Quantifying and Enhancing Puncture Resistance in 

Railroad Tank Cars Carrying Hazardous Materials

Phase II: Development and Validation of a Puncture Resistance 

Evaluation Methodology

Prepared for

Transportation Issues Team

The Chlorine Institute

Arlington, VA

Prepared by

Ted L. Anderson, Ph.D., P.E.

Brian Rose, Ph.D., P.E.

Quest Reliability, LLC

Peter C. McKeighan. Ph.D.

Southwest Research Institute

Steven W. Kirkpatrick, Ph.D.

Applied Research Associates, Inc.

December 20, 2007

2465 Central Ave., Suite 110

Boulder, CO 80301

(303) 415-1475

(303) 415-1847 (fax)

www.questreliability.com
1

EXECUTIVE SUMMARY

This report summarizes Phase II of a project to study puncture resistance in tank cars that carry 

hazardous cargo. This project consists of both material testing and extensive finite element 

simulation. The former includes a newly-developed impact test on unnotched samples, which 

appears to be a suitable compromise between conventional Charpy tests, which do not give a 

direct measure of puncture resistance, and full-scale collision experiments, which are very 

expensive.

Finite element simulations were performed on both laboratory tests and full-scale tank cars. The 

former were used to calibrate the material fracture model used in this study. A large number of 

tank car impact simulations were performed. Several key variables were considered, including 

internal pressure, the size of the striker, friction, lading mass, and material toughness. A series 

of collision simulations on cars made from traditional tank car steel were used in conjunction 

with the accident database maintained by the RSI-AAR Railroad Tank Car Safety Research and 

Test Project to benchmark the statistical distribution of the intensity of collision/puncture events. 

This calibration exercise enabled the authors to evaluate the effect of material properties and 

design features on the probability of lading loss in an accident. The finite element puncture 

simulation procedure developed in this study was benchmarked against a recent full-scale test 

conducted at the Transportation Technology Center, Inc. (TTCI). The simulation predicted the 

puncture energy in the full-scale test to within a few percent.

A series of tank car collision simulations compared the behavior of traditional tank car steel with 

modern, high-toughness alternatives. These analyses indicated that roughly a 2-fold increase in 

puncture energy is possible with improved steels. This translates to a 60-fold decrease in lading 

loss probability for shell impacts and a 6-fold decrease in lading loss probability for head 

impacts.

The material model for simulating ductile fracture that was used in this study was compared 

qualitatively with an alternative model that has been adopted by the Volpe National 

Transportation Systems Center. Further work is necessary to compare these models 

quantitatively to determine if one model is more suitable for tank car collision simulation.
2

CONTENTS

1 BACKGROUND 3

2 MATERIAL TESTING 4

2.1 Tensile Testing 4

2.1.1 TC 128B Steel 5

2.1.2 HSLA Steels 5

2.2 Impact Tests on Unnotched Specimens 19

3 MATERIAL MODEL CALIBRATION 27

3.1 Gurson-Tvergaard Ductile Fracture Model 27

3.2 Charpy Specimen 28

3.3 BFCM Specimen 30

3.4 Large-Scale Calibration Specimens 40

4 TANK CAR IMPACT SIMULATION PROCEDURES 48

5 TANK CAR IMPACT SIMULATION RESULTS 73

5.1 Parametric Study 73

5.1.1 Effect of Internal Pressure 74

5.1.2 Effect of Striker Size 74

5.1.3 Effect of Initial Velocity 74

5.1.4 Effect of Friction 74

5.1.5 Effect of Lading Mass 75

5.2 Calibration to Accident Database 84

5.3 Effect of Material Toughness on Lading Loss Probability 94

5.4 Benchmarking to Full-Scale Test Results 102

6 DISCUSSION OF RESULTS 106

6.1 Triaxiality and Fracture Models 106

6.2 Effect of an Energy-Absorbing Insulation Layer 109

6.3 Developing a Performance Standard 110

7 CONCLUSIONS 113

8 REFERENCES 114

9 APPENDICES 115

9.1 Appendix A – Summary of Literature 116

9.1.1 Tank Car References 116

9.1.2 Relevant Research in Non-Rail Applications 117

9.1.3 Conclusions 119

9.1.4 Bibliography 120

9.2 Appendix B – Tabulated Results for Tank Car Simulations. 129
3

1 BACKGROUND

When a derailment or other rail accident occurs, the resulting collision forces can lead to a loss 

of lading from tank cars. While such an event is always undesirable, it is particularly damaging 

when the cars contain a hazardous material. There is a strong desire in the rail industry to 

develop a new generation of tank cars that are more resistant to puncture in the event of an 

accident. 

A Phase I study of factors affecting puncture resistance was recently completed [1]. Key 

conclusions and recommendations from this study include the following:

 While low-temperature toughness properties are desirable in tank car steels, it is 

primarily the upper shelf toughness that governs puncture resistance.

 In previous accidents, the probability of lading loss through head or shell punctures was 

influenced by section thickness, as well as the presence or absence of head shields and/or 

jackets.

 Based on trends in the accident database, puncture resistance can be improved by various 

design modifications, including increasing section thickness and incorporating head 

shields. However, incorporation of more puncture resistant steels may also be an 

effective means to reduce the likelihood of lading loss in future accidents.

 Although it is likely that improved steels will enhance puncture resistance, the potential 

benefit of such materials has not been quantified.

 Computer simulation, benchmarked by suitable experiments, is an effective means to 

assess the effect of tank car design and material properties on puncture resistance.

This report describes the results of Phase II of this project, which consisted of both materials 

testing and finite element computer simulation. Material testing included tensile testing at 

various strain rates, which was necessary to feed into the finite element models. In addition a 

new material test, which entails impact loading of unnotched specimens, was developed in this 

project to characterize puncture resistance of steels. A literature search was also performed, the 

results of which are summarized in Appendix A.

Finite element simulations were performed on both laboratory specimens and full-scale tank 

cars. The former was used to calibrate the material fracture model that was applied to the latter. 

A large number of simulations of tank car impact/puncture events have been performed. The 

effect of a number of variables were studied, including tank car dimensions, internal pressure, 

striker size, friction, lading mass, and material properties. Simulation results were calibrated to 

the accident database maintained by the RSI-AAR Railroad Tank Car Safety Research and Test 

Project. The simulation procedure was also benchmarked against a recent full-scale experiment 

performed at Transportation Technology Center, Inc. (TTCI) in Pueblo, Colorado.

One of the main purposes of the extensive computer simulations and material testing was to 

quantify the effect of design parameters and material toughness on puncture resistance in tank 

cars. The procedures developed herein can be used to assess a proposed tank car design against a 

suitable performance standard.
4

2 MATERIAL TESTING

Two types of mechanical tests were performed in this study:

1. Tensile tests at various strain rates.

2. Impact tests on unnotched specimens.

The former was used to define the stress-strain behavior for the finite element simulations. The 

latter was used to benchmark and validate the ductile fracture material model.

2.1 Tensile Testing

Tensile testing was performed on several steels over a range of strain rates. True stress-strain 

curves were fitted to these data and were input into the various finite element simulations.

Two samples of traditional tank car steel, TC 128B, were tested. As indicated in Table 2.1 

below, these samples are normalized shell plates from two tank cars built in 1994.

Tensile testing was performed on three high strength-low alloy (HSLA) steels. These materials 

are listed in Table 2.2

TABLE 2.1

Samples of TC 128B steel used for tensile testing.

Sample ID Car ID Year Built Sample 

Location

Heat 

Treatment

Specimen 

Orientation

A PROX 31153 1994 Shell Normalized Transverse

B PROX 31218 1994 Shell Normalized Transverse

TABLE 2.2

High strength-low alloy (HSLA) steels tested in the present study.

Material Reported 

Thickness, in

Notes

A 710 0.75 Fabricated by Mittal Steel ISG Plate Inc, Melt U4749, 

Used for a bridge in Lake Villas, IL (Fine/Vanadium-Nb)

HPS 70 0.75 Fabricated by IPSCO

HPS 100 1.125 Fabricated by Mittal Steel ISG Plate Inc (supplied by M. 

Manohar)
5

2.1.1 TC 128B Steel

Figure 2.1 shows typical true stress-strain curves for TC 128B steel at various strain rates. The 

stress axis is indexed by the 0.2% offset yield strength. The strain hardening behavior is 

insensitive to strain rate but the Luder’s strain (i.e., the extent of the yield plateau region) does 

appear to be rate dependent. 

Figure 2.2 is a plot of yield strength versus strain rate. The data for the two plates, A and B, are 

indistinguishable from one another, so a single power-law fit for the combined data set was 

appropriate in this case. Figure 2.3 shows the correlation between the Luder’s strain and the 

strain rate.

The power-law expressions on the plots in Figs. 2.2 and 2.3, combined with a fit of the hardening 

portion of a typical stress-strain curve (Fig. 2.1), were used to develop the plastic constitutive 

relationship for TC 128B steel. The result of this exercise is plotted in Fig. 2.4. Note that the 

upper yield point was neglected in the fitting process. The curves in Fig. 2.4 were input into the 

various finite element simulations. The stress-strain behavior illustrated in Fig. 2.4 was assumed 

to apply to all heats of TC 128B steel. This is a reasonable assumption, since tensile 

requirements for TC 128B steel have not changed over the years. Improvements in alloy 

cleanliness (i.e., reductions in sulfur content) that have occurred over time will not have an 

appreciable effect on tensile properties. Therefore, the stress-strain curves in Fig. 2.4 should be 

reasonably representative of the existing tank car fleet.

2.1.2 HSLA Steels

Figure 2.5 is a plot of the lower yield stress (i.e., the stress on the yield plateau) versus strain rate 

for A 710 steel. As was the case for TC 128B steel, a power-law expression adequately 

describes the strain rate dependence of yield strength. The stress-strain data, indexed by lower 

yield stress, is plotted in Fig. 2.6. Neither the Luder’s strain nor the hardening behavior appears 

to be a strong function of strain rate. The modest variability in stress-strain curves in Fig. 2.6 is 

not a systematic function of strain rate. Figure 2.7 shows the idealized fit of the stress-strain 

behavior for A 710 steel.

Figure 2.8 is a plot of yield strength versus strain rate for HPS 70 steel. This material exhibits 

different strain rate dependence that the other steels considered in this study. It appears to fit the 

Cowper-Symonds model, which is given by

1

1

p

YS o C



 

               

 (2.1)

where o, C and p are material constants. For the HPS 70 plate, the following constants were 

inferred:

o = 84 ksi

C = 122.2987 s-1
6

p = 1.08478

Note that the Cowper-Symonds fit predicts a rapid increase in yield strength at strain rates above 

1 s-1. Experimental data are not available at strain rates above approximately 8 s-1, so this 

extrapolated trend may or may not be real. Some of the subsequent simulations with HPS 70 

steel assumed that the stress-strain curve remains constant above 10 s-1. That is, Eq. (2.1) was 

truncated at a  = 10 s-1. Other simulations with this material extrapolated the stress-strain 

behavior to a strain rate of 100 s-1.

Figure 2.9 shows measured stress-strain behavior for HPS 70 steel. The idealized fitted curves 

are plotted in Fig. 2.10.

Figure 2.11 is a plot of 0.2% yield strength and flow stress at 1% plastic strain versus strain rate 

for HPS 100 steel. There is no discernable, systematic relationship between strength and strain 

rate for this material. The authors are not aware of a credible metallurgical explanation for the 

apparent lack of a strain rate dependence of HPS 100 steel.

Figure 2.12 is a plot of measured stress strain curves for HPS 100 steel. In this case, the curves 

were indexed by the flow stress at 1% plastic strain. This family of curves exhibited 

considerable variability when indexed by the 0.2% yield strength, but collapse onto a common 

trend when indexed by the 1% flow stress. Note that this material does not have a yield plateau. 

Indexing to the 0.2% yield strength is not effective reducing the curves to a common trend in this 

case because the stress versus plastic strain curves are very steep at low strains.

Since the both the yield strength and hardening behavior of HPS 100 steel are insensitive to 

strain rate, a single stress-strain curve was used for all strain rates. The fitted stress strain curve 

for HPS 100 is shown in Fig. 2.13.
7

TC 128B Steel

True Stress-Strain Curves

0

5

10

15

20

25

30

35

40

45

50

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

True Plastic Strain

(Tru

e

Stre

s

s - Yield

Stre

s

s), k

si

0.002 (A7)

0.1 (B3)

1.0 (A4)

8.2 (B6)

Strain Rate, s-1

FIGURE 2.1 Typical stress-strain behavior for TC 128B steel at various train rates.
8

50

60

70

80

90

100

0.001 0.01 0.1 1 10

Plate A TC128 B Steel

Plate B

Power-Law Fit

y = 67.873 * x^(0.033301) R= 0.97412 

0.2

%

Offs

et Yield

Stre

n

gth, k

si

Strain Rate, s-1

FIGURE 2.2 Effect of strain rate on yield strength of TC 128B steel.

