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1 

Proceedings of 2008 IEEE/ASME Joint Rail Conference 

JRC2008 

April 22-23, 2008 Wilmington, Delaware, USA 

JRC2008-63052 

UPDATE ON ONGOING TANK CAR CRASHWORTHINESS RESEARCH: 

PREDICTED PERFORMANCE AND FABRICATION APPROACH 

Michael Carolan 

Brandon Talamini 

David Tyrell 

Volpe National Transportation Systems Center 

US Department of Transportation 

Cambridge, MA 02142 

ABSTRACT 

Research is currently underway to develop strategies for 

maintaining the structural integrity of railroad tank cars 

carrying hazardous materials during collisions. This research, 

sponsored by the Federal Railroad Administration (FRA), has 

focused on four design functions to accomplish this goal: 

blunting the impact load, absorbing the collision energy, 

strengthening the commodity tank, and controlling the load 

path into the tank. Previous papers have been presented 

outlining the weight and space restrictions for this new design, 

as well as the approach being taken in developing the design. 

The performance goals for the new car have also been outlined. 

A key goal for the new design is the ability to contain its lading 

at four times the impact energy of the baseline equipment. 

Presently, a preliminary design has been developed that 

will incorporate these four functions together. This new design 

features a conventional commodity tank with external 

reinforcements to strengthen the tank. The reinforced tank is 

situated on a structural foam cradle, within an external carbody. 

This carbody has been designed utilizing welded steel 

sandwich panels. The body is designed to take all of the inservice loads, removing the commodity tank from the load path 

during normal operations. Additionally, the carbody panels 

will serve as an energy-absorbing mechanism in the event of a 

collision. 

Preliminary steps for fabricating and assembling the new 

tank car design have been outlined. These steps were developed 

with the intention of paralleling existing tank car fabrication 

process as much as is practical. 

Using the commercial finite element analysis (FEA) 

software ABAQUS/Explicit, the improved design has been 

analyzed for its response to an impact by a rigid punch. 

Simulations of two generalized impact scenarios have been 

made for this rigid punch impacting the improved tank car head 

as well as the improved tank car shell. Results of these 

analyses, including the force-displacement curves for both 

impacts, are presented within this paper. These results show 

that an improved-design tank car can contain the commodity 

for a head impact with eight times the energy of the baseline 

car, and four times the energy for a shell impact. 

INTRODUCTION 

Presently, the Pipeline and Hazardous Material Safety 

Administration (PHMSA) and the Federal Railroad 

Administration (FRA) are engaged in ongoing railroad tank car 

safety rulemaking. As a part of the rulemaking effort, the 

Volpe National Transportation Systems Center (Volpe Center) 

is conducting research on improving the crashworthiness of 

these tank cars. Of specific concern are tank cars that carry 

materials classified as a Toxic Inhalation Hazard (TIH). 

A previous publication has given a background on the need 

for an improved-crashworthiness design tank car, as well as the 

key design requirements, the physical constraints on weight 

and space available for new components, and the desired 

kinematics of the tank car during an impact [1]. Additional 

papers supporting this research effort have been published on 

the topics of full-scale impact testing of the baseline tank car 

[2], material failure modeling [3], collision dynamics modeling 

[4], and an overview of the research effort in support of the 

PHMSA and FRA rulemaking activity [5]. A companion paper 

describes the detailed finite-element modeling performed on 

the baseline tank car [6]. 

 

IMPROVED DESIGN DEVELOPMENT 

A key design goal for the improved-crashworthiness tank 

car is the ability to protect its lading at four times the impact 
energy as the baseline equipment. This energy goal is to be met 

in two generalized impact scenarios. These scenarios were 

defined by previous investigations of tank car accident 

dynamics [4], and are shown schematically in Figure 1. Each 

impact scenario involves the tank car being impacted by a ram 

car, loaded to a standard freight car weight (286,000 lb), with 

the impact caused by a 6 in by 6 in square face punch. 

Figure 1 - Schematic of Head and Shell Impact Scenarios 

Selected Concept

In order to meet the performance goals set forth for the 

improved-design tank car, a number of intended functions must 

be accomplished. Design features have been selected that can 

accomplish the desired functions. Specific forms have been 

chosen as part of the preliminary design in order to implement 

the features. The preliminary improved-design tank car is 

shown in Figure 2. 

