb/in

105J600 Tank Spring 2 (K2) 2.046x105 lb/in

Impactor Mass (MI) 2.950x105 lb

Impactor Spring (KI) 9.020x102 lb/in

Reaction Wall 25’x6’ Spring (KR

1) 1.955x105 lb/in

Reaction Wall 25’x6’ Spring (KR

2) 2.590x105 lb/in

Reaction Wall 25’x1’ Spring (KR

1) 1.955x105 lb/in

Reaction Wall 25’x1’ Spring (KR

2) 2.590x105 lb/in

Figure 232. Comparison of the FEA and Impact Algorithm for Different Speed Impacts
215

A similar comparison of analyses with different BCs is shown in Figure 233. In this example, a 

series of 15 mph impacts were analyzed with the 9.55-inch-diameter impactor and different 

restraint conditions on the far side of the tank. The BCs included both a free tank with no 

restraint conditions and tanks reacted by both a 25-foot-wide and 1-foot-wide reaction wall. The 

comparison shows that the spring-mass model does a good job of reproducing the variations in 

impact behaviors produced by different reaction BCs on the far side of the tank. 

Figure 233. Comparison of the FEA and Impact Algorithm for Different BCs

The initial formulation of the spring mass system was developed for a center side impact 

scenario. However, the model can be easily modified to account for an off-center impact. The 

methodology for the offset impact scenario is illustrated in Figure 234. The local tank 

deformation and development of reaction forces are assumed to be identical to the center impact 

scenario. However, the tank motions relative to the impact point are now a combination of tank 

translation and rotation about the tank center of gravity (CG). Thus, the inertial characteristics of 

the tank are used to solve for the 2D tank motions and applied to determine the relative motions 

and dent depth at the impact point.

Using this methodology, a series of impacts were analyzed for the tank with a center impact and 

impacts with 80-inch and 160-inch longitudinal offsets. The impactors used the 9.55-inchdiameter round impactor at a 15 mph constant velocity impact condition. The tank was free to 

translate and rotate as a result of the impact forces. A comparison of the calculated behaviors 

with the FEA and spring-mass models for the three different impact conditions is shown in 

Figure 235. Again, the spring-mass model agrees well with the FEA predictions of the impact 

behaviors. 
216

Figure 234. Idealized Schematic of the Offset Side Impact Model Kinematics

Figure 235. Comparison of the FEA and Impact Algorithm for Offset Side Impacts
217

A final comparison was made for the side impact analyses of a 500-pound EO tank car at 

different impact speeds. In the above comparisons, the model was developed and optimized for 

the 600-pound chlorine tank car pressurized to 100 psi. For the EO tank car, the parameters were 

modified based on the results of analyses from Section 6.3.1. The larger radius of the tank does 

not significantly modify the algorithm, as shown in Figure 227. The tank shell thickness for the 

500-pound EO tank car is 0.918 in and the corresponding thickness for the 600-pound chlorine 

tank car is 0.981 in. This results in a thickness correction in the tank stiffness of approximately 2 

percent from Figure 226. Finally, the tank pressure of 50 psi for the EO tank car compared to the 

100 psi for the chlorine tank car results in a 36 percent reduction of the tank stiffness. As a 

result, all of the spring stiffness values for the EO tank car were scaled to 63 percent of the 

original stiffness in the chlorine tank car model. The values for the masses were maintained 

from the chlorine tank model to the EO tank model. 

A comparison of the force deflection curves from detailed FE and simplified spring mass 

analyses of side impacts on an EO tank car at different impact speeds are provided in Figure 236. 

Overall, the agreement is quite good for model parameters scaled using this approximate 

methodology. This level of correlation would be suitable for many applications. However, if an 

improved fit is desired, a secondary optimization process could be performed for alternative tank 

car designs. 

Figure 236. Comparison of the FEA and Impact Algorithm for an EO Tank Car
218

6.4 Development of the Characteristic Puncture Force

The above sections describe analyses that can predict force-deflection behaviors. However, the 

point along the force-deflection curve at which the tank is punctured also needs to be determined. 

This puncture force will be dependent on both tank geometry (materials and thicknesses) and the 

impact conditions (impactor size and impact orientation). 

