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 1 

Proceedings of the 2007 ASME Rail Transportation Division Fall Technical Conference 

RTDF2007 

September 11-12, 2007 Chicago, Illinois, USA 

RTDF2007-46038 

ANALYSIS OF IMPACT ENERGY TO FRACTURE UNNOTCHED CHARPY 

SPECIMENS MADE FROM RAILROAD TANK CAR STEEL 

H. Yu 

Chenga Advanced Solutions & Engineering, LLC 

Cambridge, Massachusetts USA 

D.Y. Jeong 

Volpe National Transportation Systems Center 

Cambridge, Massachusetts USA 

J.E. Gordon 

Volpe National Transportation Systems Center 

Cambridge, Massachusetts USA 

Y.H. Tang 

Volpe National Transportation Systems Center 

Cambridge, Massachusetts USA 

ABSTRACT 

This paper describes a nonlinear finite element analysis 

(FEA) framework that examines the impact energy to fracture 

unnotched Charpy specimens by an oversized, nonstandard 

pendulum impactor called the Bulk Fracture Charpy Machine 

(BFCM). The specimens are made from railroad tank car steel, 

have different thicknesses and interact with impact tups with 

different sharpness. The FEA employs a Ramberg-Osgood 

equation for plastic deformations. Progressive damage and 

failure modeling is applied to predict initiation and evolution of 

fracture and ultimate material failure. Two types of fracture 

initiation criterion, i.e., the constant equivalent strain criterion 

and the stress triaxiality dependent equivalent strain criterion, 

are compared in material modeling. The impact energy needed 

to fracture a BFCM specimen is calculated from the FEA. 

Comparisons with the test data show that the FEA results 

obtained using the stress triaxiality dependent fracture criterion 

are in excellent agreement with the BFCM test data. 

INTRODUCTION 

The loss of lading from railroad tank cars involved in 

accidents is commonly caused by failures in three general 

locations: (1) tank end cap or head, (2) side of the tank or 

shell, and (3) damage to fittings and valves. Failures in the 

tank car head and shell occur from collisions with objects, such 

as couplers and wheels from adjacent cars, broken rails, etc. 

Research is ongoing within the government and the 

industry to improve the safety of railroad tank cars carrying 

hazardous materials (hazmat). Scaled and full-scale impact 

testing have been performed in the past to examine the 

puncture resistance of railroad tank cars [1-2], but the 

mechanics of material failure under such loading conditions are 

not well understood. Moreover, no industry-accepted standard 

currently exists to quantify the puncture behavior of materials. 

In this paper, a nonlinear finite element analysis (FEA) 

approach is described that examines the fracture of unnotched 

specimens subjected to pendulum impact loading. Different 

material failure criteria are used in conjunction with the 

nonlinear FEA to simulate the tests and to calculate fracture 

energy. The criteria are based on the state of stress and strain in 

the impacted specimen. Moreover, a failure criterion based on 

stress triaxiality, which is a parameter related to the state of 

stress, provides excellent agreement with the test data for 

fracture energy. 

PENDULUM IMPACT TESTING 

Previous research to examine the resistance of tank car 

steels to impact loading has focused on fracture toughness or 

Charpy V-notch (CVN) energy. Industry-accepted procedures 

exist to conduct these types of tests, which use specimens 

containing a pre-existing crack (usually fatigue-sharpened) or a 

stress concentration or notch. However, the physical 

significance of fracture toughness or impact energy in a 

structure without a pre-existing crack is unclear. 

Pendulum impact testing, such as the standard CVN test, 

has been used to examine the impact resistance of materials for 

over a century because it is relatively simple, inexpensive, and 

rapid to perform [3]. In addition, the physical interpretation of 

the test is clear. The energy available to fracture the specimen 

is proportional to the initial height of the swing hammer above 

a reference level (y1 in Figure 1). The energy remaining in the 

hammer is characterized by the height to which it recovers (y2), 

and the weight of the striker times the difference (y1-y2) 

represents the energy absorbed by the specimen. The physics 

of the pendulum test are the same whether the specimen 
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 2 

contains a notch or not. However, more energy is needed to 

fracture an unnotched specimen compared to one containing a 

notch. 