Figure 2 – Preliminary Design Concept 

Table 1 lists the design features and their associated 

functions and forms that have been developed for the 

preliminary design. 

Table 1 - Preliminary Design Functions, Features, and 

Forms 

Functions Features Forms

Blunted impact 

loads 

Collision energy 

absorbed 

Stronger tank Reinforcement of 

head and shell

Ribs on Head,

Sandwich Panels 

Over Shell

Control load 

path to tank 

Detach tank from 

service loads Separate Carbody

Sacrificial structure 

that shields tank 

and absorbs 

energy

Dual-purpose 

Sandwich Structures

 

Engineered sandwich panels have been selected as the 

primary form to accomplish multiple functions in the improved 

design. Sandwich panels offer a number of advantages over 

alternative construction materials and techniques [7]. They 

possess the ability to support loads in the plane of the panel 

while offering effective energy-absorbing capability in the 

normal (out-of-plane) direction [8], as well as a high bending 

resistance. A variety of core geometries are available to be 

used within the sandwich panel, including honeycombs, egg 

crate, and wave patterns. A typical sandwich panel, with a 

wave pattern core structure, is shown in Figure 3. 

Figure 3 - Annotated Sandwich Panel 

The preliminary design described in this paper consists of 

a conventional tank reinforced with sandwich panels around 

the shell and stiffeners around the head. This tank sits within a 

structural carbody, also composed of sandwich panels. 

Between the reinforced tank and the carbody is a structural 

foam saddle, designed to support the tank while isolating it 

from the service loads in the carbody. A cutaway view of the 

preliminary design is shown in Figure 4. 

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2 
Figure 4 - Cutaway View of Preliminary Design 

One type of sandwich panel utilized in the preliminary 

design will make up the external carbody. This structure is to 

accomplish three of the functions seen in Table 1; blunting the 

impact loads, absorbing collision energy, and controlling the 

load path to the tank. The majority of the time, the carbody 

will be in normal service. It must be able to function as any 

other railcar body does, taking the buff and draft forces as well 

as the suspension loads. Additionally, the carbody must meet 

all of the applicable regulations and standards in order to enter 

service as a railcar. 

As part of the improved crashworthiness of the new 

design, the carbody has been designed to incorporate two 

additional functions: blunting the impact load and absorbing 

collision energy. By blunting the impact load, the tank will be 

loaded over a greater area, enabling more collision energy to be 

absorbed before failure of the commodity tank [1]. By 

incorporating an energy-absorbing component external to the 

tank, the loading demands on the tank can be further reduced 

during an impact. The impacting object will be traveling with a 

decreased speed by the time the commodity tank is being 

loaded, requiring the tank to absorb less collision energy [1]. 

The outer carbody sandwich panel is currently envisioned as 

square honeycomb core. 

In addition to carrying the commodity, the tank acts as a 

foundation for any external structures during a collision. In 

order to function properly, the energy-absorbing carbody must 

deform before the commodity tank. Since the load path of an 

impacting object can transmit force through the carbody and 

into the commodity tank, it is necessary to reinforce the 

commodity tank to absorb the required energy levels. 

A second type of sandwich panel can be used to 

accomplish this task. A series of curved panels designed to fit 

snugly against the shell of the tank will provide reinforcement 

to the tank, as well as absorb some amount of collision energy. 

These panels are designed to provide a stiffer load-indentation 

response than the baseline tank. 

DEVELOPMENT OF FABRICATION APPROACH 

During the development of this design, an effort was made 

to utilize existing tank car construction practice wherever 

appropriate and practical. This includes the use of some offthe-shelf railcar components. 

The construction sequence developed for this preliminary 

design can be broken into three distinct phases: construction of 

the reinforced tank, construction of the carbody, and the final 

assembly of the tank and carbody to complete the tank car. 