Our approach to developing a tank puncture criterion for the tank impact algorithm(s) was to use 

puncture data from all the detailed FE puncture analyses described in this report and develop a 

“characteristic puncture force” parameter that is a function of the impactor characteristic size 

(defined in Section 3.2.2). A collection of the calculated puncture forces for various tank and 

impact conditions is shown in Figure 237. As expected, there is a general trend in the data with 

increasing puncture loads for increasing ram characteristic size. However, for any given ram 

characteristic size, there is a large spread in puncture forces. This is because the puncture force 

for an oblique impact against a 111A100W1 tank car will be much lower than the puncture force 

for a normal impact against a 105J600 tank car. 

Figure 237. Initial Set of Tank Puncture Forces Under Various Impact Conditions

The first correction that can be made to the data is to correct for the tank design. Previous 

analyses of tank car puncture behavior have established that the puncture force for a given 

impact scenario scales approximately linearly with the combined thickness of the tank and 

jacket. This trend is consistent with the analyses performed in this study, as shown in Figure 

238. The figure plots the puncture forces for the normal impact analyses with the different 

rectangular impactors and all of the different tank cars analyzed in this study. The comparison 

shows that the puncture forces correlate well to a linear fit against the combined tank and jacket 

thickness. A similar correlation was seen for the round impactor geometries. 
219

Figure 238. Effects of Tank Thickness on Puncture Force for Various Size Impactors

One potential modification to the thickness correction is to assess the puncture performance of 

the tank and jacket thickness independently. The assumed form of the thickness correction was:

Thickness Correction: /( ) Fp = Fp Tt + ATj (12)

Where: Fp = corrected puncture force

Fp = calculated puncture force

Tt = tank thickness

Tj = jacket thickness

A = jacket thickness correction coefficient

The evaluation of the thickness correction found that the best correlation was obtained using a 

value of the 0.7 for the jacket thickness correction coefficient. Thus, the jacket material was 

found to be 30 percent less effective at resisting punctures than the material in the tank. 

However, this result may be influenced by the fact that the vast majority of the analyses used a 

0.119-inch-thick A1011 steel jacket. If we analyzed a series of double tank concepts where the 

outer tank is thicker and fabricated with a higher strength steel (e.g. TC128B) these results may 

change. The thickness corrected puncture force data for the normal side impact analyses is 

shown in Figure 239. 
220

Figure 239. Tank Thickness Correction for the Characteristic Puncture Force

A second correction that can be made to the puncture force data is to correct for the relative 

orientation of the tank and impactor face. Analyses of the effect of the impactor orientation on 

the tank puncture force were described in Section 3.2.5. Similarly, the effect of impact obliquity 

on the puncture force has been evaluated and described in Section 4.2. Figure 240 provides the 

puncture forces for the rotated and oblique impacts for the 12x12 impactor normalized by the 

corresponding force of the normal impact scenario. As the angle between the impactor and tank 

increases, the stress concentrations at the edge of the impactor increases and the puncture force 

drops. The reduction in puncture force can be fit by the following correction function:

Impactor Angle Correction: F F [1.0 0.60Sin(2θ )] p = p − (13)

Where: θ = Angle between the impactor face and 

tank wall normal
221

Figure 240. Effects of Impact Face Orientation on Puncture Force

An additional correction factor observed for the oblique impacts is an effect of the impactor 

shape. The thickness corrected 45-degree oblique impact puncture force data is shown in Figure 

241. The data shows that there are different trends for the rectangular and round impactor 

shapes. We believe this is a result of the increased concentrations in loads and deformations for 

the rectangular impactors when rotated to apply primarily an edge load. As a round impactor is 

rotated for an oblique impact there is still a relatively smooth uniform loading along the length of 

the contact zone. When we look at similar sets of analyses for 30-degree and 15-degree impacts 

we see similar trends as shown in Figure 242 and Figure 243, respectively (analyses performed 

for the 105J600 tank car only). 

The equation for the shape correction in oblique impacts is:

Shape Correction:







− − + = [( 4 10 ) (0.88 0.008 ) 4 10 ]

ˆ 5 5 F x x x

F

F p

p

p θ 

Round impactors

Square impactors

(14)

Where: Fp = thickness corrected puncture force

Fp = ˆ thickness and shape corrected puncture force

The correlation of the shape corrected 45-degree oblique impact data is shown in Figure 244. 