Figure 1. Schematic of Pendulum Impact Test 

An oversized, nonstandard pendulum impactor was built 

by Southwest Research Institute (SwRI) to examine the fracture 

energy of different tank car steels (see Figure 2). The size of 

the fixture was necessary in order to achieve the levels of 

energy needed to fracture the unnotched specimens. This 

pendulum test fixture, called the Bulk Fracture Charpy 

Machine (BFCM), was constructed specifically to conduct 

studies to assess puncture behavior. That is, the measurement 

of fracture energy is used to assess the puncture resistance of 

tank car steel. 

Figure 2. Oversized, Nonstandard Pendulum Impactor 

Figure 3 shows a drawing of a BFCM test specimen. The 

trapezoidal ends of the specimen self-engage into the test 

fixture, so they are held fixed as the impact load is applied 

through the pendulum. In this drawing, the test section is 6 

inches long, and the specimen width is 1 inch. 

Figure 3. BFCM Test Specimen 

Two batches of normalized TC128-B steel were used in the 

tests, and are identified as Materials 1 and 2 in Table 1 with 

their respective tensile properties. Properties for Material 1 are 

averages of tensile test results in longitudinal and transverse 

orientations of tank car plates, whereas properties for Material 

2 were obtained from tensile tests in the longitudinal 

orientation. Material 1 appears to have slightly higher yield 

and ultimate tensile strengths than Material 2. 

Table 1. Mechanical Properties for Normalized TC-128B 

 Material 1 Material 2 

Ultimate tensile strength 90.6 ksi 87.3 ksi 

Yield strength 64.2 ksi 59.2 ksi 

Elongation 27.5% 27% 

Reduction in area 58% 59% 

Two impact tups were used in the tests: a blunt tup with a 

0.5 inch wide contact surface (Figure 4), and a sharp tup with a 

0.125 inch wide contact surface (Figure 5). Table 2 indicates 

combinations of BFCM test conditions in terms of impact tup, 

specimen material and specimen thickness. 
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 3 

Figure 4. Blunt Impact Tup 

Figure 5. Sharp Impact Tup 

Table 2. BFCM Test Combinations of Impact Tup, 

Specimen Material and Specimen Thickness 

 Thickness (B, inches) 

Blunt tup Material 1 0.827, 0.625, 0.5, 0.375, 0.25 

Sharp tup Material 2 0.81, 0.75, 0.625, 0.5, 0.375, 0.19

Figure 6 shows data from the BFCM tests conducted on 

specimens of varying thicknesses and using different impact 

strikers or tups [4]. The error bars represent the variability in 

the test data in terms of two standard deviations above and 

below the average for a given specimen thickness. The figure 

also shows regression curves of the test data for two different 

tups. The regression curves suggest that the BFCM fracture 

energy is related to the specimen thickness squared. Moreover, 

the test data indicate that more energy is required to fracture an 

unnotched specimen with the blunt tup than with the sharp tup. 

Specimen Thickness (inches)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fracture Energy (ft-lb)

0

1000

2000

3000

4000

5000

6000

7000

8000

Test Data

Average - Blunt striker

Average - Sharp striker

Error bars represent ±2 standard deviations

Nominal specimen width is 1.0 inch

E=915+8933B2

with E (ft-lb) and B (inch)

E=-84.7+9598B2

with E (ft-lb) and B (inch)

Figure 6. Fracture Energy of Normalized TC-128B Tank 

Car Steel as a Function of Specimen Thickness from BFCM 

Tests 

FRACTURE INITIATION CRITERIA AND STRESS 

TRIAXIALITY 

Different criteria were used in the nonlinear FEA to predict 

the onset of fracture in ductile metals such as steel: (1) 

prescribed maximum effective/equivalent strain to fracture, and 

(2) effective/equivalent fracture strain as a function of stress 

triaxiality. Stress triaxiality describes the portion of the stress 

tensor that is hydrostatic. For positive stress triaxiality, a stress 

state with high stress triaxiality approaches the completely 

hydrostatic state; with lower triaxiality stress states, the 

deviatoric component becomes a more significant portion of 

the stress tensor. 