Phase I: Construction of the Reinforced Tank

The first phase of construction bears a number of 

similarities to the construction of a conventionally-built 

railroad tank car. The tank, consisting of a number of steel 

rings and a pair of steel heads, is assembled using conventional 

practices. After the heads have been formed, a number of 

precut steel arches are welded to both tank heads. These arches 

are then further reinforced with small rectangular steel plates to 

form a spider web pattern, as shown in Figure 5. A thin steel 

face sheet can then be welded over the arches. This 

arrangement of reinforcements reduces the “snap-through” 

response of the baseline tank head [9]. 

Figure 5 - Tank Head with Reinforcing Arches 

A different approach is utilized to strengthen the shell of 

the tank than was used to strengthen the head. Because of the 

considerable surface area involved, it is not practical to weld a 

series of individual reinforcements in the same manner as 

applied to the tank heads. Instead, a series of reinforcing 

sandwich panels can be manufactured separately from the rest 

of the tank and installed at a late stage of the tank’s assembly. 

The sandwich panels needed to reinforce the tank must be 

snug-fitting against the outer surface of the tank. This 

necessitates the use of a curved sandwich panel. The panels 

may be bonded to the surface of the tank to prevent slippage 

and to carry shear loads. 

The design of the reinforcement panels takes advantage of 

the ability to embed multiple orientations of material within the 

core. The final assembly of the reinforced tank is made easier 

by the ability to bolt adjacent panels to one another. Hence, the 

outermost member of each reinforcement panel can be a square 

or rectangular section with appropriate bolt hole placement. 

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The design of the reinforcement panels calls for one end of a 

given panel to have this member attached to the top face sheet 

(Panel A) while the other end of the panel has this member 

attached to the bottom (Panel B), to facilitate the mating of 

adjacent panels during assembly. This design, applied to two 

adjacent panels, is shown in Figure 6. 

Figure 6 - Adjacent Reinforcement Panels 

Once a panel is in the proper position around the 

circumference of the tank, it is bolted to the adjacent panel 

along the entire length of the mating surfaces. The next panel 

along the circumference can be installed, until the entire tank 

has been reinforced. This installation sequence is shown in 

Figure 7. 

Figure 7 - Shell Reinforcing Panel Installation Sequence 

The reinforced tank is complete with the installation of the 

reinforcing panels surrounding the shell. The tank will move 

on to Phase III for incorporation into the external carbody. 

Phase II: Construction of the External Carbody

While the construction of the individual components that 

make up the carbody are presented here in a sequential manner, 

it is anticipated that manufacturers of the carbody will 

determine their own sequence. 

In order to meet the requirements of normal service as well 

as achieve impact blunting and energy absorption during a 

collision, a series of sandwich panels are utilized for the 

carbody as well. The underframe of the car is incorporated 

within one such panel. This panel is constructed upside-down, 

with what will become the top face sheet prepared first. A 

continuous center sill can be attached directly to the face sheet. 

Two body bolsters can also be incorporated within the core of 

the sandwich panel. The energy-absorbing core structure 

would be welded to the face sheet at this point in the assembly. 

With the center sill, body bolsters, and core structure 

attached to the top facesheet, the bottom facesheet can be 

welded to the core. Finally, the draft sill components can be 

welded into the proper place. The sequence of construction of 

the underframe panel is shown in Figure 8. For clarity, this 

figure shows the panel from one draft sill to the centerline. The 

full-length panels are symmetric about the center. The body 

bolsters and core structure are not shown in this figure. The 

coupler and draft gear may be installed at this point or at any 

subsequent point in the assembly. 

Figure 8 - Underframe Sandwich Panel Sequence 

The sidewalls and head panels of the carbody are also to be 

constructed of sandwich panels. The process for 

manufacturing them is essentially the same as the underframe, 

but is simplified by the absence of the center sill and body 

bolsters. 

Once the underframe panel, sidewall panels, and head 

panels have been manufactured, the bottom half of the carbody 

can be assembled. The sidewall panels are held in place and 

are welded to the underframe panel along both the inner and 

outer face sheets. The head panels on both ends of the car are 

then welded into place. At any subsequent point in the 

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4 
assembly the bottom half of the carbody may be placed on the 

trucks, as best suits the manufacturer. The assembled “tub” 

composed of the underframe panel, sidewall panels, and head 

panels is shown in Figure 9. 