With this shape adjustment the normalized puncture forces for the various oblique impacts all are 

in agreement. Similarly, the shape corrected data for the 15-, -30-, and 45-degree oblique 

impacts are all compared to the normal impact data in Figure 245. With this shape correction the 

calculated puncture force for each impact angle obliquity correlates to a linear fit. 
222

Figure 241. Effects of Impactor Shape on Puncture Force in 45-Degree Oblique Impacts

Figure 242. Effects of Impactor Shape on Puncture Force in 30-Degree Oblique Impacts
223

Figure 243. Effects of Impactor Shape on Puncture Force in 15-Degree Oblique Impacts

Figure 244. Impactor Shape Corrected Puncture Forces for 45-Degree Oblique Impacts
224

Figure 245. Impactor Shape Corrected Puncture Forces for Various Oblique Impacts

A final correction factor observed for the oblique impacts is an effect of the impactor size. The 

angle correction factor, shown in Figure 240, was developed using the 12x12 in square impactor. 

At this size, the 45-degree oblique impact puncture forces were reduced by approximately 60

percent. However, when a wider range of impactors are analyzed in oblique impacts, as shown 

in Figure 245, we see that the drop in puncture force is much less for small impactor sizes. 

The size correction for oblique impacts was developed by comparing the average (fit) puncture 

force for the 45-degreee oblique impacts to the average normal impacts for various impactor 

sizes. The correction was normalized to the correction for the large 12-inch impactors. A fitting 

function was then developed for the oblique size effects data as shown in Figure 246. The 

resulting equation for the size correction in oblique impacts is:

Size Correction:

1.0 exp(2.3 0.58 )

1.0 ( )

x

f x

+ − = (15)

Where: x = ram characteristic size

When we apply all of the corrections, we obtain the characteristic puncture force correlation as 

shown in Figure 247. Using this characteristic puncture force allows us to assess the puncture 

conditions for a wide range of tank and impact parameters. The uncertainties in the puncture 

force can be assessed by comparing the range of errors in the corrected data for the detailed FE 

analyses to the puncture data fitting line. 
225

Figure 246. Impactor Size Correction for Oblique Impact Puncture Forces

Figure 247. Correlation of Characteristic Puncture Forces for Various Impact Conditions
226

7 Analysis of Real World Threats

7.1 Introduction and Background

The other chapters of this report are focused on the safety of tank cars in accidents and 

derailments. These events that can occur during rail operations are the most common events that 

lead to releases of hazardous materials in rail operations. However, the security of tank car from 

an intentional attack is also a consideration for these designs. The Department of Homeland 

Security (DHS) has done several small and full scale tests of components and tank cars subjected 

to different acts of terrorism. The objective of the analyses described in this section is to assess

the puncture performance in impacts (safety) of a protection concept developed by DHS for 

security against various threats. 

7.2 Protection System Design

The DHS, in collaboration with the Army Research Laboratory (ARL) evaluated a range of 

different tank car protection concepts against multiple security threats [78]. One of the best 

performing concepts, that also appeared to have potential for improving performance in 

accidents and derailments (safety applications) was the punched plate configuration illustrated in 

Figure 248. The system consists of two 1⁄4-inch-thick perforated panels made of High Hard Steel 

(HHS). The perforations were 3⁄8-inch diameter holes in a hexagonal pattern with 1⁄2-inch spacing 

between the nearest neighbor hole positions. The two panels are used in an offset configuration 

as illustrated in Figure 248(b). 

Material test data for the HHS was not made available for this study. Instead, DHS/ARL 

provided parameters for a simplified Johnson-Cook constitutive model in LS-DYNA [46], which 

they claimed was validated against test data [79]. This validated constitutive model was used to 

simulate a tensile test which was used as the material “test” data to develop the constitutive and 

failure parameters that were used in the puncture analyses. The simulated tensile test behavior 

for the HHS is shown in Figure 249. The methodologies used to develop the constitutive and 

failure parameters were described in Chapter 2. 

The analyses of the HHS show that it has a very high yield strength compared to typical tank car 

structural materials. The yield strength for the HHS is approximately 230 ksi and the elongation 

calculated for the round bar tensile test was approximately 16 percent. The greatest uncertainty 

in the calculated tensile behavior is the elongation value which is sensitive to the specimen 

geometry and gauge length used in the test or analyses (a 2-inch gauge length was used for the 

analysis). A confirmation of the elongation for this configuration cannot be made without access 

to material test data. 