Mathematically, stress triaxiality is the ratio of mean stress 

to effective or von Mises equivalent stress, or 

m

e

σ

η

σ = (1) 

In terms of principal stresses, the mean stress and the effective 

stress are defined as 

( ) 123

1

3

σ m = ++ σσσ (2) 

2 22

12 23 31

1

( )( )( )

2 e σ σσ σσ σσ = − +− +−     (3) 
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 4 

Mean or hydrostatic stress is associated with dilatation or 

the change in volume of a solid element. Effective or von 

Mises stress is directly related to octahedral shearing stress, 

which in turn is related to distortional energy or the energy to 

change the shape of a solid element. Therefore, a physical 

interpretation of stress triaxiality is that it is the ratio of volume 

change to shape change. 

Figure 7 shows a schematic of the fracture initiation 

envelope for effective strain as a function of stress triaxiality 

[5]. Different modes of fracture are represented by different 

states of stress in terms of stress triaxiality. High stress 

triaxiality promotes microvoid growth and coalescence (Region 

I). Localized shear bands develop at negative or low levels of 

stress triaxiality, which may result in shear fracture (Region 

III). Intermediate levels of stress triaxiality may result in 

mixed mode fracture (Region II). The figure also shows a 

curve with a constant fracture initiation strain, which is 

intended to represent the prescribed maximum effective strain 

criterion that is independent of stress triaxiality. 

Pure shear Stress triaxiality, η

(II) Mixed

mode fracture

(III) Shear

fracture (I) Ductile fracture

ε

_

0

pl Equivalent plastic strain

at fracture initiation,

Uniaxial tension

Constant fracture

initiation strain criterion

Figure 7. Schematic of Fracture Initiation Envelope Based 

on Stress Triaxiality 

FINITE ELEMENT ANALYSIS 

The FEA of the BFCM tests was conducted using the 

commercial software ABAQUS/Explicit [6]. Figure 8 shows a 

typical FEA model setup assuming quarter symmetries about xz and y-z planes, where x-axis is along the longitudinal 

direction, y-axis along the width and z-axis along the thickness 

of a specimen. Model components include the impact tup with 

an initial impact velocity v0, the specimen and a specimen 

fixture that holds the trapezoidal end of the specimen. The 

initial impact velocity v0 was set at 14 mph, equivalent to the 

velocity gained by a mass at the end of a 52.45 inch long 

pendulum arm with a drop angle of 120 degrees. Impact tupspecimen and specimen-fixture contacts were defined and the 

coefficient of friction was set to be 0.57. 

X Y

Z

Sharp tup

Specimen

Specimen fixture

Symmetric planes are

x-z and y-z planes

X Y

Z

Blunt tup

Specimen

Specimen fixture

Figure 8. Typical Quarter Symmetric Model of BFCM 

Tests with Blunt and Sharp Impact Tups 

Elastic properties for all specimens were assumed as: 

Young’s modulus E=30,000 ksi, and Poisson’s ratio ν=0.3. A 

Ramberg-Osgood relation for stress (σ) versus strain (ε) was 

adopted for plastic material behavior: 

( )

n ε = σ E + σ K (4) 

where K and n are material constants that can be calibrated 

from the yield and ultimate tensile strengths with the 

assumption that the yield strength corresponds to the 0.2% 

offset (plastic) strain and the ultimate tensile strength 

corresponds to a total strain of 20%. 

Figure 9(a) shows a stress-strain (σ-ε) relation employed in 

ABAQUS/Explicit for ductile metals up to complete material 

failure. Typical linear elastic and strain hardening responses 

are followed first. As the yield stress evolves to the peak level, 

an additional overall damage variable D is introduced and 

damage initiates with D=0. The equivalent plastic strain at the 

onset of damage is denoted as pl

0 ε , and it can be a function of 

stress triaxiality (η), strain rate, temperature, etc. Subsequently 

the yield stress softens and the elastic modulus degrades until 

the strain reaches pl

f ε , or the equivalent plastic strain at 

complete failure, where D reaches the maximum degradation 

Dmax≤1. Finally, elements representing failed material points 

are removed from the model. 