Figure 9 - Assembled Tub 

In order to provide complete protection to the tank, the 

carbody includes a full roof made up of sandwich panels of the 

same design as the rest of the body. While the roof assembly 

may be manufactured at this point in the fabrication process, it 

cannot be mated to the tub of the body yet, as the tank 

assembly must still be positioned in the tub. 

The roof assembly consists of two head panels, two wall 

panels, and a roof panel. The wall panels feature the same core 

arrangement as the walls in the tub. The roof panel contains 

the same core, with additional reinforcement in the area 

surrounding the cutout for manway access. Similarly to the tub 

assembly, the wall and roof panels are welded together on both 

the inner and outer facesheets. The roof assembly, without the 

head panels, is shown in Figure 10. 

Figure 10 - Roof Assembly 

Phase III: Marriage of Tank and Carbody

Once the reinforced tank has been assembled and the 

carbody has been manufactured, the two major components can 

be brought together. The tub is first fitted with a full-length 

foam saddle that is contoured to the shape of the reinforced 

tank. 

This saddle provides support to the tank while isolating it 

from the service loads being carried in the carbody. The saddle 

is designed to support the tank across its bottom 120o

. Specific 

fabrication techniques are currently being developed for the 

appropriate variety of structural foam in this tank car. 

The reinforced tank can now be wrapped in appropriate 

insulation before being lowered onto the foam saddle within 

the tub. The roof assembly is lowered over the top of the tank 

within the tub and fixed in place. Finally, the head panels can 

be attached to the roof assembly. 

Figure 11 shows a progression of the assembly of the car 

around the reinforced tank. Note that in stage 2 the tub is not 

shown to provide a clear view of the foam saddle. Stage 3 

shows the tank within the tub, on the saddle. Stage 4 is the 

fully-assembled carbody, with the roof assembly’s head panels 

attached. With the structural components of the carbody 

assembled, the remainder of the running gear can be installed 

onto the carbody. 

Figure 11 - Progression of Assembly 

Weight and Space Budgets

The commodity tank used in this design is assumed to have 

a thickness of 5/8 in. The tank is sized such that the nominal 

capacity of an existing car of this class is maintained at 17,300 

gallons. For clearance purposes, AAR Plate B was chosen for 

the design limits [10]. The carbody has an extreme width of 

128 in, the maximum width allowed. The roof of the carbody 

is approximately 13 ft., 6 in. above top-of-rail. The lengths of 

carbody between truck centers and over the strikers are shown 

in Figure 12. 

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Figure 12 - Carbody Lengths 

 The preliminary design was developed such that the entire 

car, when fully loaded, weighs less than 286,000 pounds. The 

weight estimates, based on the preliminary structures, are 

shown in Table 2. 

Table 2 - Estimated Structure Weight 

Tank Assembly 

Bare Tank 30500

Shell Reinforcement 12890

Head Reinforcement 1870

Reinforced Tank 45260

 

Carbody Assembly 

Structural Carbody Bottom 22160

Structural Carbody Top 11340

Structural Carbody Complete 33500

 

Final Assembly 

Saddle Placed in Structural Carbody 35480

Reinforced Tank Placed in Saddle 80730

Insulation Applied 82580

Carbody Placed on Trucks 103160

 

Lading 180000

 

Total Weight 283160

IMPACT ANALYSIS 

The effectiveness of the improved design has been 

compared to the performance objective with finite element 

analysis using Abaqus/Explicit [11] in the two generalized 

impact scenarios previously defined. This modeling serves two 

purposes. First, it must make a reasonable approximation of the 

impact response of the improved design to determine if the 

concept is effective. Second, it must guide selection of 

component sizes and orientations. Hence, the finite element 

models must capture the salient features of the improved 

design, but the emphasis is on comparing design iterations on 

an equal footing and with a quick turnaround. Consistent with 

this emphasis, the following simplifications have been made: 

1. No fluid lading 

2. Simplified geometry and boundary conditions 

3. No material failure 

4. Representation of the carbody sandwich panel 

core with a continuum element approximation 

(described below). 

These simplifications are being addressed in ongoing work as 

design details become more certain. 