For analysis of the impact and puncture behavior of a tank with the punched plate protection 

system, some additional model development was required. In the detailed impact zone, the 

geometry of the punched plates will be explicitly modeled. However, outside the impact zone, 

an effective material is needed that will have the equivalent stiffness and strength of the punched 

plates but can be modeled with larger shell elements. To create the “effective” material model,

we simulated a tensile test on a section of punched plate material. The simulation of the tensile 

test on the punched plate specimen is shown in Figure 250. The calculated engineering stressstrain curve for the punched plate tensile test is compared to that of the solid HHS material in 

Figure 251. The comparison shows that the punched plate geometry both significantly reduces 
227

the stiffness and strength compared to the solid material. The effective elastic modulus is less 

than 20 percent of that for the solid steel. The effective yield stress is reduced to approximately 

40 ksi and the engineering ultimate stress for the punched plate material is approximately 65 ksi 

with an elongation of 20 percent. 
228

(a) Punched plate geometry

(b) layered punched plates

Figure 248. Configuration of the Layered Punched Plate Protection Concept [78]
229

Figure 249. Simulated Tensile Test Behavior for the High Hard Steel

(a) Initial configuration

(b) Deformed specimen (before failure)

(c) Calculated failure mode

Figure 250. Simulated Tensile Behavior of the Punched Plate Material
230

Figure 251. Comparison of the Solid and Punched Plate Tensile Behavior

7.3 Side Impact Puncture Analyses

The side impact puncture analyses were performed for a 105J500 chlorine tank car protected 

with the punched plate system. The impact and puncture analyses use the methodologies 

described previously in Chapter 3 of this report. The model for a representative normal side 

impact analysis with the punched plate system is shown in Figure 252. The model has been 

reflected about the two symmetry planes used for the normal impacts. The detail of the impact 

patch shown in the figure illustrates the region of the impact patch where the punched plate 

geometry is explicitly modeled. Within that region, the model has a uniform mesh density with a 

characteristic element size of approximately 0.040 in (1 mm), as shown in Figure 253. Each 

layer of the punched plate has 6 elements through the 0.25-inch-thickness. This results in 

elements with an approximate 1:1 aspect ratio. 

The puncture behavior of the tank with the punched plate protection system is shown in Figure 

254. The example shown is for the 6x6-inch square impactor at an impact speed of 20 mph. The 

puncture response is very similar to that of tank cars with more traditional jackets. The side of 

the tank and punched plate system are dented inward by the impact. At sufficiently large 

displacements and forces the impactor punctures the tank. 

More detailed images of the impact zone and damage development for the 6x6-inch impactor and 

the punched plate system are shown at corresponding times in Figure 255 and Figure 256. The 

images in Figure 255 show both the tank wall and punched plate layers and the images in Figure 

256 show only the punched plate layers. The comparison shows that the punched plate system is 

penetrated by the impactor prior to the failure of the tank wall. This is common of most tank 

designs that the jacket fails at a time before the tank wall. 
231

Figure 252. Model for the Punched Plate Concept Impact Analyses

Figure 253. Details of the Model for the Punched Plate Impact Patch
232

Figure 254. Impact and Puncture of the 500-Pound Chlorine Car and Punched Plate 

Protection
233

(a) Early impact (b) After jacket failure (c) Tank puncture

Figure 255. Calculated Tank Impact Damage and Puncture Initiation

(a) Early impact (b) After jacket failure (c) Tank puncture

Figure 256. Calculated Punched Plate Impact Damage and Puncture Behavior

A summary of the side impact analyses performed for the 105J500 chlorine commodity tank 

protected by the punched plate concept is provided in Table 15. The table summarized the 

impact conditions and calculated puncture forces and energies for the analyses. The puncture 

forces and puncture energies for the 500-pound tank with the punched plate protection are 

compared to those of traditional 500- and 600-pound tanks in Figure 257 and Figure 258, 

respectively. The comparisons are for normal side impacts using the full range of impactor sizes 

and shapes as described in Section 3.2.1. For the 600-pound tank car, both the lower and higher 

impact speeds, discussed in Section 3.3 of this report, are included in this comparison. The 

impact velocities selected for the punched plate concept analyses are the same as the higher 

speed analyses of that section. 