0.01

0.1

0.001 0.01 0.1 1 10

TC128B Steel

y = 0.027277 * x^(0.09039) R= 0.89052 

L

u

d

er's

Strain

Strain Rate, s-1

FIGURE 2.3 Effect of strain rate on Luder’s (yield plateau) strain in TC 128B steel.
9

TC 128 B Steel

Fitted Stress-Strain Curves

0

20

40

60

80

100

120

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

True Plastic Strain

Tru

e

Stre

s

s, k

si

0.001

0.01

0.1

1

10

100

Strain Rate,

s-1 :

FIGURE 2.4 Fitted stress-strain curves for TC 128B steel, which were used in the finite element simulations.
10

70

80

90

100

0.001 0.01 0.1 1 10

A710 Steel

y = 84.467 * x^(0.011533) R= 0.9586 

L

o

w

e

r

Yield

Str

e

s

s, p

si

Strain Rate, s-1

FIGURE 2.5 Effect of strain rate on yield strength in A 710 steel.
11

A710 Steel

True Stress-Strain Curves

0

5

10

15

20

25

30

35

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18

True Plastic Strain

(T

r

u

e

Str

e

s

s - L

o

w

e

r

Y.S.), k

si

A - 0.002

B - 0.002

C - 0.1

D - 0.1

E - 1.0

F - 1.0

G - 8

H - 8

Strain Rate, s-1

FIGURE 2.6 Stress strain behavior of A 710 steel at various strain rates.
12

A 710 Steel

Fitted Stress-Strain Curves

0

20

40

60

80

100

120

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2

True Plastic Strain

Tru

e

Stre

s

s, k

si

0.001

0.01

0.1

1

10

100

Strain Rate,

s-1 :

FIGURE 2.7 Fitted stress-strain curves for A 710 steel, which were used in the finite element simulations.
13

HPS 70 Steel

Strain Rate Dependence

80

90

100

110

120

130

140

150

0.001 0.01 0.1 1 10 100

Strain Rate, s-1

Yield

Str

e

n

gth, k

si

 Experimental Data

Cowper-Symonds Fit

FIGURE 2.8 Effect of strain rate on yield strength in HPS 70 steel.
14

HPS 70 Steel

True Stress-Strain Curves

0

5

10

15

20

25

30

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

True Plastic Strain

(T

r

u

e

Str

e

s

s - Yield

Str

e

s

s), k

si

A - 0.002

B - 0.002

C - 0.1

D - 0.1

E - 1

F - 1

G - 7.6

H - 8.0

Strain Rate, s-1

FIGURE 2.9 Stress strain behavior of HPS 70 steel at various strain rates.
15

HPS 70 Steel

Fitted Stress-Strain Curves

70.000

90.000

110.000

130.000

150.000

170.000

190.000

0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16

True Plastic Strain

T

r

u

e

Str

e

s

s, k

si

0.001

0.01

0.1

1

10

100

Strain Rate,

s-1 :

FIGURE 2.10 Fitted stress-strain curves for HPS 70 steel, which were used in the finite element simulation.
16

HPS 100 Steel

Effect of Strain Rate

100

105

110

115

120

125

130

135

140

145

150

0.001 0.01 0.1 1 10

Strain Rate, s-1

Yield

Str

e

n

gth, k

si

1% Flow Stress

0.2% Offset Yield Strength

FIGURE 2.11 Yield strength and 1% flow stress versus strain rate for HPS 100 steel.
17

HPS 100 Steel

True Stress-Strain Curves

-20

-15

-10

-5

0

5

10

15

20

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

True Plastic Strain

(Tru

e

Stre

s

s - 1%

Flo

w

Stre

s

s), k

si

A - 0.002

B - 0.002

C - 0.1

D - 0.1

E - 1.0

G - 7.6

H - 8

Strain Rate, s-1

FIGURE 2.12 Stress-strain behavior of HPS 100 steel at various strain rates.
18

HPS 100 Steel

True Stress-Strain Curve Fit

100

105

110

115

120

125

130

135

140

145

150

0 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08 0.09 0.1

True Plastic Strain

Tru

e

Stre

s

s, k

si

FIGURE 2.13 Fitted stress-strain curve for HPS 100 steel, which was used for finite element simulations.
19

2.2 Impact Tests on Unnotched Specimens

In the Phase I report [1], the authors hypothesized that puncture resistance is related to the uppershelf toughness of the tank car material. Material toughness is typically characterized by Charpy 

tests, where specimens are notched, or fracture mechanics tests, where specimens contain sharp 

cracks. A typical puncture event, however, involves ductile fracture in the absence of a preexisting flaw or notch-like feature.

Performing a true puncture test on steel is problematic. The test specimen must be sufficiently 

large to be representative of a puncture event in a tank car. Such large-scale tests necessarily 

involve enormous impact energies, which are beyond the capabilities of most laboratories and 

test facilities.

As a compromise between small-scale notched Charpy tests, which are inexpensive but do not 

give a direct measure of puncture resistance, and full-scale puncture tests, which are very 

expensive and can be performed only at a few facilities (e.g. the Transportation Technology 

Center in Pueblo, Colorado), we developed an unnotched impact material test specifically for 

this Phase II study. Unnotched specimens absorb considerably more energy than notched 

specimens, so the energy requirements are substantial even for relatively small specimens. 

Southwest Research Institute (SwRI) has a large impact test machine that was built for a 

previous project. This test rig delivers an impact load with a pendulum mechanism, and 

resembles a giant Charpy machine. The SwRI pendulum test rig was modified and re-purposed 

for the present project. It has been designated as the Bulk Fracture Charpy Machine (BFCM).

Figure 2.14 is a drawing of the unnotched specimen used in the BFCM test. The plan 

dimensions are fixed, but the specimen thickness can vary. These specimens are impacted with a 

Charpy-like striker tup, which is shown in Fig. 2.15. Note that this striker is considerably blunter 

than a standard Charpy tup. Early BFCM tests with a sharper striker did not produce the desired 

results. A sharp striker essentially “plows” through the specimen rather than initiating ductile 

fracture. High speed video of BCFM tests with the striker shown in Fig. 2.15 indicate that 

fracture initiates on the side of the specimen that is opposite to the surface in contact with the 

striker.

Figure 2.16 shows two photographs that give an overall view of the BFCM. Close-up 

photographs of the specimen and fixture are provided in Fig. 2.17. Figure 2.18 shows 

photographs of fractured specimens.

The weight of the pendulum is 2378 lbs, and the arm is 52.45 inches long. For the tests reported 

in this study, a drop angle of 120 degrees was used, which results in an impact velocity of 

approximately 14 mph. A series of benchmark experiments verified that the fracture energy is 

insensitive to the drop angle, which is proportional to the available kinetic energy at impact.

Table 2.3 lists the room-temperature Charpy data for the materials on which BFCM testing was 

performed in this study. Two samples of modern normalized TC 128B steel plate, designated as 

C and D, were tested. Both samples, which were provided by Union Tank Car, were corner cutouts from the fabrication of pressure car heads. Plate C was approximately 0.82-inch thick and 
20

Plate C was 0.69-inch thick. According to information provided by Union Tank Car, both plates 

had low sulfur contents.

Plates C and D have essentially identical Charpy properties in the longitudinal orientation. 

Moreover, the longitudinal and transverse properties of Plate D are virtually identical, indicating 

that this plate was manufactured with sulfide shape control. In Plate C, however, there is a 

significant difference between transverse and longitudinal Charpy toughness, which indicates 

that the sulfide shape control process was less effective, assuming it was performed at all.

Of the HSLA steels tested in this study, the HPS 100 material has the best Charpy toughness. 

Both the HPS 100 and A 710 materials show little anisotropy between the longitudinal and 

transverse directions. The HPS 70 Charpy data indicate better toughness in the longitudinal 

direction, which is the opposite of the expected behavior. It is possible that the rolling direction 

on this plate sample was mis-labled.

Table 2.4 lists the results of the BFCM testing. The thickness was varied in the Plate C samples 

in order to establish the energy versus thickness trend. The other materials were tested at a 

single thickness. These data are compared with finite element predictions in Section 3.3.

TABLE 2.3

Room temperature Charpy data for materials on which BFCM testing was performed.

Room Temperature Charpy Data, ft-lb

Material Longitudinal Orientation Transverse Orientation

Values Mean Std. Dev. Values Mean Std. Dev.

TC 128B

Sample C

84

87

100

90 8.5

49

53

54

52 2.6

TC 128B

Sample D

79

99

83

87 10.6

98

95

82

92 8.5

A 710 192

167

167

175 14.4

180

156

157

164 13.6

HPS 70 96

107

112

105 8.2

65

65

57

62 4.6

HPS 100 154

169

167

163 8.1

194

182

179

185 7.9
21

TABLE 2.4

BFCM Test results.

Material Specimen 

Thickness, 

in

Specimen 

Orientation

Absorbed 

Energy, ftlb

Mean, ft-lb Std Dev., 

ft-lb

0.8205 6913

0.8215 7181

0.8180 7092

0.8270

Longitudinal

6824

7002 163

0.6265 4382

0.6250 4292

0.6255

Longitudinal

4156

4277 114

0.5005 3125

0.5005 3170

0.5045

Longitudinal

3214

3416 45

0.3760 2332

0.3770 2289

0.3755

Longitudinal

2289

2303 25

0.2540 1472

0.2490 1346

TC 128 B

Sample C

0.2505

Longitudinal

1472

1430 73

0.6855 5107

0.692 4835

0.6935 5016

0.6945

Longitudinal

5016

4994 114

0.6825 5062

0.686 4925

0.689 5016

TC 128 B

Sample D

0.687

Transverse

4971

4994 59

0.7835 6104

A 710 0.787 6194

0.7945

Transverse

5832*

6149 64

0.7665 5968

0.779 5877

0.7705 5968

HPS 70

0.7665

Transverse

5470

5821 238

0.773 7270

0.7785 7003

0.776 7047

HPS 100

0.776

Transverse

7448

7192 207

* Value is not used in average or standard deviation because the specimen is thinner on one end.
22

FIGURE 2.14 BCFM specimen configuration.
23

FIGURE 2.15 Striker tub used in BFCM tests.
24

(a)

(b)

FIGURE 2.16 Photographs of the BFCM test machine, which is located at Southwest Research Institute.
25

(a)

(b)

FIGURE 2.17 Close-up photos of the BCFM specimen in the test machine.
26

(a)

(b)

FIGURE 2.18 Fractured BFCM specimens.
27

3 MATERIAL MODEL CALIBRATION

The Gurson-Tvergaard material model, which was applied in the Phase I project [1], was also 

used in the present study to simulate laboratory fracture tests and full-scale tank car impact 

events.

3.1 Gurson-Tvergaard Ductile Fracture Model

The Gurson-Tvergaard model [2-6] simulates void growth and ductile fracture through a strainsoftening constitutive law. Strain softening is captured through a void volume fraction, which 

increases with plastic flow. Fracture occurs when the void volume fraction reaches a critical 

value. This material model is implemented in some commercial finite element codes, including 

ABAQUS Explicit and LS-DYNA.

The Gurson-Tvergaard yield condition is given by:

 

2

2

1 2 3

3 2 cosh 1 0

2 y y

q p q f q q f

 

   

                 (3.1)

where q is the effective Mises stress, p is the hydrostatic pressure, y is the yield stress of the 

fully dense material, q1, q2, q3 are porosity material parameters, and f is the void fraction.

The void growth and void nucleation rate gives the total change in the void volume fraction, f

 :

gr nucl f  f  f    (3.2)

where gr f

 is from the existing void growth, and nucl f is from the nucleation of new voids. The 

growth of existing voids is given by:

1  pl

gr f   f    (3.3)

and the growth of new voids due to nucleation is given by:

2

1

exp 2 2

pl

nucl m

pl

N m N

N N

f A

f A

s s



 





               

 

(3.4)

The nucleation strain is assumed to follow a normal distribution with a mean value of N, and a 

standard deviation sN. fN is the void volume fraction of the new voids; which are nucleated only 

in tension. 
28

For a numerical analysis, the initial void volume fraction, f0, is defined for the material. The 

porous failure criteria is given by the critical void volume fraction, fc. When c f  f at all the 

material points (integration points) of a finite element, the stress carrying capacity of the material 

is reduced to zero and the finite element is removed from the model. The progressive failure of 

elements results in crack growth across the mesh.

3.2 Charpy Specimen

In order to apply the Gurson-Tvergaard model to a particular problem, the model must first be 

calibrated to experimental results. In this instance, we chose to calibrate the material model to 

Charpy impact results. A series of finite element simulation of Charpy tests were performed, and 

the material model was adjusted to achieve various values of absorbed energy.

Figure 3.1 shows the finite element model used for Charpy simulations, which were performed 

with ABAQUS Explicit. The anvil and striker were treated as contact surfaces, so the specimen 

is free to move relative to the test machine during fracture. The initial velocity of the striker was 

235.9 in/sec (13.4 mph), which is equivalent to being dropped from a height of 6 ft. The velocity 

of the striker decreased as it imparted its kinetic energy to the specimen. This effect is handled 

automatically in the analysis through energy conservation. The weight of the striker was 49.15 

lb, so the total available energy was 295 ft-lb. The fracture energy is equal to the total internal 

energy absorbed by the specimen. This quantity is output by ABAQUS Explicit.

The stress-strain curves used in the analyses are given in Section 2.1. Based on the work of 

Faleskog, et al [6], the Gurson parameters listed below are appropriate for steels with the 

strength and hardening properties of TC 128 B steel. These same constants were used for the 

other materials for the sake of simplicity.

FIGURE 3.1 Finite element model for simulation of the Charpy test.
29

Gurson parameter q1 = 1.81

Gurson parameter q2 = 0.82

Gurson parameter q3 = q1

2

 = 3.2761

Nucleation strain mean value N = 0.30

Nucleation strain standard deviation sN = 0.10

Void nucleation initial void volume fraction fN = f0

Critical void fraction fc = 0.15

The initial void fraction, fo, was a fitting parameter in the model.

Figure 3.2 is a plot of absorbed energy versus initial porosity for the 4 steels considered in this 

study. It is important to note that these calibration curves apply only to 1 mm3

 elements. Finite 

element fracture models, where an element is deleted when a failure criterion is reached, are 

inherently mesh dependent. Real materials contain microstructural length scales, such as grain 

size and inclusion spacing, that govern toughness. In a finite element model, the de facto length 

scale is the element size. The material model must be re-calibrated for each element size. 

Increasing the element size shifts the calibration curve (absorbed energy vs. f0) upward and to the 

right. This point is discussed further in Section 3.4

Note that the assumed strain rate dependence on tensile properties has an effect on the calibration 

curve for HPS 70 steel. The energy versus porosity curve is considerably higher when flow 

properties are extrapolated using Eq. (2.1).

Calibration of the Gurson-Model with Charpy Simulations

Various Steels, 1 mm3 Elements

0

50

100

150

200

250

0.00 0.01 0.02 0.03 0.04 0.05 0.06 0.07 0.08

Initial Porosity (f0)

C

h

arp

y

E

n

erg

y (ft-lb)

TC 128B

HPS 70 - Truncated

Strain Rate Effects

HPS 100

NUCU A710

HPS 70 - Extrapolated

Strain Rate Effects

FIGURE 3.2 Calibration of initial porosity, fo, to Charpy energy for 1 mm3 elements.
30

3.3 BFCM Specimen

The material fracture model was calibrated to notched Charpy tests, but puncture in tank cars 

typically occurs in the absence of pre-existing notch-like features. In order to determine whether 

or not the material model calibrated to Charpy data is applicable to unnotched configurations, 

finite element simulations of the BFCM specimens were compared to the experimental results.

Figures 3.3 and 3.4 show a typical finite element model of the BFCM test. For clarity, the grips 

and endplates are not shown. In the impact zone the elements were 1 mm wide by 1 mm high, 

which corresponds to the mesh size in the Charpy specimens. (Recall the earlier discussion 

about the material model calibration being mesh sensitive.) The element dimension in the 

specimen thickness direction was very close to 1 mm, but was adjusted slightly so that the total 

specimen thickness would exactly match the desired value. For example, consider a specimen 

thickness of 0.822 inch, which corresponds to 20.88 mm. In this case, the mesh in the impact 

zone consists of 21 elements through the specimen thickness. Each element has the following 

dimensions: 1 mm x 1 mm x 0.994 mm. The latter value is the through-thickness dimension, 

which corresponds to 20.88 mm/21 elements.

Initial models neglected friction effects, as well as the gaps between the specimen and the fixure

(Fig. 2,17). Subsequent analyses incorporated these effects in order to assess their relative effect 

on fracture energy. For these latter cases, a friction coefficient of 0.1 was assumed for contact 

between the specimen, grips, end plates and striker.

Figure 3.5 shows the simulation of a BFCM test for TC128-B steel and thickness = 0.5 in. Note 

that fracture initiates from the specimen surface that is opposite the surface in contact with the 

striker. This is consistent with observations from high-speed videography of BFCM tests.

Table 3.1 compares the predicted and experimental absorbed energies in the BCFM specimens 

on various materials and thicknesses. Figure 3.6 is a plot of absorbed energy versus specimen 

thickness for both predicted and experimental BFCM tests. A single data point for TC 128B 

Plate C is included along with the Plate D data because the two samples have virtually identical 

Charpy properties in the longitudinal direction. The predictions and experimental data agree 

very well for specimen thickness of 0.5 inch and below, but the model slightly under-predicts the 

experimental data for thicker samples. As discussed in Section 6.1, the stress state in the thinner 

samples, where the simulation and experimental data agree, is more representative of the stress 

state at puncture in tank cars.