To deal with the spurious mesh dependence associated 

with strain softening or “strain localization,” an element 

characteristic length Le is introduced. For shell and 2-D 

elements, Le is the square root of the integration point area, and 

for 3-D elements, it is the cubic root of the integration point 
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 5 

volume [7]. Then a stress-displacement (σ-u) relation shown in 

Figure 9(b) replaces the σ-ε relation in Figure 9(a) in the 

material property definition, where u is related to ε by Le such 

that u= Leε. Following damage initiation, the equivalent plastic 

displacement pl u evolves according to pl

e

pl ε & & u = L until it 

reaches pl

f u at failure. In this study, displacement based 

damage evolution laws in ABAQUS/Explicit were selected and 

assigned a linear form. Thus the definition of a fracture 

initiation envelop in the η- pl

0 ε plane and that of an equivalent 

plastic displacement at complete failure ( pl

f u ) completes the 

damage and failure material characterization. 

σ

ε

ε 0

pl εfpl

σy0

E

E

D=0

(1-D)E

_ _

(a)

σ

u=L ε

L ε 0

pl u =L ε fpl

f

_ _ pl _

e e

e

(b)

Figure 9. Illustration of ABAQUS Progressive Damage 

and Failure Modeling for Ductile Metals: (a) Typical StressStrain (σ-ε) Relation, and (b) Stress-Displacement (σ-u) 

Relation with the Introduction of an Element Characteristic 

Length Le

A stress triaxiality dependent fracture initiation envelop 

such as the one shown in Figure 7 can be approximated with 

the following analytical forms [8] 

( )

( )( ) 













≤

+ − ≤ ≤

+ − < ≤

∞ ≤ −

=

η η η η

η η η η

η η

η

ε

2 0 0

0

2

1 2 1 0

1 pl

0

 

 0

1 3 1 3 0

 1 3

C ,

C C C ,

C ,

,

 (5) 

 

where C1 is equal to pl

0 ε in pure shear (η=0) and C2 is equal to 

pl

0 ε in uniaxial tension (η=η0). A so-called quick calibration 

method has been developed by Lee and Wierzbicki [8] to 

correlate C1, C2 and η0 with the uniaxial tensile properties and 

was adopted in this study. However, while Lee and Wierzbicki 

[8] defined η0 as the averaged stress triaxiality over the 

deformation history domain, in this study we treated η0 as the 

instantaneous stress triaxiality in uniaxial tension such that 

η0=1/3. 

 There has not been a known calibration method for the 

softening parameter, pl

f u , which measures the displacement 

capacity of a material beyond fracture initiation but prior to 

complete failure. In this study, pl uf was calculated as 

pl

f u = pl1f u = Lmε1f (6) 

where pl

1f u is the failure displacement in uniaxial tension, ε1f is 

the strain localization at failure in uniaxial tension and Lm is a 

material characteristic length over which ε1f is measured. With 

the limited test data available, ε1f was defined as the elongation 

in uniaxial tension and Lm the gauge length over which the 

elongation was measured. 

The calibrated plastic and damage/failure material 

parameters using the data in Table 1 are summarized in Table 3. 

The fracture initiation envelopes derived for both materials are 

shown in Figure 10. 

Table 3. Calibrated Material Parameters for Normalized 

TC-128B Materials 

K (ksi) n η0 C1 C2 pl

f u (inch)

Material 1 102.3 13.35 1/3 0.223 0.868 0.275 

Material 2 100.2 11.82 1/3 0.256 0.892 0.27 

Stress Triaxiality

0.0 0.5 1.0 1.5 2.0

Effective Strain to Fracture Initiation 0.0

0.5

1.0

1.5

2.0

Material 1

Material 2

-0.3

Figure 10. Stress Triaxiality Based Fracture Initiation 

Envelops for TC-128 Tank Car Steel 
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Figure 11 compares the post-failure shape of a BFCM 

specimen obtained from the FEA and a test. The deformed 

shapes look similar between the analysis result and the test 

photograph. An output of interest from both tests and 

simulations is the impact energy needed to fail a specimen, 

which was calculated as 

( ) 2

0

2

2

1 E = m v − v (7) 

where m=2378 pounds is the impactor mass, v0=14 mph is the 

initial impact velocity, and v is the post-impact velocity after 

the impactor completely detaches from the specimen. 