The comparison of the puncture forces for the different tank car designs, as seen in Figure 257, 

shows that the punched plate protection system increases the puncture forces over the 11-gauge 

jacket for the 500-pound commodity tank. However, the increase in puncture forces is 

approximately 10 percent. The puncture forces for the 500-pound tank and punched plate system 

are still approximately 15 percent lower than those of the 600-pound commodity tank with the 

11-gauge jacket. 
234

Table 15. Summary of Side Impact Analyses for the 105J500 Tank 

and Punched Plate Concept

Calculation Tank 

Type

Tank 

Shell

Shell 

Jacket 

Impact 

Conditions

Internal 

Pressure

(psi)

Puncture 

Force (lb)

Puncture 

Energy (ftlb)

R91A 500 lb Cl 0.777 in

TC128B

Punched 

Plate

20 mph

6”x6” ram 100 psi 9.530E+05 1.390E+06

R91B 500 lb Cl 0.777 in

TC128B

Punched 

Plate

30 mph

12”x12” ram 100 psi 1.848E+06 4.260E+06

R91C 500 lb Cl 0.777 in

TC128B

Punched 

Plate

25 mph

9”x9” ram 100 psi 1.402E+06 2.770E+06

R91D 500 lb Cl 0.777 in

TC128B

Punched 

Plate

15 mph

3”x3” ram 100 psi 4.910E+05 3.260E+05

R91E 500 lb Cl 0.777 in

TC128B

Punched 

Plate

15 mph

3”x6” ram 100 psi 8.090E+05 9.770E+05

R91F 500 lb Cl 0.777 in

TC128B

Punched 

Plate

25 mph

3”x12” ram 100 psi 1.199E+06 2.130E+06

R91G 500 lb Cl 0.777 in

TC128B

Punched 

Plate

20 mph

5.73 in dia. 100 psi 8.350E+05 8.600E+05

R91H 500 lb Cl 0.777 in

TC128B

Punched 

Plate

20 mph

7.64 in dia. 100 psi 1.125E+06 1.820E+06

R91I 500 lb Cl 0.777 in

TC128B

Punched 

Plate

25 mph

9.55 in dia. 100 psi 1.318E+06 2.720E+06

R91J 500 lb Cl 0.777 in

TC128B

Punched 

Plate

30 mph

11.46 in dia. 100 psi 1.535E+06 3.110E+06

R91K 500 lb Cl 0.777 in

TC128B

Punched 

Plate

35 mph

13.37 in dia. 100 psi 1.725E+06 3.400E+06

The comparison of the puncture energies for the different tank car designs, as seen in Figure 258, 

shows that the punched plate protection system is again closer to those of the 500-pound chlorine 

tank car than the 600-pound tank car. This result is roughly consistent with the amount of steel 

added to the various systems. The punched plate geometry removes approximately 50 percent of 

the steel in each plate. Thus, the total system is roughly equivalent in weight to a monolithic 

0.25-inch-thick steel jacket, and the punched plate system adds only 0.13 in to the effective 

jacket and tank combined thickness. By comparison, the increase from the 500-pound to the 

600-pound commodity tank adds 0.204 in to the tank thickness. 

This comparison shows that the punched plate system is reasonably effective for tank car safety 

applications. It does not result in significant improvements in puncture resistance but the 

performance is consistent with the modest levels of added weight for the concept. None of the 

analyses indicate that the punched plate protection system would introduce new damage modes 

that could result in reductions in the tank puncture resistance. 
235

Figure 257. Comparison of Side Impact Puncture Forces for Different Tank Designs

Figure 258. Comparison of Side Impact Puncture Energies for Different Tank Designs
236

To evaluate the effectiveness of the punched plate at increasing the tank resistance, additional 

analyses were performed where the punched plate system was replaced by 1⁄4-inch jackets that 

have roughly equivalent weight. The jacket materials considered were TC128B and HHS. A 

comparison of the 6x6-inch square impactor force-deflection behavior for these two jacket 

designs with those of the baseline 11 gauge jacket and the punched plate system is shown in 

Figure 259. The comparison shows that the punched plate system has a higher puncture energy 

than the 1⁄4-inch TC128B jacket but a lower puncture energy than the monolithic 1⁄4-inch HHS 

jacket. 

Figure 259. Comparison of Side Impact Puncture Energies for Different Tank Designs
237

8 Conclusion

This report describes results from a research program to improve the safety and security of 

railroad tank cars. The approach used in the research and development program was to apply a 

tank impact and puncture prediction capability using detailed finite element analyses. The 

capability was developed and validated previously in the NGRTC program. In this study, the 

analyses were applied to investigate the tank puncture behaviors for a wide range of impact 

conditions. 

In the initial phase of this program, different size and shape impactors were investigated. A new 

parameter was developed to characterize the effective size of the impactor. This impactor 

characteristic size is the square root of the area of the impactor face. The impactor characteristic 

size parameter provides a good correlation for the puncture potential of different idealized 

impactor sizes and shapes. A linear correlation was found between the puncture force and the 

ram characteristic size. This observation is consistent with the primary failure mechanism of 

exceeding the shear capacity around the perimeter of the impact patch. 