The chief products of the simulations are the punch impact 

force and the punch displacement (measured from the point of 

impact). Also of interest is the total absorbed energy, which is 

the integral of the punch force-displacement curve over the 

displacement (graphically, this is the area under the punch 

force-displacement curve). Separate models have been used for 

the head and shell impact scenarios, each including only the 

components needed to estimate the force-displacement 

characteristic. The models are shown in Figures 13 through 16. 

Note that the sandwich panels shown in Figures 13, 14 and 16 

are merely portions of the rest of the carbody (compare to 

figure 11), but it is not necessary to include the the outer 

sandwich structure remote from the impact to get an 

approximate force-displacement response accurate enough for 

this study. 

All car components are made of the tank car steel TC128B, with properties as shown in Table 3. Linear elastic 

behavior has been assumed below the yield strength, while the 

hardening behavior was computed from the Ramberg-Osgood 

law: 

n

KE ⎟

⎠

⎞ ⎜

⎝

⎛ +=

σσ

ε (1) 

Stress-plastic strain data pairs were generated using the 

Ramberg-Osgood law with the constants in Table 3. 

Table 3 - Material properties and hardening law constants 

for TC-128B tank car steel 

Property Value 

Young’s modulus, E (ksi) 30,000 

Poisson’s ratio 0.3 

Yield strength (ksi) 50 

Tensile strength (ksi) 81 

Hardening constant, K (ksi) 96.8 

Hardening exponent, n 9.41 

Weight density (lb/in3) 0.286 

The punch is modeled perfectly rigid and is given an initial 

closing velocity of 15 mph. Additionally, the punch is assigned 

a weight of 286,000 lb, which is the weight of a fully loaded 

standard freight car. 

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The head impact models are illustrated in Figures 13 and 

14. Only the affected tank head region is meshed, with 12 in of 

the cylindrical portion of the tank included to keep the 

boundary effects from influencing the computed head response. 

(A study was performed to verify that 12 in is adequate for this 

purpose). The open end of the tank portion is fully fixed 

(displacements and rotations) and the punch is constrained to 

move in the tank longitudinal direction only. The free edges of 

the carbody sandwich panel segment are left unconstrained.1

Figure 13 – Left: Baseline Tank Head Impact Model 

Right: Improved Tank Head Impact Model 

Figure 14 – Improved Tank Head Impact Model, Shown 

with Translucent Components to Illustrate Hidden 

Components 

In the shell impact models, the tank is constrained by 

pinning the centers of both tank heads to ground. The sandwich 

panel edges are unconstrained. Additionally, the punch is 

 1

 Fully fixed sandwich panel edges have also been examined, producing 

similar overall force-displacement characteristics. These boundary conditions 

are intended to represent the connections of the meshed portions of the outer 

sandwich panel to the omitted portions. Difficulties in representing these 

connections with boundary conditions will be obviated in later models where 

the entire carbody sandwich structure is present in the model. 

permitted to move only in the direction perpendicular to the 

tank. 

Figure 15 – Baseline Shell Impact Model 

Figure 16 – Improved Shell Impact Model 

The tank, reinforcement members and skin, and the outer 

carbody sandwich face sheets have been modeled with first 

order quadrilateral shell elements with reduced integration. A 

small number of triangular elements are utilized to avoid poorly 

shaped elements. The carbody sandwich panel core has been 

modeled using a continuum element approximation with the 

metal foam plasticity model due to Deshpande and Fleck [12]. 

Xue and Hutchinson successfully employed this technique in 

preliminary sandwich panel analyses, justifying it as a firstorder approximation of the behavior of the core due to its open 

nature (i.e., the core undergoes large volume changes during 

crushing) [13]. Replacing the geometric details of the core 

with continuum elements permits the core to be modeled 

economically2

, in keeping with the stated constraints of these 

simulations. 

The metal foam model parameters have been chosen to 

match the desired crushing behavior of the sandwich panel. 

Details of this calibration are in the Appendix. Out-of-plane 

shearing strength and stretching strength of the core are 

somewhat overestimated with this technique [14]; subsequent 

 

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2

 Detailed meshing of the sandwich core requires many elements through 

the core web depth to capture the collapse mode; this leads to small stable time 

increments and long computation times. Additionally, a separate buckling 

eigenmode calculation must be performed to seed imperfections into the mesh. 