Test

FEA

Figure 11. Deformed Shapes of BFCM Specimen from FEA 

and Test 

Both continuous and tied solid elements were employed in 

the FE models of the BFCM specimens, and mesh sensitivity 

was examined by varying the number of solid element layers 

through the thickness while keeping the solid element aspect 

ratios close to 1:1:1. The main advantage of employing the tied 

solid element technique is that low to moderate computational 

cost can be maintained when finer mesh is needed in the 

relatively small impact zone but not necessary in the rest of the 

specimen. Simulations of the test combination {Blunt tup, 

Material 1, B=0.827 inches} were selected for the mesh 

sensitivity study. Figure 12 plots the impact energy calculated 

according to Equation (7) versus the number of through-thethickness element layers. The tied and continuous solid 

element methods yield very comparable results. Furthermore, 

the FEA results in terms of impact energy appear to converge 

with six layers of through-the-thickness elements. As a result, 

in this study the number of elements through the specimen 

thickness was set to be six, and tied solid elements were used. 

Number of element layers through thickness

4567

Fracture Energy (ft-lb) 6300

6400

6500

6600

6700

6800

6900

7000

Test

Tied solid elements

Continuous solid elements

Specimen thickness = 0.83 inch

Figure 12. Convergence of Impact Energy with Mesh 

Refinement 

RESULTS 

Figure 13 compares the results from the FEA using the 

maximum effective strain criterion with the test data for the 

blunt impactor. The constant fracture initiation strain in the 

analyses was assumed to be 20%, whereas the plastic (K, n) 

and softening parameters ( pl

f u ) were the same as those in Table 

3. This approach underestimates the impact energy for the 

thicker specimens and overestimates it for the thinner ones. 

Specimen Thickness (inches)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fracture Energy (ft-lb)

0

1000

2000

3000

4000

5000

6000

7000

8000

Test Data

Average

FEA

Error bars represent ±2 standard deviations

Nominal specimen width is 1.0 inch

MAXIMUM EFFECTIVE STRAIN CRITERION

With linear softening

E=915+8933B2

with E (ft-lb) and B (inch)

Figure 13. Comparison Between Tests and Analyses with 

Maximum Effective Strain Criterion for Blunt Tup 
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Similarly, Figure 14 shows the comparison between test 

and analysis using the criterion based on stress triaxiality for 

the blunt impactor. The close agreement between the test data 

and the results from the analysis is self-evident especially for 

the thicker specimens. 

Specimen Thickness (inches)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fracture Energy (ft-lb)

0

1000

2000

3000

4000

5000

6000

7000

8000

Test Data

Average

FEA

Error bars represent ±2 standard deviations

Nominal specimen width is 1.0 inch

STRESS TRIAXIALITY CRITERION

E=915+8933B2

with E (ft-lb) and B (inch)

Figure 14. Comparison Between Tests and Analyses with 

Stress Triaxiality Based Criterion for Blunt Tup 

Figure 15 shows the comparison between test and analysis 

using the stress triaxiality based criterion with the sharp tup. 

The figure shows that test data and results from the analysis are 

within reasonable agreement. 

PARAMETRIC STUDIES 

Although parameters calibrated mainly according to Table 

1 and Table 3 were used in the above analyses, it was of 

interest to investigate the effects of the parameter changes. 

Four categories of parameters were identified: plasticity (yield 

and ultimate tensile strengths), fracture initiation (C1 and C2), 

softening ( pl

f u ) and contact (coefficient of friction). Sensitivity 

of the predicted impact energy to changes in these parameters is 

summarized in Table 4 for simulations again of the test 

combination {Blunt tup, Material 1, B=0.827 inches}. 