In the second phase of the program, complex shape impactors such as a rail section and coupler 

head were investigated. The impactor characteristic size parameter was useful for quantifying 

the puncture potential of these complex impactors. For example, a rail section impactor has a 

characteristic size of approximately 5 in in a normal impact configuration. Alternatively, the 

puncture potential of a more complex impactor, such as a coupler head, can be quantified in 

different impact conditions using the characteristic size. Here the impact behavior is 

complicated by an impact face profile that is not flat. As a result, the puncture force can vary

significantly with relatively small changes in the orientation of the impact. For a limited set of 

impact orientations analyzed, the coupler head was found to have a characteristic size as small as 

5 in and as large as 12 in. 

In the third phase of the program, more general impact conditions were investigated. These 

include offset and oblique impacts with different tank boundary conditions. Two different series 

of analyses were performed to investigate the effects of the impactor orientation. The first series 

of analyses rotated the impactor orientation and maintained the normal impact trajectory. The 

second series of analyses used an oblique impact configuration. Both sets of analyses found that 

the rotation of the impactor face relative to the tank surface results in load concentrations at the 

edge of the impactor and significant reductions in the puncture force. As a result, the 

characteristic size of the 12x12 impactor drops from 12 in in the normal impact to approximately 

4.5–5 in in an edge impact. The characteristic size is further reduced to approximately 3 in for 

the corner impact. These results show that impacting objects with corners and edges can have 

the penetration potential of a much smaller object if the orientation of the impactor concentrates 

the loading to the edge or corner. 

A series of analyses were performed to investigate the effects of the constraint level on the tank 

side impact response. The analysis of the different tank boundary constraints shows that the 

effects on the late time behavior and puncture energy can be significant. However, the initial 

portion of the loading is dominated by the inertial resistance of the tank and the puncture will 

occur in this initial phase of the impact for many combinations of impactor sizes and impact 

speeds. Thus, for many side impacts, the constraint on the back side of the tank is not 

significant. 
238

A corresponding series of analyses were performed to investigate the effects of the constraint 

level on the tank head impact response. The constraint conditions were found to be more 

significant for head impacts. The tank constraint effects for head impacts are observed much 

earlier in the response than for side impacts for two reasons. The first is that the tank cylinder is 

much stiffer in axial loading compared to lateral loading. As a result, the head impact forces are 

very rapidly transmitted to translations of the tank center of gravity (CG). The second reason for 

increased constraint effects in head impacts is the behavior of the lading in head impacts. For the 

duration of the impact, only a fraction of the total lading mass is coupled to the motions of the 

unconstrained tank. Analyses to quantify the lading effect show that less than 10 percent of the 

lading is coupled to the motion of the tank for a typical head impact scenario. 

The fourth phase of the program was to assess the performance of a tank protection concept 

developed for real world threats. The Department of Homeland Security (DHS) evaluated

several proposed tank car protection concepts subjected to different acts of terrorism. A 

promising design identified by DHS was analyzed to assess the puncture performance in a 

variety of impact scenarios involving derailments and collisions. The analysis shows that the 

DHS concept can provide a similar level of puncture protection in safety scenarios compared 

with other protection concepts examined with an equivalent added weight. 

The final phase of this program was to evaluate other tank car designs. The primary tank design 

used in Phases 1–3 of this report is the 105J600 chlorine tank car required by the interim rule. 

The condition used for the analyses was a tank at 78 o

F resulting in a 100 psi internal pressure 

and outage volume of 10.6 percent. In this final phase, analyses were performed to both assess 

the effects of the internal pressure and outage volume, as well as the changes in the tank 

dimensions that occur for different commodity tank designs. 

A set of analyses was performed to assess the effects of the temperature of the tank and lading 

for the chlorine tank car. As the equilibrium temperature of the tank rises, the vapor pressure 

increases and the liquid density is reduced. A decrease in the liquid density will produce an 

increase in the liquid volume with a corresponding reduction in the outage volume. Both 

increasing the pressure and reducing the outage can reduce the puncture resistance of a tank car. 

The condition analyzed is a 105J600W chlorine tank car at an equilibrium temperature of 105 oF. 