Figure 3.7 compares predicted and experimental energies for all of the materials tested. There is 

very good correlation between prediction and experiment for A 710 and HPS 100 steel, but the 

simulation under-predicts the fracture energy in the HPS 70 steel samples. The agreement 

between prediction and experiment for HPS 70 steel is improved when the strain rate dependence 

of the tensile properties is extrapolated using Eq. (2.1). The open symbols in Fig. 3.7 correspond 

to analyses that incorporated friction effects as well as gaps between the specimen and the 

fixture. In most cases, the predicted fracture energy was not significantly affected by simplifying 

assumptions of the initial simulations.
31

Overall, the model predictions are good, but not perfect. Ideally, the model should predict 

energies to within 5 or 10% of experimental values in this case, which is consistent with scatter 

in individual experimental values. The reasons for under-predictions of > 15% in some cases are 

not fully understood at present. Perhaps these predictions could be improved by varying more 

than one parameter in the Gurson-Tvergaard material model to optimize the fit to experimental 

data. An exhaustive parameter study with the Gurson-Tvergaard model was beyond the scope of 

this project.

.
32

Anvil modeled as a 

frictionless rigid surface

Direction of 

striker travel

Blunt striker, 

14 mph, 

2,378 lbs, 

modeled as a rigid surface

Finest mesh zone, 

Gurson material model 

Mass scaled by 64x

Fine mesh zone, 

Plastic material model 

Mass scaled by 16x

Medium mesh zone, 

Plastic material model 

Mass scaled by 4x

Medium mesh zone, 

Plastic material model 

No mass scaling

12”

varies

1”

TIE’d boundaries

6”

Anvil modeled as a 

frictionless rigid surface

Direction of 

striker travel

Blunt striker, 

14 mph, 

2,378 lbs, 

modeled as a rigid surface

Finest mesh zone, 

Gurson material model 

Mass scaled by 64x

Fine mesh zone, 

Plastic material model 

Mass scaled by 16x

Medium mesh zone, 

Plastic material model 

Mass scaled by 4x

Medium mesh zone, 

Plastic material model 

No mass scaling

12”

varies

1”

TIE’d boundaries

6”

FIGURE 3.3 Finite element model of BFCM specimen (grips and end plate not shown).
33

View from anvil side

Top view Close up of finest mesh region

View from striker side

FIGURE 3.4 Meshing of finite element model of BFCM specimen (grips and end plate not shown).
34

(a) Time = 0 ms

(b) Time = 5.2 ms

(c) Time = 6.5 ms

FIGURE 3.5 Typical results from a simulation of a BFCM test (end plates, platens & grips not shown).
35

(d) Time = 7.4 ms

(e) Time = 8.0 ms

(f) Time = 9.5 ms

FIGURE 3.5 (cont.) Typical results from a simulation of a BFCM test (end plates, platens & grips not shown).
36

(g) time = 15 ms

FIGURE 3.5 (cont.) Typical results from a simulation of a BFCM test (end plates, platens & grips not shown).
37

TABLE 3.1

Comparison of experimentally-determined fracture energies for the BFCM specimens with finite element predictions. The gaps between the fixture and 

specimen, as well as friction effects, were neglected in the results tabulated below.

BFCM Energy, ft-lb

Material Specimen 

Thickness, in

Charpy Energy, ftlb Experiment Simulation Sim./Exp. Ratio

0.822 89 7002 5098 73%

0.624 89 4277 3804 89%

0.502 89 3170 3005 95%

0.370 89 2303 2058 89%

TC 128B

Sample C

0.251 89 1430 1410 99%

TC 128B

Sample D

0.689 90 4993 4226 85%

A 710 0.777 170 6149 5925 96%

HPS 70 0.777 62 5938 4611* 78%

HPS100 0.777 170 7192 7190 100%

*Strain rate effects on tensile properties were truncated at 10 s-1.
38

TC 128B Steel BFCM Tests

Samples C & D

Charpy Energy = 89 ft-lb

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

0.0000 0.1000 0.2000 0.3000 0.4000 0.5000 0.6000 0.7000 0.8000 0.9000

Specimen Thickness, in

A

b

s

orb

e

d

E

n

erg

y, ft-lb

Model Prediction

Experiment

FIGURE 3.6 Effect of specimen thickness on BFCM absorbed energy for both the experiments and finite element simulations. Data for both Plates C 

and D are included in this plot.
39

BFCM Tests on Various Steels

0

1,000

2,000

3,000

4,000

5,000

6,000

7,000

8,000

0 1,000 2,000 3,000 4,000 5,000 6,000 7,000 8,000

Measured Absorbed Energy, ft-lb

Pre

dicte

d

A

b

s

orb

e

d

E

n

erg

y, ft-lb

TC 128B Steel (Original)

HPS 70 Steel (Original)

HPS 100 Steel (Original)

A710 Steel (Original)

TC 128B Steel (Friction & Gaps)

HPS 70 Steel (Friction & Gaps)

HPS 100 (Friction & Gaps)

±15%

1:1 Trend

Truncated Strain 

Rate Effects

Extrapolated Strain 

Rate Effects

FIGURE 3.7 Predicted versus experimental absorbed energy in the BCFM tests.
40

3.4 Large-Scale Calibration Specimens

Given existing computational resources, it was not practical to perform full-scale tank car 

puncture simulations with 1 mm3

 elements in the target zone. We chose to increase the element 

length and width to 5 mm while maintaining the through-thickness mesh refinement. Thus the 

element dimensions for the most of the tank car simulations were 5 mm x 5 mm x ~ 1 mm.1 As 

was the case for the BFCM simulations, the element thickness dimension was adjusted slightly 

from 1 mm so that the overall model conformed exactly to the desired section thickness.

As discussed earlier, the Gurson-Tvergaard ductile fracture model must be re-calibrated when 

the element dimensions change. In this case, however, it is not possible to calibrate using 

Charpy specimens, since their cross section is only 10 mm x 10 mm. Even the BFCM specimens 

are not suitable to calibrate a mesh with 5 mm x 5 mm elements because the striker would be less 

than three elements wide. 

We chose to re-calibrate the material model with a simulation of puncture in a flat plate. The 

plate dimensions were chosen to induce a tension dominated failure in the plate, to match the 

expected failure mode in a tank car collision. Figure 3.8 shows the model used for this exercise. 

Note that the model is 1⁄4 - symmetric. A 6-inch x 6-inch square striker (or 3” x 3” in the 1⁄4 -

symmetric model) with a 0.5-inch chamfer radius was impacted into the plate, and the resulting 

puncture energy was computed. This striker configuration is identical to that used in the tank car 

puncture simulations (Sections 4 and 5), so this simulation is representative of the tank car 

configuration, but with a much smaller model. The plate puncture is simulated with 1 mm x 1 

mm elements, and then repeated with 5 mm x 5 mm elements. One or more parameters in the 

material model can then be adjusted in the coarser mesh so that the two meshes give the same 

puncture energy. Figure 3.9 shows the results of a typical plate puncture simulation.

As a check on the material model re-calibration, a second configuration was analyzed. Figure 

3.10 shows the notched tension configuration that was used for this purpose. As was the case 

with the plate puncture simulation (Figs. 3.8 and 3.9), this configuration was analyzed with both 

1 mm x 1mm and 5 mm x 5 mm elements in the fracture zone in order to adjust the material 

model for the coarser mesh. Figure 3.11 shows the results from a typical simulation of the 

notched tension configuration.

Figure 3.12 illustrates a typical re-calibration to a coarser mesh. In this example, we wish to 

model TC 128B steel with 50 ft-lb Charpy energy. The corresponding initial porosity, fo, for 1 

mm3 elements be inferred from Fig. 3.2. The plate model is simulated with 1 mm3 elements to 

obtain puncture energy, which in this case is 13,955 ft-lb. A second mesh with 5 mm x 5 mm x 1 

mm elements is analyzed with a range of fo values. The fo value need to match the 13,955 ft-lb 

puncture energy is obtained by interpolation.

Ideally, the fo values inferred from the plate puncture and notched tension configurations should 

be identical. In reality, they typically differ by a few percent. Reasonably close agreement 

between the two fo estimates provides confidence that the material model is insensitive to the 

geometry of the component or specimen being analyzed. The fo values used in the tank car 

impact simulations (Sections 4 and 5) were obtained by averaging the fo estimates inferred from 

the plate and notched tension configurations.

 

1 Some early tank car simulations used 2.5 mm x 2.5 mm x ~1 mm elements, but computation times were excessive.
41

6”

6”

24”

Fine mesh zone, 

brick elements, 

Gurson material model

Medium mesh zone, 

brick elements, 

plastic material model

Coarse mesh zone, 

shell elements, 

plastic material model

Striker 

3” x 3” and 1⁄2” rounded edges 

25 mph 

77 kips for whole striker 

Fixed boundaries conditions 

(rotation & translation restrained)

Symmetry planes

magnified

magnified

1 x 1 x 1mm mesh

11 mm = 0.433”

~

TIE’d boundaries

6”

6”

24”

Fine mesh zone, 

brick elements, 

Gurson material model

Medium mesh zone, 

brick elements, 

plastic material model

Coarse mesh zone, 

shell elements, 

plastic material model

Striker 

3” x 3” and 1⁄2” rounded edges 

25 mph 

77 kips for whole striker 

Fixed boundaries conditions 

(rotation & translation restrained)

Symmetry planes

magnified

magnified

1 x 1 x 1mm mesh

11 mm = 0.433”

~

TIE’d boundaries

FIGURE 3.8 Flat plate impact specimen for calibrating the material model for various element sizes.
42

(a) Time = 8.4 ms

(b) Time = 9.2 ms

FIGURE 3.9 Typical results of the plate puncture simulation.
43

(c) Time = 11.0 ms

(d) Time = 14.8 ms

FIGURE 3.9 (Cont.)
44

Finest mesh zone, 

Gurson material model

Medium mesh zone, 

plastic material model

Fine mesh zone, 

Gurson material model

Coarse mesh zone, 

plastic material model

Fixed end: 

Axial translation fixed 

Lateral translation allowed

Displaced end: 

Axial displacement impose

Lateral translation allowed

TIE’d boundaries

300mm

50mm

50mm

20mm” 45o

10mm

Finest mesh zone, 

Gurson material model

Medium mesh zone, 

plastic material model

Fine mesh zone, 

Gurson material model

Coarse mesh zone, 

plastic material model

Fixed end: 

Axial translation fixed 

Lateral translation allowed

Displaced end: 

Axial displacement impose

Lateral translation allowed

TIE’d boundaries

300mm

50mm

50mm

20mm” 45o

10mm

magnify

Example mesh: 

Finest mesh region: 

1.11 (x) x 1.11 (y) 1 mm (z)

FIGURE 3.10 Finite element model for notched tension specimens
45

(a) Time = 0.0 ms

(b) Time = 2.2 ms

FIGURE 3.11 Typical fracture simulation in the notched tension configuration.
46

(c) Time = 5.8 ms

(d) Time = 7.2 ms

FIGURE 3.11 (Cont.)
47

Calibration of Initial Porosity, f0, from 1 to 5 mm Mesh 

Plate Specimen, TC 128B Steel

12,000

13,000

14,000

15,000

16,000

17,000

18,000

19,000

20,000

21,000

22,000

0.020 0.025 0.030 0.035 0.040 0.045 0.050 0.055 0.060 0.065 0.070

Initial Porosity (f0)

A

b

s

orb

e

d

E

n

erg

y, ft-lb

1 mm mesh

5 mm mesh

Compute the absorbed energy in the plate 

specimen with 1 mm3 elements using the 

initial porosity corresponding to desired 

Charpy energy (50 ft-lb in this case).

Match the absorbed energy of 

the plate specimen with 1 mm3 

elements and a 50 ft-lb 

material. Determine the 

corresponding initial porosity for 

the plate specimen with 5 mm x 

5 mm x 1 mm elements.

FIGURE 3.12 Calibration of material model for different element sizes. The initial porosity, fo, is adjusted to give the same absorbed energy in the two 

meshes.
48

4 TANK CAR IMPACT SIMULATION PROCEDURES

This chapter describes the finite element models and modeling techniques for tank car 

simulations. The objective of the tank car simulations is determining energy absorbed by the tank 

car during an impact event. Absorbed energy values are subsequently used to determine 

sensitivity to various design and simulation parameters.

The base tank car configurations included in this study are listed in Table 4.1. The base 

configurations were modified to add or remove jackets and/or head shields as appropriate to 

quantify the relative effect of these design features.

A total of 6 collision scenarios were considered for each base tank car specification, as outlined 

in Table 4.2. In addition, a series of parametric analyses were performed to determine the effect 

of variables such as internal pressure, striker size, initial impact speed, friction, lading mass, and 

material toughness.

Table 4.1 Tank car configurations included in the finite element simulation study.

Car 

Specification

Shell 

Thickness, 

in

Head 

Thickness, 

in

Inside 

Diameter,

in

Head-toHead 

Length, in

Design 

Pressure, 

psi

Assumed 

Operating 

Pressure, 

psi*

111A100W 0.4375 0.4688 119.2 648 - 55

105J300W 0.5625 0.603 117.9 568 300 71

105J500W 0.777 0.8281 100.6 524 500 115

105J600W 0.981 1.136 106.0 494 600 138

*Based on typical operating pressures, but adjusted to maintain a constant hoop stress in all four 

tank car sizes.

Table 4.2

Collision scenarios considered in the present study

Impact Location Tank Car Configuration

Shell Bare shell (no jacket)

0.112-inch thick jacket

Bare head (no jacket or head shield)

0.112-inch thick jacket

0.500-inch thick head shield without standoff

Head

0.500-inch thick head shield with standoff (jacketed car)

For the shell impact scenario, the striker impacts the tank car at mid-span and half height with 

the striker traveling laterally with respect to the tank car as shown in Fig. 4.1. For a head impact, 

the striker impacts the tank car at the center of the head with the striker traveling longitudinal 
49

with respect to the tank car axis, as shown in Fig. 4.2. For computational efficiency, only 1⁄4 of 

the tank car was modeled, as illustrated in Figs. 4.1 and 4.2.

For most simulations, a striker weight 280,000 lb and an initial striker velocity of 40 mph were 

assumed. Higher initial velocity simulation results in impact events of shorter duration, which 

translates to shorter computation times. The initial impact velocity was varied in a limited 

number of simulations to demonstrate its effect on puncture energy.

Figures 4.3 and 4.4 compare finite element models with and without head shields and jackets. 

In all models, the tank car abuts a reaction wall as shown in Figs. 4.1 to 4.7 The reaction walls 

are idealized as rigid, frictionless surfaces.

Figures 4.6 and 4.7 show the mesh configuration for shell and head impacts of an unjacketed car. 

