Mark Pankow and Anthony M. Waas

University of Michigan, Ann Arbor, Michigan 

Brett Bednarcyk

Glenn Research Center, Cleveland, Ohio

Blast Loading of Epoxy Panels Using a Shock Tube

NASA/TM—2010-216941

December 2010
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Mark Pankow and Anthony M. Waas

University of Michigan, Ann Arbor, Michigan 

Brett Bednarcyk

Glenn Research Center, Cleveland, Ohio

Blast Loading of Epoxy Panels Using a Shock Tube

NASA/TM—2010-216941

December 2010

National Aeronautics and

Space Administration

Glenn Research Center

Cleveland, Ohio 44135
Available from

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Hanover, MD 21076–1320

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Level of Review: This material has been technically reviewed by technical management. 
Abstract

The high strain rate mechanical response of thin polymer plates

has been studied using a modified shock tube. Diagnostics include

the pressure-time history of the incident and reflected pulses and the

use of digital image correlation (DIC) techniques to extract the timehistory of the out-of-plane displacement distribution. Additionally,

finite element models have been developed to understand the plate

response and to validate and modify plate material constitutive models that have been proposed.

Key Words: Shock Loading, High Strain rate, Shock Impact, Material

Characterization

1 Introduction

The study of the response of materials subject to blast loading is imperative to the understanding of how to build blast resistant materials. Until

recently the only way to test the materials was through actual blast tests

on large size panels, that are costly. However recent developments have

used a modification to a shock tube to simulate blast conditions, providing an alternative way to investigate material behavior subjected to blast

loading [1].

The shock tube is a well understood instrument, with much of the theory and validation available in the early literature [2]. The corresponding

Blast Loading of Epoxy Panels Using a Shock Tube 

Mark Pankow and Anthony M. Waas 

University of Michigan 

Ann Arbor, Michigan 48109–2140 

Brett Bednarcyk 

National Aeronautics and Space Administration 

Glenn Research Center 

Cleveland, Ohio 44135 

NASA/TM—2010-216941 1
fluid dynamic equations can be found in [3]. In the present work, a modified version of the shock tube is used to understand how a shock wave

deforms an initially flat panel. By removing the very thick end cap of

the driven tube and replacing it with a relatively thin panel specimen, it

becomes possible to subject the panel to a very large pressure pulse acting over a very short-time duration. This method of loading is a very

recent development and the literature reflects the novelty of the test at

this point [1]. Many of the initial tests conducted using a shock tube were

only minimally instrumented and subsequently post-shock tests were conducted to determine the compressive strength or other material property

degradation [4, 5]. Additional shock tube tests have been performed on

composite plates [6–9], however a lack of data during the deflection and

straining of the plate makes it difficult to evaluate the properties and response.

Shock tube studies in conjunction with the development of finite element models have been previously investigated. Initial studies focused

on validating an anisotropic damage evolution model for metal plates [10].

Another study attempted to match experimental data of viscoplastic plate

vibrations caused by the shock wave impact with finite element simulations [11]. Ultimately the goal would be to blend both problems, i.e that

of the shock interaction with the plate response, which becomes a fluidstructure interaction problem. Initial attempts to combine both a fluid dynamics code with a finite element code have been undertaken, with very

primitive results [12]. On the other hand if the timescale associated with

the shock wave loading is significantly smaller than the plate response

time, then the shock loading approximates to a steep pressure step pulse

and the ensuing response, if accurately measured, can be used to validate

and refine the constitutive models for a variety of rate-dependent materials.

In this paper, results from shock wave loading of epoxy panels are presented. The time-resolved panel response, which is accurately measured

using digital image correlation (DIC) techniques, is studied in conjunction

with a finite element simulation of the response. This provides a means to

validate a rate-dependent constitutive model for the epoxy material.

NASA/TM—2010-216941 2
2 Method

Figure 1, shows a schematic of the shock tubes in the Composite Structures Laboratory (CSL) at the University of Michigan. The driver section

is loaded with a high pressure gas which is separated from the driven

section by a diaphragm designed to burst at a desired driver pressure.

When the diaphragm ruptures, a shock wave is formed which travels

down the tube at a much faster rate than the pressure can equilibrate.

When the shock wave hits the panel specimen, the specimen surface experiences a sudden rise in the pressure and temperature. The shock tube is

equipped with pressure transducers (see figure 2), along the driven tube.