This temperature increases the internal vapor pressure for the tank to 155 psi and lowers the 

corresponding outage volume for a tank loaded to the specified limit of 7.5 percent. These 

compare with the 100 psi internal pressure and outage volume of 10.6 percent at a tank 

temperature of 78 o

F. On average, the increase in temperature dropped the puncture energies by 

20 percent. However, the puncture energies for smaller impactor sizes are more similar at the 

two temperatures. This is because the impact response for small impactors is dominated more by 

the structural stiffness. The internal pressure (and pressure increase) plays a smaller roll for the 

small dent sizes from small impactors prior to puncture.

In addition to the analyses performed on the 105J600 tank car, a series of other tank car types 

were analyzed. The evaluations were performed for the 500-pound chlorine tank car, the 340-

and 500-pound AA tank cars, and 300-, 400-, and 500-pound EO tank cars. A full set of normal 

and 45-degree oblique side impacts was performed for each of the chlorine, EO, and AA tank car 

designs considered. For comparison of the various designs, we normalized the calculated 

puncture energies from all of the various designs to those of the 105J500W chlorine tank car. 
239

In this comparison, the puncture energies for the 105J500W EO tank car are considerably higher 

than for any of the other tank car designs. The EO tanks have relatively high puncture energies 

as a result of the lower tank pressures and larger diameter tanks. The 105J500W, 105J400W, 

and 105J300W EO tank cars have puncture energies on average 82 percent higher, 17 percent 

higher, and 12 percent lower, respectively, than the 105J500W chlorine tank car. The puncture 

energies for the 105J600W chlorine tank car were on average 37 percent higher than the 

105J500W chlorine tank car. The 112J500W and 112J340W AA tank cars are on average 10 

percent above and 39 percent below the 105J500W chlorine tank car, respectively. 

The FE modeling approach used for all of the above impact analyses is very useful for 

understanding the mechanics of tank impacts and punctures. However, at times, a simplified 

analysis methodology or impact algorithm is useful for the assessment of various factors on tank 

impact safety. In this study, we developed analytical tank impact algorithms that can be applied 

to future analyses of tank car safety. When assessing appropriate analysis methodologies, we 

examined the response characteristics of both head and side impacts. We found that the 

behaviors for these two impact conditions are sufficiently unique that different analysis 

methodologies were appropriate for the head and side impacts. The resulting models were 

compared to the FE analyses of different impact conditions and found to provide good 

correlation with the FE results. 
240

9 Recommendations for Future Work

This research program assessed the puncture behaviors of tank cars under general impact 

conditions. A wide range of tank cars and impact scenarios were evaluated. During the 

performance of this study, a few areas were identified where the results of this study could be 

applied or the range of the study expanded. These recommendations for future work are 

summarized here. 

1. The analyses methodologies applied in this study used primarily the simple 

commodity tank structure. The effect of various attachments such as the top fittings 

or sill and bolster were not investigated. Some analyses to assess the effect of 

different attachment designs on the puncture performance of tank cars would be 

useful.

2. Evaluation of current tank car safety regulations and development of improved 

performance-based criteria is needed. An example that was partially investigated in 

this study is the tank car head impact protection requirements. The evaluation found 

that there is a significant amount of variability and uncertainty allowed under the 

current head impact test requirements. A rigorous evaluation of the current 

requirements could be used to develop simplified performance-based criteria that

would both ensure a desired level of puncture protection as well as reproducible and 

replicable conditions for testing and analyses of the performance. 

3. Welds have been previously identified as potential failure sites in tank cars. For 

example, the guidelines for emergency responders require different safety procedures 

if the damage from an accident or derailment crosses a weld. However, there has 

been little work done to assess the performance of welds in impact conditions and 

evaluate if modified welding procedures can improve tank car safety. A study to 

characterize current tank car weld performance and assess modifications to the 

current weld procedures (e.g., overmatched and undermatched welds) would be 

useful.

4. The methodologies applied in this study would be applicable to forensic 

investigations of real world tank failures. A research program to forensically 

reproduce past (and/or future) tank car failures could identify tank car modifications 

for potential safety improvement. The forensic investigations would identify the 

loads and mechanisms that resulted in accidental releases of hazardous materials. 

The analyses can then be used to investigate different tank designs or protection 

concepts that would eliminate the failures. 

5. A final area of investigation identified involves developing a relationship between the 

results of this research program with the probabilistic data of accidents, derailments, 

and releases for tank cars. A correlation of the statistical accident database with the 

analyses in this study could potentially identify the critical impact scenarios that 

produce the greatest number of releases and assist in the optimization of tank car 

designs for safety. 
241

10 References

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Technical Report, Prepared for the Next Generation Railroad Tank Car (NGRTC) Project, 

January, 2009.