The mesh is progressively refined, with the finest mesh adjacent to the striker. “Tied” interfaces 

connect the various mesh zones, in lieu of using a mesh size transition zone. The element size in 

the refined zone was either 5 x 5 x ~1mm or 2.5 x 2.5 x ~1 mm, as shown in Fig. 4.6. The ~1 

mm dimension in the thickness direction assures that through thickness gradients of stress, strain, 

etc have adequate resolution. The early tank car models had a 2.5 mm refined zone mesh, but 

computation times were on the order of several days per simulation. The mesh size was 

increased to 5 mm x 5 mm x ~1 mm to reduce computation time to a reasonable level. 

Benchmarks were performed to ensure that the same results were achieved in both mesh 

configurations, provided the material model was properly calibrated to the corresponding mesh.

The refined and medium zone meshes contain first-order, reduced integration brick elements, 

while the remainder of the model contains continuum shell elements. Continuum shell elements 

resemble brick elements when viewed in a pre/postprocessor, but behave like shell elements 

located at the element mid-surface. Continuum shell elements efficiently capture plate-bending 

effects in areas away from the impact zone. Meshes for the five other combinations of tank car 

configuration and impact location are similar to the mesh for the broadside impact of an 

unjacketed car.

The symmetry boundaries are constrained with the appropriate boundary conditions. There are 

no additional boundary conditions applied to the model.

For jacketed configurations, the jacket is separated 4 in. from the shell by studs. The studs are 

idealized by a solid layer with an equivalent stiffness, as shown in Figs. 4.3 and 4.4. The 

equivalent stiffness of the solid layer is only 0.12% of the stiffness of steel. For shell impact, the 

insulation layer is located on the half of the model away from the impact zone, providing a 

means to transfer impact forces to the reaction wall. The remaining half of the model lacks an 

insulation layer, to ease model construction. Omission of the equivalent insulation layer from 

the impact side of the model will not affect the absorbed energy because the studs and insulation 

do not contribute significantly to the strength of the tank shell. Similarly, for head impacts, the 

head region lacks an equivalent insulation layer.

The interactions between the striker, tank shell, jacket and head shield are modeled with the 

penalty contact formulation. A few simulations incorporate friction and contact between the 

striker and fracture surfaces. However the majority of the simulations assume friction-less 

interaction.
50

A few simulations incorporate the effect of the lading mass. The mass of the lading is distributed 

to the shell wall by increasing the density of the shell wall. 

Mass scaling of 6.25x is applied to the refined zone during the impact portion of the simulation, 

resulting in a modest decrease in computation time. Larger mass scaling has proven to degrade 

the accuracy of the solution. Portions of the model incorporating lading mass are not mass 

scaled.

The inner surface of the shell wall is pressurized as shown in Figures 4.5 and 4.7. Simple 

calculations showed that the volume of the tank does not decrease significantly during the impact 

event up to rupture, justifying the use of constant pressure during the impact event.

Accommodating both pressurization and impact events in one simulation requires a special 

technique. The explicit solution does not allow static analyses and therefore, the simulations 

capture tank vibrations caused by pressurization. This technique ensures that pressure induced 

vibrations are damped out before the impact event and damping is negligible during the impact 

event. Mass proportional damping eliminates unwanted vibrations and is described below:

C   M (4.1)

where

C = the damping matrix,

M = the mass matrix, incorporating mass scaling,

 = mass proportional damping coefficient, on the order of 0.4.

To minimize vibrations, mass scaling is tuned to result in critical damping in the first mode of 

the tank. This requires a large amount of mass scaling and the resulting natural period is on the 

order of 500 seconds. The pressure is ramped up over a duration exceeding the natural period of 

the tank. The pressure is then held constant, allowing vibrations to dissipate. At the end of the 

hold period, mass scaling is reduced, thereby decreasing the damping ratio to a miniscule 

fraction of critical. 

The energy absorbed during the impact event is calculated from velocities:

  2 2 1 E  2 m Vi Vf (4.2)

where

Vi = initial velocity of the striker,

Vf = final velocity of the striker,

m = mass of the striker.

This energy measure is convenient because it includes strain, kinetic, plastic deformation and 

rupture energies, as well as frictional dissipation. Energy at two occurrences are examined:
51

 First leak: when a rupture propagates through the entire thickness of the tank shell or 

head, allowing the lading to escape the tank 

 Puncture: when the shell/head material at the impact zone completely separates from the 

remainder of shell/head.

Figures 4.8 through 4.14 show snapshots from a series of simulations for the size impact 

scenarios listed in Table 4.2. In each illustration, the left, middle and right frames show a view 

from the outside of tank, a view from the inside of tank and the striker velocity time history, 

respectively. The snapshots illustrate a sequence of bending of the tank wall, initiation of tank 

wall rupture, propagation of a rupture through the entire thickness resulting in a leak, and 

puncture (complete tear-through) of the steel in the impact zone.

Figure 4.15 is a plot of energy versus time for shell impact on a tank car with and without a 

jacket. The base car configuration for this example is 105J500W. The absorbed energy of the 

jacketed car is somewhat higher than for the unjacketed car, as one would expect. For the 

jacketed car, there is a brief period in which the absorbed energy increases only slightly 

immediately after impact. During this brief time window, the jacket bends inward and contacts 

the shell. Because the jacket has low stiffness, minimal energy is dissipated during this event. 

The energy increases more rapidly once the shell begins to bend inward.

Two points are labeled on each of the curves in Fig. 4.15: where initial leak would occur and 

where complete puncture occurs. These two events occur in rapid succession, as the simulation 

results in Figs. 4.8 to 4.14 indicate. Minimal energy is absorbed between the initial leak and 

complete puncture. Figure 4.16 is a plot of energy for leak and puncture as a function of shell 

thickness in jacketed and unjacketed cars.
52

Full model

1⁄4 symmetry model

Direction of 

striker travel

FIGURE 4.1 Typical tank car finite element model for shell impact.
53

Full model

1⁄4 symmetry model

Direction of 

striker travel

FIGURE 4.2 Typical tank car finite element model for head impact.
54

Unjacketed car

Jacketed car

11ga jacket

~

Equivalent insulation layer

FIGURE 4.3 Finite element models of tank cars for shell impact, with and without a jacket.
55

Unjacketed car

Jacketed car

With or without head shield

11ga jacket over head 

or 1⁄2” head shield

Unjacketed car with head shield

11ga jacket

magnify

11ga jacket 1⁄2” head shield

~

Equivalent 

insulation layer

FIGURE 4.4 Finite element models for head impact, with and without a jacket or head shield.
56

magnifymagnify

6”

6”

Fine mesh zone, 

brick elements, 

Gurson material model 

Mass scaled by 6.25x 

(most models)

Medium mesh zone, 

brick elements, 

plastic material model

Striker 

6” x 6” and 1⁄2” rounded edges 

(in full model) 

modeled as a rigid surface

Symmetry boundary 

conditions

Coarse mesh zone, 

shell elements, 

plastic material model

~

TIE’d boundaries

~

Direction of 

striker travel

TIE’d boundaries

Reaction wall 

modeled as a frictionless rigid surface

Pressure applied to 

shell inner wall

FIGURE 4.5 Details of a typical finite element model for shell impact.
57

magnifymagnify

2.5 x 2.5 x ~1mm mesh 

in refined zone

5 x 5 x ~1mm mesh 

in refined zone

1⁄2 size elements along 

symmetry boundaries 

within refined zone

magnify

FIGURE 4.6 Typical finite element mesh for tank car subject to shell impact
58

magnify

6”

Fine mesh zone, 

brick elements, 

Gurson material model 

Mass scaled by 6.25x 

(most models)

Medium mesh zone, 

brick elements, 

plastic material model

Striker 

6” x 6” and 1⁄2” rounded edges 

(in full model) 

modeled as a rigid surface

Symmetry boundary 

conditions

Coarse mesh zone, 

shell elements, 

plastic material model

~

TIE’d boundaries

Direction of 

striker travel

TIE’d boundaries

Reaction wall 

modeled as a frictionless 

rigid surface

6”

View of mesh

Pressure applied to 

shell inner wall

FIGURE 4.7 Details of a typical finite element model for head impact 
59

(a) Time = 0 ms

(b) Time = 13 ms

FIGURE 4.8 Typical simulation of a shell impact on an unjacketed car.
60

(c) Time = 18 ms

(d) Time = 20.5 ms

FIGURE 4.8 (Cont.)
61

(a) Time = 0 ms

(b) Time = 20 ms

(c) Time = 24 ms

FIGURE 4.9 Typical simulation of a shell impact on a jacketed car.
62

(d) Time = 24.5 ms

(e) Time = 29 ms

FIGURE 4.9 (Cont.)
63

(a) Time = 0 ms

(b) Time = 9 ms

(c) Time = 11.3 ms

FIGURE 4.10 Typical simulation of a head impact (no head shield or jacket).
64

(d) Time = 14.2 ms

(e) Time = 14.9 ms

(f) Time = 17.1 ms

FIGURE 4.10 (Cont.)
65

(a) Time = 0 ms

(b) Time = 14.1 ms

(c) Time = 18.3 ms

FIGURE 4.11 Typical simulation of a jacketed head impact.
66

(d) Time = 22.8 ms

(e) Time = 25.5 ms

FIGURE 4.11 (Cont.)
67

(a) Time = 0 ms

(b) Time = 19 ms

(c) Time = 21 ms

FIGURE 4.13 Typical simulation of a head impact on a jacketed car with head shield.
68

(d) Time = 24 ms

(e) Time = 25 ms

(f) Time = 27 ms

FIGURE 4.13 (Cont.)
69

(a) Time = 0 ms

(b) Time = 15.6 ms

(c) Time = 17.4 ms

FIGURE 4.14. Typical simulation of a head impact on an unjacketed car with a head shield.
70

(d) Time = 20.4 ms

FIGURE 4.x Simulation, 500W, head impact, unjacketed car with head shield, at time = 24 ms

FIGURE 4.14 (Cont.)
71

105J500W Car

Shell Impact

0

100

200

300

400

500

600

0 5 10 15 20 25 30 35 40

Time, ms

E

n

erg

y

A

b

s

orb

e

d, kip-ft

With Jacket

Without Jacket

Leak

Puncture

FIGURE 4.15 Absorbed energy versus time for a 105J500W car with and without a jacket.
72

Shell Impact

TC 128B Steel, CVN Energy = 50 ft-lb

6" Square, 280,000-lb Striker

0

100

200

300

400

500

600

700

0.4 0.5 0.6 0.7 0.8 0.9 1

Shell Thickness, in

A

b

s

orb

e

d

E

n

erg

y, kip-ft

No Jacket, Puncture

With Jacket, Puncture

No Jacket, Leak

With Jacket, Leak

FIGURE 4.16 Effect of shell thickness and a jacket on the energy required for leak or puncture.
73

5 TANK CAR IMPACT SIMULATION RESULTS

Over 100 finite element simulations of tank car impacts were performed in this project. 

Appendix B list the 83 successful simulations that were considered. A parametric study was 

conducted to quantify the effect of a number of variables and modeling assumptions on 

computed puncture resistance. A series of simulations were calibrated to the RSI-AAR Accident 

Database to relate puncture energy to probability of lading loss. In addition, the simulation 

methodology employed here was benchmarked against a recent full-scale test conducted at the 

Transportation Technology Center, Inc. (TTCI) in Pueblo, Colorado.

The energy to cause a leak or complete puncture was computed from Eq. (4.2). The minimum 

velocity for a leak or puncture can be estimated from the corresponding energy as follows:

2E V

m  (5.1)

The above relationship assumes that the puncture energy does not depend on initial velocity. 

This assumption is not strictly correct, so the inferred puncture velocities should be viewed as 

approximate.

The calculated puncture velocities should not been applied literally to actual accidents. For 

example, if the computed puncture velocity is 9 mph, it should not be assumed that a 9 mph 

collision will necessarily result in lading loss in an accident. The velocity required for puncture 

is a function of a number of factors, including the mass driving the collision, the object 

impacting the tank, and the location of the impact. Moreover, the collision speed is not 

necessarily the same as the train speed, since rail cars typically decelerate during a derailment.

Unless otherwise stated, the values of energy and velocity (or speed) that are reported and plotted 

correspond to that required for complete puncture. The conditions for leak are somewhat 

subjective, but the puncture energy can be defined unambiguously. In any case, the difference 

between puncture energy and energy to leak is generally small, as Figs. 4.15 and 4.16 illustrate.

5.1 Parametric Study

A number of variables were considered in the parametric study: pressure, striker size, initial 

velocity, friction, and lading mass. The effect of jackets and head shields is considered in 

Section 5.2, and the effect of material toughness is addressed in Section 5.3. The analyses that 

follow are all shell impacts on unjacketed tank cars. Tables 4.1 and 4.2 describe the tank car 

configurations that were analyzed.

Note that the parametric study was conducted in parallel with the material model calibration 

(Section 3). Consequently the initial porosity in the analyses below varies from one parametric 

analysis to the next, and differs from the material properties used in the benchmark to the 

Accident Database. Once the material model calibration task was complete, we determined the -

Charpy toughness that corresponds to the initial porosity used for each of the parametric 
74

analyses. The corresponding Charpy values are indicated in the plot titles. We have not 

investigated the effect of varying toughness on the conclusions drawn from the various 

parametric studies, but the relative effects of other variables such as pressure and section 

thickness should not be sensitive to the assumed material toughness.

5.1.1 Effect of Internal Pressure

Figures 5.1 and 5.2 are plots of puncture energy and speed, respectively, as a function of internal 

pressure. The puncture resistance of a tank car at full design pressure is considerably lower than 

at normal operating levels. The empty tank car did not puncture during the simulated 40 mph 

collision event.

5.1.2 Effect of Striker Size

The 6-inch square striker geometry was chosen to coincide with the Next Generation Rail Tank 

Car Project test recently conducted at TTCI. As Figs. 5.3 and 5.4 illustrate, the puncture energy 

and minimum speed (for a weight of 280,000 lb) is sensitive to the size and shape of the object 

that impacts the tank car. The 6-inch square striker represents an extreme case.

5.1.3 Effect of Initial Velocity

Most simulations assumed an initial impact velocity of 40 mph. The higher the impact speed, the 

shorter the duration of the impact event, which translates to a shorter computation time in the 

simulation. In this particular parametric analysis, the initial speed was varied from 20 to 40 mph. 

The results are plotted in Figs. 5.5 and 5.6. In the initial set of simulations, the puncture energy 

and inferred minimum speed for puncture were relatively insensitive to the initial speed. 

However, subsequent simulations that incorporated lading mass (Section 5.5.1) did show a 

marked effect of initial impact velocity on puncture energy. When simulating a specific collision 

event (e.g. the Next Generation Project test at TTCI), it is best to use the actual velocity, but for a 

comparative study, it is reasonable to use a high velocity that guarantees puncture.