The continuum approximation can achieve reasonable accuracy for the 

purposes of a preliminary design evaluation with a single element through the 

core depth. 
analysis (not included in this paper) is being conducted with a 

continuum plasticity law approximation developed especially 

for structural sandwich cores due to Xue and Hutchinson [14] 

that mitigates this effect. Nevertheless, the metal foam 

approximation provides useful information on the sandwich 

panel response and is suitable for the preliminary design 

assessment here. 

Head Impact Results

For reasons stated in the previous section, failure is not 

computed directly in the finite element code. The failure point 

must be estimated to compare the approximate energy 

absorption totals for the baseline and improved designs. For the 

baseline tank, failure is assumed to occur at approximately 12 

in. of indentation, based on experience with testing and 

modeling of tank cars [2,6]. An approximate measure of tank 

failure has been used for the improved design: the punch was 

allowed the same displacement as the baseline tank, plus the 

thickness of the sacrificial structure. The reinforcement is 

approximately 2 in. thick and the external carbody sandwich 

panel is approximately 6 in. thick, so the improved design is 

assumed to fail at 20 in. of impactor displacement. 

The performance of the improved head is greatly improved. 

Figure 17 illustrates this using the force-displacement curves of 

the punch during the impact. The arches resist snap-through 

buckling of the elliptical tank head, making the improved 

design much stiffer. Integrating the characteristic to obtain the 

energy absorption reveals that the improved design absorbs 8 

times as much impact energy as the baseline tank head. The 

deformed baseline head is shown in Figure 18. The blunting 

effect of the outer sandwich panel is evident from the deformed 

plot in Figure 19. 

Figure 17 - Comparison of Head Impact Forcedisplacement for Baseline and Improved Tank Car 

Figure 18 - Section View of Baseline Design Head Impact 

Analysis at Assumed Failure Point 

Figure 19 – Section View of Improved Design Head Impact 

Analysis at Assumed Failure Point 

 

Shell Impact Results

In Figure 20, the improved tank car design shows 

increased strength and energy absorption in shell impacts as 

well, although the improvement is more modest than seen in 

the head impact scenario. The corrugated plate reinforcement 

on the tank (illustrated in Figure 6) strengthens the improved 

design significantly in the longitudinal direction; however, 

strengthening the tank circumferentially is difficult to do 

without adding a large amount of weight. The absorbed energy 

of the improved design is approximately 4.5 times greater than 

the baseline tank car, which fulfills the performance objective. 

The blunting effect of the outer carbody sandwich panel, 

visible in the deformed plot in Figure 21, serves to delay the 

rupture point of the force-displacement curve and increases the 

total impact energy absorption. 

0

500

1000

1500

2000

2500

0 5 10 15 20 25

Punch Displacement (in)

Force x103

Baseline

Improved

~2.6 million ft-lb 

absorbed 

~300,000 ft-lb 

absorbed 

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0

100

200

300

400

500

600

700

800

900

1000

0 5 10 15 20 25

Punch Displacement (in)

Force (lb x 103

)

Baseline

Improved

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Figure 20 - Comparison of Shell Impact Forcedisplacement for Baseline Tank and Improved Tank Car 

Figure 21 – Above: Baseline Shell Impact at Assumed 

Failure Point 

 Below: Improved Design Shell Impact at Assumed Failure 

Point 

SUMMARY AND NEXT STEPS 

A preliminary design for a railroad tank car capable of 

absorbing four times the collision energy of a conventional car 

has been developed. This design incorporates four functions 

that work together to improve the crashworthiness of the car: 

ability to blunt the impact load, energy-absorption capabilities, 

a reinforced commodity tank, and an external carbody. ~820,000 ft-lb 

absorbed This design utilizes a number of existing tank car 

components and manufacturing practices, including the 

commodity tank and draft components. Additional 

manufactured parts are welded steel sandwich panels, which 

serve as the tank’s reinforcement as well as the external 

carbody. The sandwich panels can be manufactured at the site 

of the tank components or at a separate manufacturing facility. 