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Proceedings of the 2007 ASME Rail Transportation Division Fall Technical Conference, 

RTDF2007-46013, September 2007.

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Dakota; January 18, 2002,” Railroad Accident Report NTSB/RAR-04/01.

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Appendix A. Tank Head Puncture Resistance Performance Standards

49 CFR § 179.16

Tank-head puncture-resistance systems.

(a) Performance standard. When the regulations in this subchapter require a tank-head 

puncture-resistance system, the system shall be capable of sustaining, without any loss of lading, 

coupler-to-tank-head impacts at relative car speeds of 29 km/hour (18 mph) when:

(1) The weight of the impact car is at least 119,295 kg (263,000 lb);

(2) The impacted tank car is coupled to one or more backup cars that have a total weight of at 

least 217,724 kg (480,000 lb) and the hand brake is applied on the last “backup” car; and

(3) The impacted tank car is pressurized to at least 6.9 bar (100 psig).

(b) Verification by testing. Compliance with the requirements of paragraph (a) of this section 

shall be verified by full-scale testing according to appendix A of this part.

Appendix A to Part 179—Procedures for Tank-Head Puncture-Resistance Test

1. This test procedure is designed to verify the integrity of new or untried tank-head punctureresistance systems and to test for system survivability after coupler-to-tank-head impacts at 

relative speeds of 29 km/hour (18 mph). Tank-head puncture-resistance is a function of one or 

more of the following: head thickness, jacket thickness, insulation thickness, and material of 

construction.

2. Tank-head puncture-resistance test. A tank-head puncture-resistance system must be tested 

under the following conditions:

a. The ram car used must weigh at least 119,295 kg (263,000 lb), be equipped with a 

coupler, and duplicate the condition of a conventional draft sill including the draft 

yoke and draft gear. The coupler must protrude from the end of the ram car so that 

it is the leading location of perpendicular contact with the impacted test car.

b. The impacted test car must be loaded with water at 6 percent outage with internal 

pressure of at least 6.9 bar (100 psig) and coupled to one or more “backup” cars 

which have a total weight of 217,724 kg (480,000 lb) with hand brakes applied on 

the last “backup” car.

c. At least two separate tests must be conducted with the coupler on the vertical 

centerline of the ram car. One test must be conducted with the coupler at a height of 

53.3 cm (21 in), plus-or-minus 2.5 cm (1 in), above the top of the sill; the other test 

must be conducted with the coupler height at 79 cm (31 in), plus-or-minus 2.5 cm 

(1 in), above the top of the sill. If the combined thickness of the tank head and any 

additional shielding material is less than the combined thickness on the vertical 

centerline of the car, a third test must be conducted with the coupler positioned so 

as to strike the thinnest point of the tank head.
249

3. One of the following test conditions must be applied:

Minimum weight of attached 

ram cars in kg (lb)

Minimum velocity of 

impact in km/hour (mph) Restrictions

119,295 (263,000) 29 (18) One ram car only

155,582 (343,000) 25.5 (16) One ram car or one car plus 

one rigidly attached car

311,164 (686,000) 22.5 (14) One ram car plus one or more 

rigidly attached cars

4. A test is successful if there is no visible leak from the standing tank car for at least one hour 

after impact.
250

Abbreviations and Acronyms (Example)

1D One Dimensional

AA Anhydrous Ammonia

AAR Association of American Railroads

API American Petroleum Institute

ARL Army Research Laboratory

BC Boundary Condition

BW Bao-Wierzbicki

CG Center of Gravity

DHS Department of Homeland Security

DOT Department of Transportation

EO Ethylene Oxide

EPFM Elastic-Plastic Fracture Mechanics

FE Finite Element 

FEA Finite Element Analysis

FRA Federal Railroad Administration

FMVSS Federal Motor Vehicle Safety Standards

HHS High Hard Steel

LFM Local Fracture Mechanics

LEFM Linear Elastic Fracture Mechanics

NGRTC Next Generation Railroad Tank Car 

PHMSA Pipeline and Hazardous Materials Safety Administration

RAIRS Railroad Accident and Incident Reporting System

RFA Renewable Fuels Association

SPH Smoothed Particle Hydrodynamics

TC Transport Canada

TCC Tank Car Committee

TTCI Transportation Technology Center, Inc.