5.1.4 Effect of Friction

Most of the simulations performed in this study assume frictionless interaction between the 

striker, shell, jacket, etc. Figures 5.7 and 5.8 illustrate the effect of friction on the puncture 

energy and inferred puncture speed, respectively. As one would expect, including friction does 

increase the energy dissipation, but not to a large extent. The static coefficient of friction for 

steel on steel is approximately 0.5, but the dynamic value is considerably lower. A reasonable 

estimate for coefficient of friction for a dynamic impact event is around 0.1, where the effect on 

puncture energy is modest.
75

5.1.5 Effect of Lading Mass

Most analyses in this project incorporated the mass of the steel in the tank, jacket and head shield 

(where applicable), but did not consider the mass of the lading. In one set of runs, whose results 

are plotted in Figs 5.5 and 5.6, the lading mass was modeled by adjusting the density of the tank. 

This assumption does not place the center of gravity of the lading in the correct location, nor

does it consider liquid sloshing effects. Therefore, incorporating lading mass by increasing the 

density of the shell and head is an approximation.

Table 5.1 compares the puncture energy with and without the lading mass incorporated by 

adjusting the density of the shell and head. In this case, incorporating lading mass increases the 

puncture energy and reveals a sensitivity to initial collision velocity. Thus the parametric study, 

which neglected lading mass in most cases, is suitable for comparison purposes, but the absolute 

values may not be reliable.

TABLE 5.1 Effect of including lading mass in the finite element simulation. 300W car without jacket.

Computed Puncture Energy, kip-ft

Initial Collision Velocity, mph Without Lading Mass With Lading Mass

20 545 896

30 552 781

40 505 636
76

Shell Impact, Effect of Pressure

6" Square, 280,000-lb Striker

0.777-inch Thick Shell (500W Car), No Jacket

TC 128B Steel, CVN Energy = 112 ft-lb

0

100

200

300

400

500

600

0 50 100 150 200 250 300 350 400 450 500

Internal Pressure, psi

P

u

n

ctu

r

e

E

n

e

r

g

y, kip-ft

FIGURE 5.1 Effect of internal pressure on puncture energy for a shell impact. The shell did not puncture at zero internal pressure.
77

Shell Impact, Effect of Pressure

6" Square, 280,000-lb Striker

0.777-inch Thick Shell (500W Car), No Jacket

TC 128B Steel, CVN Energy = 112 ft-lb

0

2

4

6

8

10

12

14

16

0 50 100 150 200 250 300 350 400 450 500

Internal Pressure, psi

Minim

u

m

P

u

n

ctu

r

e

S

p

e

e

d, m

p

h

FIGURE 5.2 Effect of internal pressure on minimum puncture speed for a shell impact. The shell did not puncture at zero internal pressure.
78

Shell Impact, Effect of Striker Dimensions

Square, 280,000-lb Striker

0.777-inch Thick Shell (500W Car), No Jacket

TC 128B Steel, CVN Energy = 92 ft-lb

0

500

1000

1500

2000

2500

3000

3500

0 2 4 6 8 10 12 14 16

Striker Width, inches

P

u

n

ctu

r

e

E

n

e

r

g

y, kip-ft

FIGURE 5.3 Effect of striker size on puncture energy for a shell impact.
79

Shell Impact, Effect of Striker Dimensions

Square, 280,000-lb Striker

0.777-inch Thick Shell (500W Car), No Jacket

TC 128B Steel, CVN Energy = 92 ft-lb

02468

10

12

14

16

18

20

02468 10 12 14 16

Striker Width, inches

Minimum Puncture Speed, mph

FIGURE 5.4 Effect of striker size on the minimum puncture speed.
80

Shell Impact, Effect of Initial Striker Speed

6" Square, 280,000-lb Striker

0.563-inch Thick Shell (300W Car), No Jacket

TC 128B Steel, CVN Energy = 86 ft-lb

0

100

200

300

400

500

600

700

800

900

1000

0 5 10 15 20 25 30 35 40

Initial Striker Speed, mph

P

u

n

cture

E

n

erg

y, kip-ft

Without Lading Mass

With Lading Mass

FIGURE 5.5 Effect of initial striker speed on puncture energy for a shell impact.
81

Shell Impact, Effect of Initial Striker Speed

6" Square, 280,000-lb Striker

0.563-inch Thick Shell (300W Car), No Jacket

TC 128B Steel, CVN Energy = 86 ft-lb

0

1

2

3

4

5

6

7

8

9

10

0 5 10 15 20 25 30 35 40

Initial Striker Speed, mph

Minim

u

m

P

u

n

ctu

r

e

S

p

e

e

d, m

p

h

Without Lading Mass

With Lading Mass

FIGURE 5.6 Effect of initial striker speed on minimum puncture speed for a shell impact
82

Shell Impact, Effect of Friction

6" Square, 280,000-lb Striker

0.777-inch Thick Shell (500W Car), No Jacket

TC 128B Steel, CVN Energy = 96 ft-lb

800

850

900

950

1000

1050

1100

1150

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Coefficient of Friction

P

u

n

ctu

r

e

E

n

e

r

g

y, kip-ft

FIGURE 5.7 Effect of friction on puncture energy for a shell impact. 
83

Shell Impact, Effect of Friction

6" Square, 280,000-lb Striker

0.777-inch Thick Shell (500W Car), No Jacket

TC 128B Steel, CVN Energy = 96 ft-lb

8

8.5

9

9.5

10

10.5

11

11.5

12

0 0.05 0.1 0.15 0.2 0.25 0.3 0.35 0.4 0.45 0.5

Coefficient of Friction

Minim

u

m

P

u

n

cture

S

p

e

e

d, m

p

h

FIGURE 5.8 Effect of friction on minimum puncture speed for a shell impact.
84

5.2 Calibration to Accident Database

An extensive database of prior rail accidents and resulting lading loss, created and maintained by 

the RSI-AAR Railroad Tank Car Safety Research and Test Project, has been used in a number of 

projects over the years. In a recent RSI-AAR project [7], a regression analysis was performed on 

the database to extract smooth trends for lading loss probability as a function of a number of key 

variables. Some of these trends are plotted in Figs. 5.9 and 5.10.

These curves show that lading loss probability decreases with section thickness. The addition of 

a jacket or head shield also reduces lading loss probability. Such trends make intuitive sense. 

Rail accidents such as derailments are complex and chaotic events. Collisions of varying 

degrees of severity have occurred in rail accidents over the years, some of which result in lading 

loss. A given collision that causes lading loss in an unjacketed car may not have resulted in 

lading loss if the car had a jacket and head shield, if it had a greater section thickness, or if it 

were made from a higher-toughness steel.

The Phase I report [1] introduced the concept of puncture intensity, I, which can be viewed as the 

driving force for puncture:

Puncture Intensity I  Kinetic Energy  f G G G  1, 2 , 3 , (5.2)

The available kinetic energy in the collision   2 mV 2 is multiplied by a function of geometry 

factors, Gi, which include the size and geometry of the object that strikes the car, the location of 

the impact, and the angle of impact. Puncture occurs when the driving force, I, exceeds the 

puncture resistance, IR, which depends on material properties, section thickness, etc.

It is possible to describe the puncture intensity statistically by combining the trends inferred from 

the accident database with finite element simulation of head and shell impacts. Consider, for 

example, a jacketed tank car with 9/16 –inch (0.5625”) shell thickness. According to Fig. 5.9, this 

configuration has a 4% probability of lading loss through the shell in a mainline accident. Stated 

another way, an impact event in the 96th percentile or greater is required to cause lading loss 

through the shell in this case. Referring to Eq. (5.2), there are an infinite number of 

combinations of kinetic energy and geometry factors that will produce a given I value. For the 

present finite element study, f(Gi) is fixed, so we can quantify puncture intensity in terms of 

kinetic energy, and substitute puncture energy for IR. Therefore, the 96th percentile kinetic 

energy for shell impacts is equal to the puncture energy for a jacketed car with 9/16 –inch shell 

thickness. The puncture energy of a variety of tank car configurations can be determined from 

finite element simulation, and the corresponding percentiles determined in a similar matter. The 

results can then be fit to a statistical distribution.

A series of finite element simulations of tank car impacts were performed in order to benchmark 

to the accident database. The 4 base car configurations in Table 4.1 were subjected to the 6 

collision scenarios listed in Table 4.2 (24 simulations total). A Charpy toughness of 50 ft-lb was 

assumed, which should be reasonably representative of properties of the existing tank car fleet.
85

The results of the benchmark simulations are given in Figs. 5.11 to 5.14. These results can be 

combined with Figs. 5.9 and 5.10 to construct a statistical distribution of impact energy in past 

accidents. Note that the specific collision scenario considered here (6” striker and 280,000 lb 

weight) is meant to be a surrogate for the infinite range of possibilities, as expressed by Eq. (5.2). 

To reiterate, f(Gi) is held constant, and energy (for this specific collision scenario) is described 

statistically in place of the more general parameter, I. Given that f(Gi) is fixed, energy and I

should exhibit the same statistical variance.

As was the case in the Phase I project [1], the Weibull model was used to describe the statistical 

distribution of impact energy:

1 exp E F





            

(5.3)

where F is cumulative probability and  &  are fitting constants. For the purpose of plotting 

and fitting data, Eq. (5.3) can be linearized as follows:

ln ln 1  F    lnE   ln     (5.4)

Figures 5.15 and 5.16 are Weibull plots for shell and head impacts, respectively. The Weibull fit 

for shell impacts is given by

0.72733

1 exp 72.173

E F

            

(5.5)

The fit for head impacts is as follows:

0.4526

1 exp 28.876

E F

            

(5.6)

where energy has units of kip-ft. The above expressions can be used to predict the effect of 

design modifications and improved material properties, as discussed in Section 5.4.

Note that for the Weibull plot of shell impacts (Fig. 5.15), the data for jacketed and unjacketed 

tanks are consistent with one another. For head impacts, however, the data are more scattered 

(Fig. 5.16). The most likely explanation for the greater scatter in Fig. 5.16 is uncertainty in the 

thickness of head jackets and head shields. In Report RA-05-02, jacketed cars without head 

shields are lumped into one group and jacketed cars with head shields are in a second group. In 

the finite element study, we assumed a 0.112-inch head jacket for the first case and a 0.5-inch 

head shield (with a standoff) for the latter group. In reality, the thicknesses of head shields and 

head jackets can vary, and these values are not recorded in the accident database. Given these

unknown dimensions, the scatter in Fig. 5.16 is reasonable.
86

Shell Loss in Mainline Accidents

RSI-AAR Report RA-05-02

0.00%

2.00%

4.00%

6.00%

8.00%

10.00%

12.00%

0 0.2 0.4 0.6 0.8 1 1.2

Shell Thickness, inches

L

a

din

g

L

o

s

s

Pro

b

a

bility

Non-Jacketed

Jacketed

FIGURE 5.9 Effect of shell thickness on lading loss probability, based on regression fits to the RSI-AAR Accident Database. Data taken from RSI-AAR 

Report RA-05-02 [7].
87

Head Loss in Mainline Accidents

RSI-AAR Report RA-05-02

0.00%

1.00%

2.00%

3.00%

4.00%

5.00%

6.00%

7.00%

8.00%

9.00%

0 0.2 0.4 0.6 0.8 1 1.2

Head Thickness, inches

L

a

din

g

L

o

s

s

Pro

b

a

bility

No Head Shield or Jacket

Non-Jacketed with Head Shield

Jacketed with Head Shield

Jacketed without Head Shield

FIGURE 5.10 Effect of head thickness on lading loss probability, based on regression fits to the RSI-AAR Accident Database. Data taken from RSI-AAR 

Report RA-05-02 [7].
88

Shell Impact

TC 128B Steel, CVN Energy = 50 ft-lb

6" Square, 280,000-lb Striker

0

100

200

300

400

500

600

700

0.4 0.5 0.6 0.7 0.8 0.9 1

Shell Thickness, in

P

u

n

ctu

r

e

E

n

e

r

g

y, kip-ft

No Jacket

With Jacket

FIGURE 5.11 Effect of shell thickness on puncture energy for a shell impact.
89

Shell Impact

TC 128B Steel, CVN Energy = 50 ft-lb

6" Square, 280,000-lb Striker

0

1

2

3

4

5

6

7

8

9

0.4 0.5 0.6 0.7 0.8 0.9 1

Shell Thickness, in

Minim

u

m

P

u

n

ctu

r

e

S

p

e

e

d, m

p

h

No Jacket

With Jacket

FIGURE 5.12 Effect of shell thickness on minimum puncture speed for a shell impact.
90

Head Impact

TC 128B Steel, CVN Energy = 50 ft-lb

6" Square, 280,000-lb Striker

0

100

200

300

400

500

600

700

800

900

1000

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Head Thickness, in

P

u

n

ctu

r

e

E

n

e

r

g

y, kip-ft

No Jacket or Head Shield

0.112-inch Jacket

0.5-inch Head Shield

0.5-inch Head Shield, Jacketed Car

FIGURE 5.13 Effect of head thickness on puncture energy for a head impact.
91

Head Impact, TC 128B Steel

TC 128B Steel, CVN Energy = 50 ft-lb

6" Square, 280,000-lb Striker

0

2

4

6

8

10

12

0.4 0.5 0.6 0.7 0.8 0.9 1 1.1 1.2

Head Thickness, in

Minim

u

m

P

u

n

ctu

r

e

S

p

e

e

d, m

p

h

No Jacket or Head Shield

0.112-inch Jacket

0.5-inch Head Shield

0.5-inch Head Shield, Jacketed Car

FIGURE 5.14 Effect of head thickness on minimum puncture speed for a head impact.
92

Weibull Plot of Shell Impacts

TC 128B Steel, CVN Energy = 50 ft-lb

6" Square, 280,000-lb Striker

0

0.5

1

1.5

2

2.5

5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7

Ln(Impact Energy)

L

n[-L

n(1-F)]

Shell Only

Shell + Jacket

Weibull Fit

FIGURE 5.15 Weibull fit to shell impact energy, corresponding to the 6-inch striker that weighs 280,000 lb. This plot was constructed from Figs. 9 and 11.
93

Weibull Plot of Head Impacts

TC 128B Steel, CVN Energy = 50 ft-lb

6" Square, 280,000-lb Striker

0

0.2

0.4

0.6

0.8

1

1.2

1.4

1.6

1.8

2

5 5.2 5.4 5.6 5.8 6 6.2 6.4 6.6 6.8 7

Ln(Impact Energy)

L

n[-L

n(1-F)]

Head

Jacketed Head

Head Shield, No Jacket

Head Shield, Jacketed Car

Weibull Fit

FIGURE 5.16 Weibull fit to head impact energy, corresponding to the 6-inch striker that weighs 280,000 lb. This plot was constructed from Figs. 10 and 12.
94

5.3 Effect of Material Toughness on Lading Loss Probability

Improvements in toughness should result in improvements in puncture resistance. A series of 

tank cars impacts were simulated to verify this contention. The effect of improvements in TC 

128B steel was evaluated, as well as the effect of switching to modern HSLA steels. Of the 

HSLA steels tested in this study, HPS 100 exhibits the best toughness. As a result, this steel was 

evaluated in a series of finite element simulations of tank car impacts.

Figures 5.17 and 5.18 are plots of puncture energy and minimum puncture speed, respectively, 

versus shell thickness for TC 128B and HPS 100 steel. For the former material, A Charpy 

energy of 50 ft-lb was assumed, which conforms to the assumed toughness of the existing fleet

(Section 5.2). For the HPS 100 steel, a Charpy energy of 185 ft-lb was used in the simulations. 