The tank may be manufactured in an existing facility, with the 

addition of the reinforcement panels at the end of the assembly 

process. The integration of the reinforced tank and the carbody 

is the final step in the assembly of the preliminary design. 

~180,000 ft-lb 

absorbed 

Initial simulations of the generalized impact scenarios 

indicate that the performance objective is attainable with the 

preliminary design. Following this success, each component 

may now be specified and examined in greater detail. 

Accordingly, the next iteration of modeling will include greater 

complexity, with increased geometric detail, a fluid-filled 

pressurized tank, and material failure. 

Component-level testing is being planned to verify the 

modeling of critical and difficult-to-analyze components. The 

tank car design will be refined, as determined to be appropriate 

from the results of the detailed analysis and testing. 

ACKNOWLEDGEMENTS 

The work described in this paper was sponsored by FRA 

Office of Research and Development. Ms. Claire Orth is the 

Chief of the Equipment and Operating Practices Division. Mr. 

Francisco Gonzalez is the FRA program manager for research 

on railroad tank cars. 

Mr. Grady Cothen, Deputy Associate Administrator for 

Safety Standards and Program Development, FRA, is leading 

the effort to develop tank car safety standards. Mr. Eloy 

Martinez, FRA program manager, is developing the technical 

information needed to support the FRA and PHMSA 

rulemaking effort. The authors thank Ms. Jo Strang, Associate 

Administrator for Safety Enforcement, FRA, for her efforts to 

coordinate the standards development and the tank car safety 

research. 

Dr. David Jeong, Senior Engineer, Volpe Center, is leading 

the effort to evaluate the performance of baseline equipment. 

The authors would like to thank Professor A. Benjamin 

Perlman, Senior Engineer, Volpe Center, for his assistance 

through all aspects of this project. The authors also wish to 

thank Kari Jacobsen, Mechanical Engineer, Volpe Center, for 

developing the target kinematics and energy absorption goals, 

Michelle Priante, Mechanical Engineer, Volpe Center, for 

assisting with the concept generation, and Philip Mallon, 

Mechanical Engineer, Volpe Center, for researching sandwich 

structures and weight-efficient methods of energy absorption. 

REFERENCES 
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10 

 

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Hutchinson, J.W., Wadley, H.N.G. “Metal Foams: A Design 

Guide,” Butterworth-Heinemann: London, 2000. 

[8] Wadley, H.N.G., Fleck, N.A., Evans, A.G., “Fabrication and 

Structural Performance of Periodic Cellular Metal Sandwich 

Structures,” Composite Science and Technology 63, 2003. 

[9] Jeong, D.Y., Tang, Y.H., and Perlman, A.B., "Engineering 

Analyses of Railroad Tank Car Head Puncture," Proceedings of 

2006 ASME International Mechanical Engineering Congress 

and Exposition, November 5-10, 2006. 

[10] Association of American Railroads, Technical Services 

Division, Mechanical Section – Manual of Standards and 

Recommended Practices. 

[11] Abaqus Version 6.7. Providence: Dassault Systèmes, 

2007. 

[12] Fleck, N.A., Deshpande, V.S. “Isotropic constitutive 

models for metallic foams,” Journal of the Mechanics and 

Physics Solids, 48:1253-1283. 2000. 

[13] Xue, Z., Hutchinson, J.W. “Preliminary assessment of 

sandwich plates subject to blast loads,” International Journal of 

Mechanical Sciences, 45, 687-705. 2003. 

[14] Xue, Z., Hutchinson, J.W. “Constitutive model for quasistatic deformation of metallic sandwich cores,” International 

Journal for Numerical Methods in Engineering. 61:2205-2238. 

October 2004. 

APPENDIX 

The Deshpande-Fleck metal foam model is a reasonable 

approximation of the aggregate behavior of the carbody 

sandwich panel cores in impacts since it allows volume change 

during plastic deformation. In this paper, it is calibrated to 

reproduce the crushing behavior of a structural sandwich core, 

following essentially the same procedure as Xue and 

Hutchinson [13]. Refer to this paper for a more detailed 

derivation. 