The pressure transducer mounted on the tube is located 9 in.(0.23 m) from

the location of the specimen. The pressure transducers used were made

by PCBPiezotronics (model number 113A22) which have a measurement

range between 0-5000psi (0-34.5 MPa ) and a resonant frequency greater

than 500kHz. They are connected to a 4 channel signal conditioner (model

number 482A22). The signal from the signal conditioner then enters the

oscilloscope. The driven section always remains at atmospheric pressure.

A complex viewing port system for providing lighting, using flashbulbs, and access for high speed cameras to obtain images to perform the

DIC measurements is also present. A schematic of the shock tube hardware incorporating the camera, that was used to obtain the DIC measurements, is shown in figure 3. Prior to testing, the back surface of the specimen is sprayed with a speckle pattern that is suitable for subsequent DIC

measurements.

The DIC system provides full-field displacement measurements on the

back surface of the panel at pre-selected instances as the deformation progresses. The images are captured using two synchronized Photron SA.1

cameras, that capture images at a rate of one hundred thousand frames per

second at a resolution of 320 x 128 pixels. The displacement information

can be used to determine the strain components; X,Y , γXY as a function

of position and time on the back surface, and also the time rate of change

of these components at different locations on the panel back surface. This

is very useful since different areas of the panel experience different levels

of strain and rates of straining, depending on the spatial location.

The accuracy of the measurements can be related to the facet size in

the DIC software. The resolution of the measurement is 0.16in.( 4mm).

Although the step size is 0.0094in.(0.238mm) the size of the computation

NASA/TM—2010-216941 3
Figure 1: Schematic of the shock tube setup.

NASA/TM—2010-216941 4
Tube Plate

Figure 2: Pressure transducer locations on tube and the plate (specimen).

Specimen Pressure 

Transducer

Lights

High Speed 

Cameras

Lexan Panel

Figure 3: DIC setup for Shock tube Measurements.

NASA/TM—2010-216941 5
box will determine the spatial resolution. The random speckle pattern uses

a dot size that is roughly 5-7 pixels in diameter, as recommended by the

software manufacturer. The software used in this analysis was ARAMIS,

provided by GOM.

The epoxy material was provided to the University of Michigan by

NASA Glenn research center. No details on the type of material nor the

expected mechanical properties, etc. were provided. It was simply presented as a matrix that would be used in a composite.

Additional tests were performed with a steel plate that was 0.75 in.(19

mm) thick, with mounting holes situated as specified by the manufacturer,

at the center, half the radius and edge, to determine the pressure experienced on the surface of the plate. Test results showed that the shock pressure on the plate was uniform, allowing us to assume that the shock wave

was normal to the surface.

3 Experimental Results

A series of tests were conducted using different thickness epoxy plates.

For each thickness test, identical shock tube diaphragms were used so that

the burst pressure, and hence the pressure pulse on the specimen, would

be nearly the same for materials of the same thickness. The time history of

the maximum out-of-plane displacement for a representative test can be

seen in figure 4 along with the diaphragm burst pressure. Also indicated

is the maximum pressure imposed by the specimen. These results were

obtained using the DIC software, and the results of a single frame can be

seen in figure 5, which corresponds to a known pressure history of the

thickest panel.

In addition to the panel tests performed, another test was run with a

“rigid” plate mounted with pressure transducers to record the pressure

that was imposed on the impacted plate surface. This pressure-time history is assumed to correspond to those experienced by the epoxy panel

specimen. This assumption is valid if the epoxy panel response time is significantly larger than the rise time of the shockwave pressure pulse. The

two tests (’rigid’ panel and epoxy panel) were performed to experimentally determine the effect of panel deflection on the pressure felt by the

panel (i.e. the fluid-structure interaction issue). This information is very

important in the subsequent finite element modeling, since one needs to

NASA/TM—2010-216941 6
 

 

 

 

 

0 0.05 0.10 0.15 0.20 0.25 0

0.05

0.10

0.15

0.20

Center 

Deflection

(in) 

Time (ms)

0.060 in. 1230psi, 140 psi

0.125 in. 630 psi, 120 psi

0.192 in. 1215 psi, 225 psi

0.242 in. 990 psi, 240 psi

Figure 4: Comparison of maximum out of plane displacement for various

specimen thicknesses. The pressure denotes the corresponding diaphragm

burst pressure for the test, and the maximum pressure on the specimen.

Figure 5: Contour plot of out of plane displacement deformation for a pure

epoxy panel.