These analyses predict more than a two-fold improvement in puncture energy with HPS 100 steel 

relative to the existing fleet.

Equation (5.5) can be used to predict the effect of material toughness on lading loss probability. 

Figure 5.19 is a plot of probability of lading loss versus thickness for the two materials. For 

thicker shells, there is more than a ten-fold reduction in lading loss probability when HPS 100 

steel is compared to a 50 ft-lb TC 128B material.

Puncture energy and lading loss probability can also be improved by increasing the toughness of 

TC 128B steel, as Figs. 5.20 to 5.22 illustrate. Modern low-sulfur steels with sulfide shape 

control have significantly improved upper-shelf toughness relative to the existing fleet. Thus 

even in the absence of mandated changes to tank car steel specifications, the overall lading loss 

probability should improve over time as older cars are retired and new cars are built.

Tables 5.2 and 5.3 show a comparison between the puncture resistance of 50 ft-lb TC 128B steel 

and 185 ft-lb HPS 100 steel for a chlorine car (105J500W). The six scenarios listed in Table 4.2 

were considered. As is the case with Figs. 5.17 to 5.22, the potential improvement is significant, 

particularly when defined in terms of lading loss probability for shell impacts. An approximately 

2:1 improvement in puncture energy is predicted for all six scenarios, but the predicted 

improvement in lading loss probability is much greater for shell impacts than it is for head 

impacts.

Note that the six scenarios considered above assumed that the head, shell, jacket, and head shield 

in a given case were all made from the same material. In reality, the jacket and head shield are 

not necessarily made from the same material as the head and shell. The assumption of a single 

material was made for convenience. Simulations that included multiple materials gave 

anomalous results, and we were unable to resolve this numerical difficulty within the time frame 

of the project. Given that the jacket has a modest effect on the puncture resistance (e.g., see Fig. 

4.15), the assumed toughness properties of the jacket are of relatively minor importance for shell 

impacts. In the case of head impacts, our results correspond to the scenario in which both the 

head and head shell are made with a tougher steel. If only one of these components is made with 

a toughness material, the puncture resistance will fall between the extremes of both components 

made from either a conventional carbon steel or a tough HSLA steel.
95

Shell Impact, Comparison of 2 Materials

6" Square, 280,000-lb Striker 

No Jacket

0

200

400

600

800

1000

1200

1400

1600

0.4 0.5 0.6 0.7 0.8 0.9 1

Shell Thickness, in

P

u

n

ctu

r

e

E

n

e

r

g

y, kip-ft

TC 128 B Steel, 50 ft-lb

HPS 100 Steel, 185 ft-lb

FIGURE 5.17 Effect of shell thickness and material toughness on puncture energy for a shell impact.
96

Shell Impact, Comparison of 2 Materials

6" Square, 280,000-lb Striker

No Jacket

0

2

4

6

8

10

12

14

0.4 0.5 0.6 0.7 0.8 0.9 1

Shell Thickness, in

Minim

u

m

P

u

n

ctu

r

e

S

p

e

e

d, m

p

h

TC 128 B Steel, 50 ft-lb

HPS 100 Steel, 185 ft-lb

FIGURE 5.18 Effect of shell thickness and material toughness on minimum puncture speed for a shell impact
97

Shell Impact, Comparison of 2 Materials

6" Square, 280,000-lb Striker

No Jacket

0.0001

0.001

0.01

0.1

1

0.4 0.5 0.6 0.7 0.8 0.9 1

Shell Thickness, in

L

a

din

g

L

o

s

s

P

r

o

b

a

bility

TC 128 B Steel, 50 ft-lb

HPS 100 Steel, 185 ft-lb

FIGURE 5.19 Effect of shell thickness and material toughness on lading loss probability, as computed from Fig. 5.17 and Eq. (5.5).
98

Shell Impact, Effect of Toughness

6" Square, 280,000-lb Striker

0.777-inch Thick Shell (500W Car), No Jacket

0

200

400

600

800

1000

1200

1400

0 20 40 60 80 100 120 140 160 180 200

Charpy Impact Toughness, ft-lb

P

u

n

ctu

r

e

E

n

e

r

g

y, kip-ft

TC 128 B Steel

HPS 100 Steel

FIGURE 5.20 Effect of toughness on puncture energy for a shell impact.
99

Shell Impact, Effect of Toughness

6" Square, 280,000-lb Striker

0.777-inch Thick Shell (500W Car), No Jacket

0

2

4

6

8

10

12

0 20 40 60 80 100 120 140 160 180 200

Charpy Impact Toughness, ft-lb

Minim

u

m

P

u

n

ctu

r

e

S

p

e

e

d, m

p

h

TC 128 B Steel

HPS 100 Steel

FIGURE 5.21 Effect of toughness on minimum puncture speed for a shell impact.
100

Shell Impact, Effect of Toughness

6" Square, 280,000-lb Striker

0.777-inch Thick Shell (500W Car), No Jacket

0.0001

0.001

0.01

0.1

0 20 40 60 80 100 120 140 160 180 200

Charpy Impact Toughness, ft-lb

L

a

din

g

L

o

s

s

P

r

o

b

a

bility

TC 128 B Steel

HPS 100 Steel

FIGURE 5.22 Effect of material toughness on lading loss probability, as computed from Fig. 5.17 and Eq. (5.5).
101

TABLE 5.2

Effect of design features and material toughness on puncture resistance in a 105J500W tank car .

Puncture Energy, 

kip-ft

Minimum Puncture Speed, 

mph

Estimated Lading Loss 

Impact Probability

Location

Jacket/Head 

Shield* TC 128 B

50 ft-lb

HPS 100

185 ft-lb

TC 128 B

50 ft-lb

HPS 100

185 ft-lb

TC 128 B

50 ft-lb

HPS 100

185 ft-lb

Bare Shell 422 1197 6.7 11.3 2.94 x 10-2 4.73 x 10-4 Shell

0.112” Jacket 484 1304 7.2 11.8 2.05 x 10-2 3.57 x 10-4

Bare Head 373 691 6.3 8.6 3.13 x 10-2 1.02 x 10-2

0.112” Jacket 503 1009 7.3 10.4 1.98 x 10-2 4.76 x 10-3

0.5” Head 

Shield, No 

Standoff

733 1594 8.9 13.1 9.10 x 10-3 1.31 x 10-3

Head

0.5” Head 

Shield, with 

Standoff

696 1434 8.6 12.6 1.01 x 10-2 1.69 x 10-3

*In these analyses, the jacket and head shield material was assumed to be the same as for the shell and head.

TABLE 5.3

Relative Improvement Computed from Table 5.2

Predicted Improvement from Switching to HPS 100 Steel (185 ft-lbs CVN) from 

Impact Location Jacket/Head Shield* TC 128B Steel (50 ft-lb CVN)

Puncture Energy

Minimum Puncture 

Speed Lading Loss Probability

Shell Bare Shell 284% 169% 62 Times Lower

0.112” Jacket 269% 164% 57 Times Lower

Bare Head 185% 137% 3.1 Times Lower

0.112” Jacket 201% 142% 4.2 Times Lower

0.5” Head Shield, No 

Standoff

Head 217% 147% 6.9 Times Lower

0.5” Head Shield, with 

Standoff

206% 147% 6.0 Times Lower
102

5.4 Benchmarking to Full-Scale Test Results

The Next Generation Rail Tank Car Project, which is organized by Dow, Union Pacific and 

Union Tank Car, has been working in parallel with this project to study improvements in tank car 

puncture resistance. The Next Generation Project recently completed a full-scale puncture test of

a 105J500W tank car at the Transportation Technology Center, Inc. (TTCI) in Pueblo, Colorado. 

This was actually the second test performed at TTCI for the Next Generation Project. The first 

test was preliminary, and did not result in a puncture. One of the authors of this report (SWK) 

has performed finite element simulations of these tests under the auspices of the Next Generation 

Project.

The second test was very similar to the collision scenarios assumed in the finite element 

simulations presented in this report. A bullet car weighing 286,000 lb struck the shell of the 

target car at the equator and midpoint along the length (as in Fig. 4.1). The striker was 6 in x 6 

in, with a 0.5-in chamfer radius, which is identical to the striker used for most of the simulations 

in the present study. The initial speed of the bullet car was 15.1 mph.

Mechanical testing was performed on the shell material following the test. Table 5.4 lists the 

measured tensile and Charpy properties.

The second test from the Next Generation Project was simulated in the present study using the 

procedures outlined in Section 4. Lading mass and friction effects were incorporated into the 

model, and the actual initial collision speed of 15.1 mph was used. The initial simulation of this 

test was conducted before material testing was completed, so a Charpy toughness of 50 ft-lb was 

assumed. The subsequent mechanical testing indicated that the shell material actually had a

mean Charpy energy of 106 ft-lb in the transverse direction, so the simulation was repeated with 

Gurson-Tvergaard coefficients that correspond to this higher toughness.

Figure 5.23 is a plot of energy versus time for the actual and simulated tests. Both simulations 

match the experiment very well up to the point of puncture, which indicates that the simulations 

accurately modeled the deformation of the tank car in the impact zone. The initial simulation 

that assumed a 50 ft-lb Charpy energy significantly under-predicted the puncture energy in the 

test. When the simulation was repeated with the actual material toughness, however, the 

prediction matched the experiment to within a few percent. Minimum puncture speeds of 11.1 

and 10.6 mph were inferred for the experiment and simulation, respectively. 

Figure 5.24 is a photograph of a section of the tank car shell that was removed after the test. 

When the 6-inch striker penetrated the shell, a small flap of steel rotated inward. A larger 

opening was created when the fixturing to which the striker was attached penetrated the shell. 

The events that followed the initial puncture resulted in energy dissipation, which is why the 

experimental energy v. time trend in Fig. 5.23 has a positive slope after the knee in the curve.

Typical simulations of collision and puncture events do not predict the inward rotation of a flap, 

as seen in Fig. 5.24. Rather, square piece is punched through the shell, as Figs 4.7 to 4.14 

illustrate. This is because compute simulations normally assume perfect symmetry and material 

homogeneity. In an actual experiment, the collision is not perfectly orthogonal and the material 

is not perfectly homogeneous. In order to assess the effect of a slight deviation from perfect 
103

symmetry, we performed an additional simulation of the Next Generation Test #2 in which the 

striker was oriented 2o from orthogonal to the shell. That is, the striker impacted the mid point of 

a shell at an angle of 88o

. This caused fracture to initiate on only one side of the striker, which in 

turn created a flap somewhat like that shown in Fig. 5.24. The puncture energy was not 

significantly affected by the 2o offset from perpendicular.

Table 5.4

Measured tensile and fracture toughness properties for Car 3074 in test no. 2

Specimen

Orientation

UTS,

ksi

YS,

ksi

Elong,

%

RA,

%

CVN,

ft-lbs

L 81.7 55.0 34 68 132

80.8 55.1 34 70 122

80.7 52.3 32 71 154

average = 81.1 54.1 33.3 69.7 136

T 81.2 58.9 32 68 104

81.3 57.4 33 69 110

81.1 56.9 33 66 103

average = 81.2 57.7 32.7 67.7 106
104

Next Generation Project Test #2

105J500W Car

Shell Impact

0

200

400

600

800

1,000

1,200

0 20 40 60 80 100 120 140

Time, ms

A

b

s

orb

e

d

E

n

erg

y, kip-ft

Experiment

Simulation, CVN = 106 ft-lb

Simulation, CVN = 50 ft-lb

- Puncture

FIGURE 5.23 Comparison of predicted and measured energy curves for Test # 2, performed as part of the Next Generation Project.
105

FIGURE 5.24 Experimental Test # 2, performed as part of the Next Generation Project. Cut out of impact zone.
106

6 DISCUSSION OF RESULTS

Overall, the computer simulation methodology developed in this project appears to be an 

effective tool for charactering puncture resistance in tank cars as a function of material properties 

and design parameters. There are some practical implications of this work, as well as a number 

of unresolved issues. Several of these topics are addressed below.

6.1 Triaxiality and Fracture Models

The Volpe National Transportation Systems Center has been performing simulations of dynamic 

collision, fracture, and puncture using the Bao-Wierzbicki material model [8-10]. The present 

project, as stated earlier, uses the Gurson-Tvergaard ductile fracture model. There has been 

some discussion among individuals associated with Volpe, the Next Generation Project, and this 

project as to which material model is better suited for simulation of puncture in tank cars. A 

definitive answer to this question would require an extensive comparative study of the two 

models, which is beyond the scope of this project. However, some qualitative comparisons are 

possible.

Both the Gurson-Tvergaard and Bao-Wierzbicki models purport to account for the effect of 

stress triaxiality on ductility. The former is a continuum damage model that captures the 

formation and growth of microscopic voids. The Bao-Wierzbicki model is purely empirical. 

When any failure model is incorporated into finite element analysis, where elements are deleted 

when a failure criterion is reached, the analysis must deal with length scale effects. This can be 

accomplished either by tuning the model to the specific mesh refinement or by introducing a 

length scale into the model. We applied the former approach in this study, and Volpe apparently 

uses the latter approach. When a length scale is introduced into a failure model to avoid mesh 

dependence, a convergence study should be performed to prove that the results are, in fact, mesh 

insensitive.

Figure 6.1 schematically compares the two models. The strain at fracture is plotted against the 

triaxiality ratio, which defined as follows

m

e

T 

  (6.1)

where m is the mean stress, which is the average of the three principal normal stresses:

1 2 3

3 m

  



   (6.2)

and e is the von Mises stress, which is given by

     

1 2 2 2 2

1 2 1 3 2 3

1

2

 e              (6.3)
107

The Gurson-Tvergaard model, which is based on growth of microvoids, predicts that the strain at 

fracture monotonically increases with decreasing triaxiality. According to the Bao-Wierzbicki 

model, the ductility decreases between T = 

1

/3 and T = 0, where T = 

1

/3 corresponds to uniaxial 

tension. The Gurson-Tvergaard model can be tuned to match the Bao-Wierzbicki model for 

triaxiality greater than or equal to 1/3, but the two models obviously diverge for T < 1/3. Thus a

critical issue as to the appropriateness of either or both models is whether puncture initiates by 

tensile fracture, where T > 1

/3, or if puncture is shear dominated, and T < 1/3.

Figure 6.2 shows the time history of triaxiality of elements at or near the fracture origin in 

BFCM specimens and the simulation for the Next Generation Project test #2. In all cases, T > 

1

/3, which indicates that either material model might be suitable to predict puncture. Note that 

the triaxiality decreases with increasing thickness in the BFCM specimens, and that the 

triaxiality in the thinnest specimens is most representative of the stress state in the tank car prior 

to puncture.

Although the low-triaxiality regime is apparently not important in puncture events, there are 

other important differences in the two models. For a given material, the two models can be 

tuned to give identical predictions in the tensile fracture regime. However, the two models 

appear to predict different levels of sensitivity to Charpy toughness. The Gurson-Tvergaard 

model predicts a strong relationship between Charpy toughness and puncture resistance, as Fig. 