The yielding criterion in the Deshpande-Fleck model is 

determined by an effective stress σe, defined as 

[ ] 222

2

2

)3/(1

1 e vm σασ m α

σ +

+ =

p

long

p

lat

p εε

 (A1) 

where σvm is the standard von Mises stress and σm is the mean 

normal stress. Yielding occurs when the effective stress equals 

the yield strength of the material. The parameter α controls 

plastic compressibility by defining a “plastic Poisson’s ratio” 

ν −= / through the relation 

p

p

ν

ν

α

+

− = 12/1 3 (A2) 

A value of ν

p

 = 1/2, corresponding to α = 0, models the material 

as plastically incompressible - as in the case of standard metal 

plasticity - and the effective stress reduces to the von Mises 

stress. In the present case, ν

p

 is taken to be zero (α = 3/21/2), 

since the crushing strain of the sandwich core is virtually 

independent of the in-plane strains. 

The effective yield strength and elastic properties of the 

core material are estimated analytically after specifying the 

geometry of the core. Square honeycomb was chosen for 

improved design since it is equally strong in both in-plane 

directions. A schematic of square honeycomb is shown in 

Figure A1. The goal here is to replace the core webs with 

approximately equivalent continuum elements (see Figure A2). 

Figure A1 – Square honeycomb sandwich panel 
This material is declared a work of the U.S. Government and is not subject to copyright protection in the United States. Approved for 

public release; distribution is unlimited. 

11 

 

Figure A2 – Continuum core approximation 

Referring to Figure A1, the core web thickness is t and the 

core web width is B. The relative density of the core (the ratio 

of the average density of the core to the density of the core 

material, or equivalently, the fraction of solid material in the 

core compared to the core volume) is ρ c , and is given by 

2

2 ⎟

⎠

⎞ ⎜

⎝

⎛ −= B

t

B

t

ρ c (A3) 

The nominal uniaxial stress in the core volume during 

compression of the sandwich panel under an overall stress of σ

is 

σ nom = ρcσ Y σ c

 (A4) 

The nominal yield strength of the smeared core material is 

therefore 

Yc

Y

c = σρσ (A5) 

The crush strength of the chosen core is 600 psi. This crush 

strength is a result of the core geometry and available weight 

for the core. The core geometry was chosen to be a 6 inch by 6 

inch by 6 inch egg-crate arrangement, shown in Figure A1. For 

simplicity, the tank car material TC-128B was chosen for the 

sandwich panel, with σY = 50 ksi. Using this yield strength and 

the desired core strength in (A5), the relative density may be 

computed as ρ c = 012.0 . (A3) may now be solved for t/B, 

yielding one useful root of t/B ≈ 0.006. Choosing 6 inches for 

the web width B, the corresponding web thickness is 0.036 in. 

The core depth D can be chosen freely, and was selected as 6 

inches based on geometric restrictions on the railcar from 

regulations and industry standards. 

The effective elastic modulus of the core in the 

crushing direction is 

Ec

= ρ cc EE

 

 (A6) 

This value was used in the present work. Alternatively, the 

effective elastic modulus could be set to the in plane behavior, 

which is half of the value computed from (A6), since half of 

the webs are aligned in either in-plane direction. The Poisson’s 

ratio was taken to be zero. 

The hardening behavior of the core material must be 

characterized to fully specify the Deshpande-Fleck model. The 

hardening curve is assumed to behave like Figure A3, based on 

a similar core studied in [14] (note that the strain measure is 

logarithmic, not nominal). The steep hardening slope at an 

equivalent plastic strain of 1.4 (a nominal strain of 

approximately 75%) characterizes the panel response after total 

collapse of the webs. 

0

100

200

300

400

500

600

700

800

900

1000

0.0 0.2 0.4 0.6 0.8 1.0 1.2 1.4

Equivalent Plastic Strain

Stress (psi)

Figure A3 – Effective hardening curve for core elements 

Finally, the effectiveness of structural sandwich panels can 

be seen from the details of this procedure. The average strength 

of the core in the present design is about 500 psi, with a density 

of approximately 6 lb/ft3

. These values compare favorably to 

alternative sandwich panels cores of metal foams and polymer 

foams.