Specimen Thickness (inches)

0.0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 0.8 0.9 1.0

Fracture Energy (ft-lb)

0

1000

2000

3000

4000

5000

6000

7000

8000

Test Data

Average

FEA

Error bars represent ±2 standard deviations

Nominal specimen width is 1.0 inch

STRESS TRIAXIALITY CRITERION

E=-84.7+9598B2

with E (ft-lb) and B (inch)

Figure 15. Comparison Between Tests and Analyses with 

Stress Triaxiality Based Criterion for Sharp Tup 

In the plasticity category, the parameters were changed to 

those of a TC128-B material with lower yield and ultimate 

strengths. In the fracture initiation category, the C1 and C2

parameters calibrated according to data from a different source 

(normalized TC128-B steel tested in T-L orientation at 0oF [9]) 

were used. The failure displacement pl

f u was varied by ±100% 

relative to the baseline. Last, two other commonly used 

coefficients of friction for contacts between steel and steel, 0 

and 0.16, were examined in addition to the baseline value of 

0.57. Only one category of parameters was changed each time 

while the remaining parameters retained their baseline Material 

1 values. 

Table 4. Percent Changes in Impact Energy with Key 

Model Parameter Changes 

Parameter Baseline

value 

New 

value 

Change in 

parameter

Change in 

impact energy

Yield strength 64.2 ksi 50 ksi -22.1% 

Ultimate 

tensile strength 90.6 ksi 81 ksi -10.5% -15.0% 

C1 0.223 0.345 54.7% 

C2 0.868 0.977 12.6% 3.1% 

pl 0 -100.0% -30.9% 

f u

0.275 

inch. 0.55 inch. 100.0% 19.5% 

Coefficient of 0 -100.0% -8.6% 

friction 0.57 0.16 -71.9% -5.8% 
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It may be concluded from Table 4 that (1) the plasticity 

parameters have the most significant effect on model 

predictions, as the percent changes in yield and ultimate 

strengths lead to the same order of percent changes in the 

predicted impact energy, (2) damage/failure parameters, 

especially C2 and pl

f u , have secondary but considerable effects, 

and (3) the effect of the coefficient of friction is much less 

significant. 

CONCLUDING REMARKS 

Nonlinear FEA with different failure criteria has been 

conducted to simulate tests on unnotched Charpy specimens 

and to calculate fracture energies. The FEA with a material 

failure criterion based on stress triaxiality provided excellent 

agreement with the test data for different impacting strikers. 

Moreover, the agreement between test and analysis 

provides a benchmark for which the failure criterion can be 

applied to other impact loading scenarios. For example, FEA 

using the stress triaxiality criterion to examine the failure of a 

railroad tank car under impact loading will be described in a 

future communication. 

ACKNOWLEDGMENTS 

The Federal Railroad Administration (FRA), Office of 

Research & Development (R&D) sponsored the work 

described in this paper. Ms. Claire Orth is the Chief of the 

Equipment and Operating Practices Division. Mr. Francisco 

Gonzalez is the FRA project manager for research on railroad 

tank cars. Mr. Eloy Martinez of FRA’s R&D also provides 

technical direction to the project. Discussions with Professor 

A. Benjamin Perlman are gratefully appreciated and 

acknowledged. 

REFERENCES 

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

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

Research and Test Project, RA-05-17. 

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

Puncture Resistance Evaluation,” Final Report, 

DOT/FRA/ORD-92/11. 

[3] Siewert, T.A., Manahan, Sr., M.P., Eds. 2000: Pendulum 

Impact Testing: A Century of Progress, STP 1380,

American Society for Testing and Materials, West 

Conshohocken, PA. 

[4] McKeighan, P., 2007: “Mechanical Properties of Tank Car 

Steels Retired from the Fleet,” Southwest Research 

Institute Report to the Volpe Center. 

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

equivalent strain and stress triaxiality space,” International 

Journal of Mechanical Sciences 46, 81-98. 

[6] ABAQUS Inc., 2006: ABAQUS Analysis User’s Manual. 

[7] ABAQUS Inc., 2006: ABAQUS Keywords Reference 

Manual. 

[8] Lee, Y.W., Wierzbicki, T., 2004: “Quick Fracture 

Calibration for Industrial Use,” Massachusetts Institute of 

Technology, Impact & Crashworthiness Laboratory Report 

No. 115. 

[9] Hicho, G.E., D.E. Harne, 1991: “Mechanical Properties 

and Fracture Toughness of AAR TC-128B Steel in the 

Normalized, and Normalized and Stress Relieved 

Conditions,” NISTIR 4660, Report No. 24, National 

Institute of Standards and Technology.