5.23 illustrates. The Volpe studies have not included simulations of Charpy tests, so the precise 

effect of toughness on puncture resistance, as predicted by the Bao-Wierzbicki model, has not 

been quantified. However, there is limited indirect evidence that Bao-Wierzbicki failure locus

(Fig. 6.1) is not a strong function of upper shelf toughness. Further work is needed to understand 

which model provides more accurate predictions over a range of materials.

-

1/

3 1/3 0

Pure

Shear

Uniaxial

Tension

Equivalent

Strain at

Fracture

Triaxiality Ratio

Gurson-Tvergaard Model

Bao-Weirzbicki Model

FIGURE 6.1 Schematic comparison of two ductile fracture models.
108

Triaxiality v. Time History for BFCM Tests and 

Tank Car Simulation (Next Generation Test #2)

TC128-B Steel

0.0

0.2

0.4

0.6

0.8

1.0

1.2

0 1 2 3 4 5 6 7 8 9 10

Time, ms

Tria

xiality

R

atio

BFCM, t = 0.82 in

BFCM, t = 0.62 in

BFCM, t = 0.50 in

BFCM, t = 0.37 in

BFCM, t = 0.25 in

Tank Car, t = 0.777 in, timescale compressed by 10x

Uniaxial Tension

Decreasing Thickness

FIGURE 6.2 Triaxiality at the fracture origin in BFCM specimens and the Next Generation Project test #2.
109

6.2 Effect of an Energy-Absorbing Insulation Layer

At the request of The Chlorine Institute, we estimated the increase in energy absorption resulting 

from a layer of metal foam between the tank shell and jacket. Figure 6.3 illustrates the concept of 

an energy-absorbing insulation layer. When a jacketed car is impacted, there are three stages. In 

the first stage, the jacket and insulation layer collapse into the shell. For a conventional tank car 

design, minimal energy is absorbed in Stage 1, as Fig. 5.23 indicates. An energy-absorbing 

material, such as metal foam, could provide energy dissipation in Stage 1. In Stages 2 and 3, 

which involve deformation and puncture of the shell, respectively, the behavior during would not 

likely be affected by the insulation layer. Thus the overall increase in puncture energy would be 

governed by the additional energy absorption during Stage 1.

Metal foam is a product designed for acoustic and thermal insulation. It also has good energy 

absorption in crushing applications such as in automobiles in which a hollow compression 

member is filled with metal foam. During a crash event, the compression member and the metal 

foam crushes, thereby fully engaging the foam’s crushing-absorption capabilities. However, for 

tank cars, the primary resisting mechanism is flexure & catenary tension, which does not directly 

engage the foam’s crushing-absorption capabilities.

We estimated the energy absorption by examining the crushing of metal foam between the jacket 

and shell within the striker foot-print. Using this rough estimate, we inferred the increase in 

energy absorption due to installation of metal foam. We considered an aluminum metal foam 

product, Alporas produced by Shinko Wire Company, which is intended for structural energy 

absorption.

We assumed metal foam replaces the 4 inch insulation layer between the shell and the jacket. 

The energy required to crush the metal foam underlying the striker impact area (6 in x 6 in) is 2 

kip-ft or approximately 0.2% of the puncture energy for in the Next Generation Project test #2. 

In a puncture event, the zone of crushed foam will be larger than the striker footprint and energy 

will also be absorbed by flexure of the foam. Therefore, the additional energy absorption due to 

metal foam installation might range from 1 to 5% of the total puncture energy in the absence of

metal foam. Therefore, this particular metal foam product likely will not significantly increase

energy absorption during tank car collisions.

We have not simulated or performed rigorous calculations of jacketed tank cars with metal foam 

in this project. Simulations or full-scale testing might reveal secondary resisting mechanisms that 

are not apparent at present.
110

1 2 3

ENERGY

ABSORBED

TIME

Stage 1 - Deformation of Jacket & Insulation

Stage 2 - Deformation of Shell

Stage 3 - Puncture

Conventional Design

Energy-Absorbing Insulation

Energy Absorbed

by Insulation

FIGURE 6.3 Effect of an energy-absorbing insulation layer on puncture resistance of a jacketed tank car.

6.3 Developing a Performance Standard

In order to develop a performance standard for new tank car designs, there are two key questions 

that must be answered:

1. How is performance defined and quantified?

2. What level of performance is “good enough”?

The second question must be addressed by the appropriate regulatory bodies, which may include

both Government and private-sector entities. We can, however, recommend suitable approaches 

for quantifying performance with respect to puncture resistance. Moreover, we can provide 

estimates of the improvements that can be realized with existing designs combined with 

advanced steels.

Puncture resistance can be defined in at least three ways:

1. The puncture energy for a given collision scenario.

2. The minimum puncture velocity for a given collision scenario.

3. The probability of lading loss by puncture in an accident.

When comparing various design and/or material alternatives, each of the above criteria will give 

a different answer as to the relative benefit of a given alternative. For example, if the 
111

performance standard dictates that new tank cars must have twice the puncture resistance of 

traditional designs made from TC 128 B steel, then the standard must also specify whether this 

2-fold improvement is measured by puncture energy, puncture velocity, or lading loss 

probability.

When a performance standard is based on puncture energy or velocity, the precise collision 

scenario must also be defined because the energy necessary for puncture is not a fixed quantity 

for a given tank car. For example, Fig. 5.3 shows that puncture energy is sensitive to the size of 

the object that strikes the shell or head. When using puncture energy as a performance criterion, 

it is best to consider relative effects. That is, one can determine the relative improvement in 

puncture energy in a proposed tank car configuration compared to the existing fleet, given the 

same collision scenario. The implicit assumption of such a comparative exercise is that the same 

relative improvement in puncture energy will apply to other collision scenarios.

The concept of puncture intensity was introduced in the Phase I report [1] and is described in 

Section 5.2 of the present report. Puncture intensity, I, provides a means to normalize an infinite 

variety of collision scenarios into a single parameter. In Eq. (5.2), I is defined as the available 

kinetic energy in the collision times an unspecified function of other variables. Puncture occurs 

at a critical puncture intensity, IR, which characterizes the resistance to puncture of a given tank 

car. When comparing two tank cars with differing designs and/or materials of construction, the 

ratio of puncture resistance of the two cars is equal to the ratio of puncture energies because the 

unknown function on the right-hand side of Eq. (5.2) cancels in the ratio.

The puncture intensity concept makes it possible to relate a specific known and controlled 

collision scenario (e.g. the Next Generation Project test #2) to the large number of unknown and 

uncontrolled collision scenarios in the RSI-AAR accident database. Since puncture intensity 

scales with puncture energy, the exemplar collision event (where the unknown function in Eq. 

(5.2) is held constant) serves as a surrogate for the population of unknown collision events in 

past rail accidents. If we assume that past rail accidents are representative of future accidents, 

then we can predict the probability of lading loss of a proposed tank car if and when it is 

involved in a rail accident. The procedure for calibrating an exemplar collision scenario to the 

accident database is described in Section 5.2.

Figure 6.4 illustrates the application of a performance standard based on lading loss probability. 

A tank car that meets this standard exhibits an increased puncture energy in a given collision 

event, which translates to a particular lading loss probability. Note that a performance standard 

based only on puncture energy is of limited value. Unless the standard is connected to lading 

loss probability, it provides no information about the expected reduction in releases compared to 

the existing fleet. The performance standard may be expressed in terms of a specific collision 

scenario. Consider a hypothetical example: “the tank car must survive a 25 mph impact by a 

bullet car weighing 286,000 lb with a 6-inch x 6-inch chamfered striker.” A proposed 

modification in design or material of construction could be compared against this standard with 

computer simulation or full-scale testing. However, any such standard based on a specific 

scenario should be related to a maximum acceptable lading loss probability.

Table 5.3 illustrates the potential improvement in puncture resistance in chlorine cars that would 

come from constructing them out of HPS 100. Note that this comparison assumed a 185 ft-lb 

Charpy energy for HPS 100 and 50 ft-lb for the existing fleet that is made from TC 128B steel. 
112

As we have seen in the Charpy tests performed on modern, low-sulfur heats of TC 128B steel, 

the toughness can be considerably higher than 50 ft-lb. However, older vintages of TC 128B 

steel can have upper shelf Charpy values as low as 20-30 ft lb. Thus 50 ft-lb is a reasonable 

estimate of the aggregate toughness of the existing fleet.

The comparison in Table 5.3 shows a 2- to 3-fold improvement in puncture energy. The 

corresponding effect on lading loss depends on whether the car is subject to a head impact or 

shell impact. With the latter, approximately a 60-fold reduction is expected if the chlorine cars 

are built with the current design and high-toughness steel. For head impacts, only a 6-fold 

improvement is predicted.

Cumulative

Probability

100%

0%

Puncture Intensity (I)

Increasing Accident Severity

Probability

Density

100%

0%

Puncture Intensity (I)

Performance

Standard

Performance

Standard

Existing

Fleet

Existing

Fleet

FIGURE 6.4. Relationship between improved puncture energy and reduced lading loss probability.
113

7 CONCLUSIONS

1. Computational procedures were developed to simulate collision and puncture in tank cars. 

The methodology was used to quantify the effect of variables such as wall thickness, material 

toughness, internal pressure and striker size. Over 100 simulations of tank car collision 

events were performed.

2. The simulations were benchmarked against laboratory experiments and a full-scale test on a 

retired tank car. The simulation matched the puncture energy of the full-scale test to within a 

few percent. The simulations of laboratory impact tests largely matched experimental data, 

but there were some slight discrepancies in a few cases.

3. Further work is necessary to compare the material model used in this study with an 

alternative model that has been adopted by the Volpe National Transportation Systems 

Center.

4. The puncture intensity parameter, which was introduced in the Phase I study, provides a 

means to calibrate the collision simulations to the AAR-RSI accident database, which in turn 

enables us to predict the effect of design modifications and material substitutions on the 

probability of lading loss in future rail accidents.

5. The analyses indicated that fabricating chlorine cars with ultra high toughness steels would 

result in a 2- to 3-fold improvement in puncture energy, assuming the existing design 

parameters. For shell impacts, this translates to a 60-fold decrease in lading loss probability 

in an accident. For head impacts, a 6-fold decrease in lading loss probability was predicted.
114

8 REFERENCES

1. Anderson, T.L. and Kirkpatrick, S.W., “Quantifying and Enhancing Puncture Resistance in 

Railroad Tank Cars Carrying Hazardous Materials. Phase I: Preliminary Study.” 

Transportation Issues Team, the Chlorine Institute, Arlington, VA, September 2006.

2. Gurson, A.L., “Continuum Theory of Ductile Rupture by Void Nucleation and Growth: Part 

1––Yield Criteria and Flow Rules for Porous Ductile Media.” Journal of Engineering 

Materials and Technology, Vol. 99, 1977, pp. 2-15.

3. Tvergaard, V., “On Localization in Ductile Materials Containing Spherical Voids.” 

International Journal of Fracture, Vol. 18, 1982, pp. 237-252.

4. Tvergaard, V., “Material Failure by Void Growth to Coalescence.” Advances in Applied 

Mechanics, Vol. 27, 1990, pp. 83-151.

5. Chu, C.C. and Needleman, A., “Void Nucleation Effects in Biaxially Stretched Sheets.” 

Journal of Engineering Materials and Technology, Vol. 102, 1980, pp. 249-256.

6. Faleskog, J., Gao, X., and Shih, C.F., “Cell Model for Nonlinear Fracture Analysis – I. 

Micromechanics Calibration.” International Journal of Fracture, Vol. 89, 1998, pp. 355-373.

7. Treichel, T.T., Hughes, J.P., Barkan, C.P.L., Sims, R.D., Phillips, E.A., and Saat, M.R., 

“Safety Performance of Tank Cars in Accidents: Probabilities of Lading Loss.” Report 05-

02, RSI-AAR Railroad Tank Car Safety Research and Test Project, 2006.

8. Bao, Y., Wierzbicki, T., “On Fracture Locus in the Equivalent Strain and Stress Triaxiality 

Space,” International Journal of Mechanical Sciences, 2004, pp. 81-98.

9. Yu, H., Jeong, D.Y., Gordon, J.E., and Tang, Y.H., “Analysis of Impact Energy to Fracture 

Unnotched Charpy Specimens Made from Tank Car Steel.” Proceedings of the 2007 ASME 

Rail Transportation Division Fall Technical Conference, RTDF2007-46038.

10. Tang, Y.H., Yu, H., Gordon, J.E., Priante, M., Jeong, D.Y., Tyrell, D.C., and Pearlman, 

A.B.., “Analysis of Full-Scale Tank Car Shell Impact Tests.” Proceedings of the 2007 ASME 

Rail Transportation Division Fall Technical Conference, RTDF2007-46010.
115

9 APPENDICES
116

9.1 Appendix A – Summary of Literature

When the original Phase II proposal was submitted, the Transportation Issues Team requested 

that a literature search be added to the work scope. The results of this literature search are 

summarized below.

Note that this report is not a literature review, which entails an extensive treatise and critique of 

relevant published work. Rather, this is a literature summary, which catalogs and categorizes the 

available literature. Brief comments on the ramifications of published work to the Phase II 

project are provided herein.

A total of 119 references were collected and examined for relevant information. The complete 

bibliography is provided at the end of this appendix. References were numbered as they were 

collected, so the ordering has no particular relevance. Each reference was assigned a category 

that corresponded to the primary focus of the report or article.

9.1.1 Tank Car References

The group of references outlined below pertain specifically to the performance of railroad tank 

cars. The bulk of the references are reports from private organizations such as AAR and 

government agencies such as FRA, DOT, and the NTSB.

9.1.1.1 Damage Assessment & Characterization

References: 1, 2, 7, 40, 41, 65

This series of reports and articles discuss the appropriate way to characterize rail car damage 

following accidents.

9.1.1.2 Experiments and Semi-Empirical Models for Puncture

References: 3, 4, 6, 8, 9, 11, 36, 52, 53, 55

This group of references includes several reports that contain the results of head puncture tests. 

A semi-empirical model for puncture velocity was developed from these test data. This 

information will be used as a reality check for the computer models.

9.1.1.3 Risk Assessment

References: 5, 10, 12, 19, 21, 26, 27, 38, 49, 57, 62
117

These articles and reports address the factors that contribute to risk of release of hazardous cargo 

from tank cars. This subject matter provides a global perspective on risk, including variables 

such as human factors, environmental factors, as well as the design of individual tank car 

components.

9.1.1.4 Computer Modeling

References: 13, 24, 35, 48

Published work on computer modeling of collision and puncture in tank cars is limited. Only a 

handful of organizations, such as VOLPE, ARA, and HLA, appear to be involved in this type of 

work.

9.1.1.5 Design and Regulation

References: 14, 17, 18, 20, 34, 37, 67

This group of references includes DOT documents, public testimony, and committee 

correspondence.

9.1.1.6 Accident Reports

References: 16, 22, 42, 45, 46, 47

This set includes NTSB reports on recent rail accidents, such as Minot and Graniteville.

9.1.1.7 Properties of Tank Car Steels

References: 23, 25, 28, 29, 30, 31, 32, 33, 50, 51, 59, 60, 61

The properties of existing and proposed tank car steels have been extensively studied over the 

past 30 years. The primary focus has been on improving the resistance to brittle fracture. The 

upper-shelf toughness, which is related to puncture resistance, has largely been ignored in prior 

studies on tank car steel.

9.1.2 Relevant Research in Non-Rail Applications

In addition to tank cars, there are other structural applications in which collision, puncture, and 

fracture are of concern. Examples include marine structures and aerospace structures. A 

significant amount of research has been performed on constitutive model development and 

computer simulation.
118

9.1.2.1 Constitutive Model Development

References, Gurson-Tvergaard and Related Models: 70, 87, 91, 93, 96, 97, 98, 101

References, Other Models: 69, 75, 78, 82, 94, 95, 100, 106, 107

The Gurson-Tvergaard (GT) model is, by far, the most widely referenced model for ductile 

rupture. It is a physically-based damage model that represents a porous material (i.e., a ductile 

metal with microvoids) as a smeared continuum. This model was chose for the Phase II 

simulation work.

A variety of other constitutive models have been published. Most are not suitable for the Phase 

II work for a variety of reasons:

 Some of the published failure models are highly theoretical and esoteric (e.g., models of 

fracture at the atomic level), so they are not suitable for computer simulation of full-scale 

structures.

 Lesser-known models do not have a proven track record and they are not implemented in 

commercial explicit finite element software such as ABAQUS and LS-DYNA.

 Several articles in the list of references pertain to failure models in composites. While 

such models may prove useful in the Next Generation project, they are not relevant to the 

Phase II work.

There are alternatives to the GT model that could have been applied in the Phase II work. 

However, we did not find a model that has clear advantages over GT. For example, the JohnsonCook model appears to be the second-most widely referenced approach. Reference 68 describes 

a modified Johnson-Cook model that accounts for adiabatic heating at very high strain rates. 

Such an approach is appropriate for ballistic impact modeling. Tank car collisions do not 

experience sufficiently high strain rates to result in significant adiabatic heating of the steel.2

 

2

 The “bow-tie” specimens tested in the BFCM at Southwest Research Institute did experience significant heating, 

but videos clearly show that this heating occurred as a result of the striker rubbing on the fracture surface after the 

specimen failed.
119

9.1.2.2 Impact/Puncture/Fracture Simulation

References, Gurson-Tvergaard and Related Models: 71, 72, 76, 85, 86, 88, 90, 92, 102, 104, 

109, 110, 114

References, Other Models: 68, 73, 74, 77, 79, 80, 81, 83, 84, 89, 99, 103, 103, 108, 112, 113, 

115, 116, 117, 118, 119

The bibliography contains a roughly equally-divided number of simulations with the GT model 

versus other approaches. The most common failure criterion in these simulations, aside from the 

GT model, is a critical fracture strain or some variation thereof. Critical strain as a failure 

criterion suffers from two key disadvantages:

 Fracture strain is sensitive to the stress state, particularly the degree of stress triaxiality. 

Consequently, a failure strain inferred from a tensile test is not applicable to a more 

complicated load case.

 A strain-based criterion does not enable one to quantify the effect of material toughness 

on puncture resistance.

As is the case with other failure models that are applied to a simulation involving element 

deletion, critical fracture strain in a simulation is mesh-dependent. In other words, if the mesh 

refinement is varied in a series of simulations where an element is deleted when it reaches the 

assumed fracture strain, the results will change with element size. Simulations that use the GT 

ductile fracture model are also mesh dependent, so it important to calibrate the model to the 

particular mesh that is used for the analysis.

NASA has studied puncture resistance of the outer skin of the International Space Station to 

ensure that it can withstand collisions by small debris. However, they use a fracture mechanics 

model to quantify puncture resistance. This approach is not suitable for the Phase II work. A 

fracture mechanics-based failure model assumes propagation from a pre-existing crack. The 

predictions are highly sensitive to the assumed initial crack size. Puncture normally involves the 

creation of an opening in the absence of a significant pre-existing flaw.

9.1.3 Conclusions

While the GT model is not universally used to characterize and predict ductile rupture in metals, 

there is certainly a consensus behind this model. It has the advantage of being physically based, 

so there is a high likelihood that laboratory data can be reliably transferred to structural 

applications using the GT material model.

There is ample precedent in the published literature for using the GT model in dynamic 

simulations of puncture and rupture. Some of the common alternative criteria, such as critical 

failure strain, are over-simplified and do not recognize the inherent mesh dependence of 

simulations that involve element deletion.
120

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124

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129

9.2 Appendix B – Tabulated Results for Tank Car Simulations.

shell only / 

jacketed / 

shield

impact material charpy 

value size initial velocity

weight

if ≠ 280k final at leak final at leak

ft-lb mm psi in. mph kip kip*ft kip*ft mph mph

100W 6 shell only broadside TC128-B 50 5.0 55.0 none 6 40.0 223 211 4.9 4.7

100W 7 jacketed broadside TC128-B 50 5.0 55.0 none 6 40.0 312 300 5.8 5.7

100W 8 shell only head TC128-B 50 5.0 55.0 none 6 40.0 187 185 4.5 4.4

100W 10 jacketed head TC128-B 50 5.0 55.0 none 6 40.0 354 347 6.2 6.1

100W 11 jacket+shield head TC128-B 50 5.0 55.0 none 6 40.0 619 609 8.1 8.1

100W 12 shell only broadside HPS-100 185 5.0 55.0 none 6 40.0 575 543 7.8 7.6

100W 13 shield head TC128-B 50 5.0 55.0 none 6 40.0 647 636 8.3 8.2

300W 10 shell only broadside TC128-B 112 2.5 300.0 none 6 40.0 302 297 5.7 5.6

300W 11 shell only broadside TC128-B 112 2.5 150.0 none 6 40.0 409 400 6.6 6.5

300W 12 shell only broadside TC128-B 86 2.5 71.4 none 6 40.0 505 481 7.3 7.2

300W 15 shell only head TC128-B 86 2.5 71.4 none 6 40.0 441 429 6.9 6.8

300W 16 shell only broadside TC128-B 86 2.5 71.4 none 6 30.0 552 536 7.7 7.6

300W 17 shell only broadside TC128-B 86 2.5 71.4 none 6 20.0 545 537 7.6 7.6

300W 18 jacketed broadside TC128-B 91 5.0 71.4 none 6 40.0 611 579 8.1 7.9

300W 20 shell only broadside TC128-B 50 5.0 71.4 none 6 40.0 292 279 5.6 5.5

300W 21 jacketed broadside TC128-B 50 5.0 71.4 none 6 40.0 367 352 6.3 6.1

300W 22 shell only head TC128-B 50 5.0 71.4 none 6 40.0 248 247 5.1 5.1

300W 24 jacketed head TC128-B 50 5.0 71.4 none 6 40.0 356 345 6.2 6.1

300W 25 jacket+shield head TC128-B 50 5.0 71.4 none 6 40.0 647 635 8.3 8.2

300W 26 shell only broadside HPS-100 185 5.0 71.4 none 6 40.0 894 823 9.8 9.4

300W 27 shield head TC128-B 50 5.0 71.4 none 6 40.0 671 653 8.5 8.4

300W 28 shell only broadside TC128-B 86 2.5 71.4 none 6 40.0 636 8.2

300W 29 shell only broadside TC128-B 86 2.5 71.4 none 6 30.0 781 9.1

300W 30 shell only broadside TC128-B 86 2.5 71.4 none 6 20.0 896 9.8

300W 31 shell only broadside TC128-B 86 2.5 71.4 none 6 40.0 402 6.6

300W 32 shell only broadside TC128-B 86 2.5 71.4 none 6 30.0 530 7.5

300W 33 shell only broadside TC128-B 86 2.5 71.4 none 6 20.0 796 9.2

absorbed 

energy equiv velocity tank 

car 

model

FEM 

# friction mesh size pressure lading

config material props striker
130

shell only / 

jacketed / 

shield

impact material charpy 

value size initial velocity

weight

if ≠ 280k final at leak final at leak

ft-lb mm psi in. mph kip kip*ft kip*ft mph mph

500W 17 shell only broadside TC128-B 112 2.5 250.0 none 6 40.0 603 595 8.0 8.0

500W 18 shell only broadside TC128-B 112 2.5 125.0 none 6 40.0 898 898 9.8 9.8

500W 19 shell only broadside TC128-B 112 2.5 62.5 none 6 40.0 1,300 1,300 11.8 11.8

500W 20 shell only broadside TC128-B 112 2.5 31.3 none 6 40.0 2,084 2,011 14.9 14.7

500W 21 shell only broadside TC128-B 112 2.5 0.0 none 6 40.0 2,436 2,436 16.1 16.1

500W 22 shell only broadside TC128-B 86 2.5 115.2 none 6 40.0 793 754 9.2 9.0

500W 23 shell only head TC128-B 86 2.5 115.2 none 6 40.0 614 603 8.1 8.0

500W 24 shell only head TC128-B 86 2.5 500.0 none 6 40.0 334 326 6.0 5.9

500W 25 shell only head TC128-B 86 2.5 250.0 none 6 40.0 443 430 6.9 6.8

500W 26 shell only head TC128-B 86 2.5 88.7 none 6 40.0 671 658 8.5 8.4

500W 27 shell only head TC128-B 86 2.5 31.3 none 6 40.0 822 799 9.4 9.2

500W 28 shell only head TC128-B 86 2.5 0.0 none 6 40.0 1,044 994 10.6 10.3

500W 29 shell only broadside TC128-B 114 5.0 88.7 none 6 40.0 795 765 9.2 9.0

500W 30 shell only broadside TC128-B 76 5.0 115.2 none 6 40.0 603 583 8.0 7.9

500W 31 shell only broadside TC128-B 93 5.0 115.2 none 6 40.0 800 784 9.3 9.2

500W 32 shell only broadside TC128-B 96 5.0 115.2 none 6 40.0 860 834 9.6 9.4

500W 33 shell only broadside TC128-B 86 5.0 115.2 none 6 40.0 747 719 8.9 8.8

500W 34 shell only broadside TC128-B 126 5.0 125.0 none 6 40.0 1,076 1,052 10.7 10.6

500W 35 shell only broadside TC128-B 118 5.0 125.0 none 6 40.0 1,035 991 10.5 10.3

500W 36 shell only broadside TC128-B 92 5.0 115.2 none 6 40.0 673 647 8.5 8.3

500W 37 shell only broadside TC128-B 92 5.0 115.2 none 12 40.0 2,187 2,029 15.3 14.7

500W 38 jacketed broadside TC128-B 92 5.0 115.2 none 6 40.0 937 920 10.0 9.9

500W 40 shell only broadside TC128-B 92 5.0 115.2 none 15 40.0 3,214 2,837 18.5 17.4

500W 41 shell only broadside TC128-B 96 0.5 5.0 115.2 none 6 40.0 1,097 1,047 10.8 10.6

500W 42 shell only broadside TC128-B 50 5.0 115.2 none 6 40.0 422 408 6.7 6.6

500W 43 jacketed broadside TC128-B 50 5.0 115.2 none 6 40.0 484 467 7.2 7.1

500W 44 shell only head TC128-B 50 5.0 115.2 none 6 40.0 373 371 6.3 6.3

config absorbed 

energy equiv velocity tank 

car 

model

FEM 

# friction mesh size pressure lading

material props striker
131

shell only / 

jacketed / 

shield

impact material charpy 

value size initial velocity

weight

if ≠ 280k final at leak final at leak

ft-lb mm psi in. mph kip kip*ft kip*ft mph mph

500W 44 shell only head TC128-B 50 5.0 115.2 none 6 40.0 373 371 6.3 6.3

500W 46 jacketed head TC128-B 50 5.0 115.2 none 6 40.0 503 488 7.3 7.2

500W 47 jacket+shield head TC128-B 50 5.0 115.2 none 6 40.0 696 694 8.6 8.6

500W 48 shell only broadside HPS-100 185 5.0 115.2 none 6 40.0 1,197 1,185 11.3 11.3

500W 49 jacketed broadside HPS-100 185 5.0 115.2 none 6 40.0 1,305 1,246 11.8 11.5

500W 50 jacketed head HPS-100 185 5.0 115.2 none 6 40.0 1,009 970 10.4 10.2

500W 51 shell only head HPS-100 185 5.0 115.2 none 6 40.0 691 689 8.6 8.6

500W 54 jacket+shield head HPS-100 185 5.0 115.2 none 6 40.0 1,478 1,435 12.6 12.4

500W 55 jacket+shield head HPS-100 / 

TC128-B 185 5.0 115.2 none 6 40.0 917 915 9.9 9.9

500W 56 shell only broadside TC128-B 50 5.0 115.2 chlorine 6 40.0 354 325 6.2 5.9

500W 57 shield head TC128-B 50 5.0 115.2 none 6 40.0 733 729 8.9 8.8

500W 58 jacketed broadside TC128-B 50 0.1 5.0 100.0 water 6 15.1 286 1,151 1,122 11.0 10.8

500W 59 shield head HPS-100 185 5.0 115.2 none 6 40.0 1,595 1,564 13.1 12.9

500W 60 shell only broadside TC128-B 96 0.1 5.0 115.2 none 6 40.0 909 870 9.9 9.6

500W 61 shell only broadside TC128-B 96 0.2 5.0 115.2 none 6 40.0 991 953 10.3 10.1

500W 64 jacketed broadside TC128-B 50 0.1 5.0 100.0 chlorine 6 15.1 286 495 478 7.2 7.1

500W 65 jacketed broadside TC128-B 50 0.1 5.0 100.0 chlorine 6 40.0 286 397 6.4

500W 67 jacketed broadside TC128-B 50 0.1 5.0 100.0 chlorine 6 15.1 286 477 437 7.1 6.8

500W 68 jacketed broadside TC128-B 106 0.1 5.0 100.0 chlorine 6 15.1 286 1,066 1,035 10.6 10.4

500W 69 jacketed broadside TC128-B 106 0.1 5.0 100.0 chlorine 6 40.0 286 767 1 9.1 0.4

600W 3 shell only broadside TC128-B 86 2.5 137.9 none 6 40.0 1,028 988 10.5 10.3

600W 5 jacketed broadside TC128-B 91 5.0 137.9 none 6 40.0 985 944 10.3 10.0

600W 6 shell only broadside TC128-B 50 5.0 137.9 none 6 40.0 573 562 7.8 7.8

600W 7 jacketed broadside TC128-B 50 5.0 137.9 none 6 40.0 637 612 8.3 8.1

600W 8 shell only head TC128-B 50 5.0 137.9 none 6 40.0 536 505 7.6 7.3

600W 10 jacketed head TC128-B 50 5.0 137.9 none 6 40.0 720 700 8.8 8.6

600W 11 jacket+shield head TC128-B 50 5.0 137.9 none 6 40.0 914 900 9.9 9.8

600W 12 shield head TC128-B 50 5.0 137.9 none 6 40.0 882 866 9.7 9.6

600W 13 shell only broadside HPS-100 185 5.0 137.9 none 6 40.0 1,394 1,366 12.2 12.1

config striker absorbed 

energy equiv velocity

pressure lading

tank 

car 

model

FEM 

# friction mesh size

material props

Simulations resembling Next Generation Project Test #2 are marked yellow.