NASA/TM—2010-216941 7
know the input pressure time-history. Figure 6(a) shows the two pressuretime histories (that have been shifted in time) corresponding to the rigid

plate and the thinner epoxy plate as measured. The pressure time history

measured on the tube is shown in figure 6(b) along with the pressure measured on the surface of the plate. The results show that the pressure-time

histories are very similar, even on the deformable panel. One clear reason

for this is the time scales involved in the problem. The pressure pulse increase occurs over a time duration of 0.5 μs, while the panel deflection, in

response to this pressure pulse, occurs over a time duration of 250 μs, as

can be seen in figure 6(c). In summary, the reflected pressure that is measured by the tube pressure transducer can be used as the pressure pulse

experienced by the panel specimen. It should be noted that this does not

account for fluid-structure interaction that can occur from a rapidly deforming material or interaction with a specimen that fails.

A comparison of the pressure-time history, to the center deflection-time

history is shown in figure 6(c). Since the center deflection-time history

shows a clear separation in scale, the center plate pressure now appears

very similar to a square wave. This result is important in simulations because the shock pulse can be modeled as a square wave to determine what

pressure level is needed to induce the desired strains and stresses in a

given plate specimen. This calculated pressure can then be related back to

a needed burst pressure to produce the required pressure pulse.

With an understanding of the pressure-time histories, the pressure imposed on each panel during testing can be evaluated. The results are

shown in table 1 with the corresponding reflected shock pressure being

measured from the pressure transducer mounted on the shock tube. The

variation in specimen pressure has to do with how the shock wave is reflected off the specimen. If the shock has enough time to compress the

specimen the pressure will build however, if the specimen fails or has

too great of a deflection, the shock wave will not be completely reflected.

Since the thinner specimens failed with larger deflections the strength of

the shock wave will not be as strong as if a rigid plate had reflected the

shock wave.

NASA/TM—2010-216941 8
 

 

 

 

 

−0.25 0 0.25 0.50 0.75 1.0 0

100

200

300

400

Shock 

Pressure

(psi) 

Time (ms)

Rigid Plate

Epoxy Panel

(a) Comparison of tube pressure signals

 

 

 

 

 

−0.25 0 0.25 0.50 0.75 1.0 0

100

200

300

400

Shock 

Pressure

(psi) 

Time (ms)

Tube Rigid

Rigid Plate

(b) Pressure Transducer in tube vs Pressure

transducer on surface of rigid plate

−0.25 0 0.25 0.5 0.75 1

0

100

200

300

400

Shock 

Pressure

(psi) 

Time (ms)

−0.25 0 0.25 0.5 0.75 1

0

0.01

0.02

0.03

0.04

0.05

0.06

Disp 

(in.)

Rigid Plate Pressure

Epoxy Plate Deflection

(c) Pressure on rigid plate and center deflection of epoxy panel

Figure 6: Pressure-time histories and center deflection (Epoxy Panel) of

shock tube test. Time has been shifted to show relative data comparison.

NASA/TM—2010-216941 9
Table 1: Burst and shock pressures for various thicknesses.

Thickness

(in.)

Diaphragm

Burst

Pressure

(psi)

Shock

Pressure

(psi)

0.060 1230 140

0.125 630 120

0.192 1215 225

0.242 990 240

4 Computational Model

A finite element (FE) model was developed to understand the pulse-loaded

panel response. Initially, a homogeneous isotropic plate model using nonlinear geometry was created in ABAQUS version 6.8, to simulate the epoxy

panel response, using an explicit solver. The measured pressure-time history is used as a “square wave” input loading. This assumption does not

allow for fluid-structure interaction and the propagation of further shock

waves. The epoxy material was modeled using J2 small strain theory of

plasticity with isotropic hardening and a von Mises yield criterion, where

the material properties are to be determined through inverse modeling, by

correlation with the test data. A circular 3 inch specimen corresponding

to the specimen dimensions used in the shock tests, was analyzed using

the FE method. The panel mesh contains 458 elements with 254 nodes,

with S3R shell elements being used. The mesh size was determined using

a convergence study, the results of which are shown in figure 7

For materials which have a rate-independent modulus the CowperSymonds overstress power law is used to approximate the effects of strain

rate on yield stress.

 ̇

pl = D(R − 1)n

, (1)

where D and n are material constants and R is the yield stress ratio, σ

σ0

.

Since the rate dependence of the epoxy is an unknown, an initial attempt

was made using the rate-dependent properties of a similar polymer maNASA/TM—2010-216941 10
 

 

 

 

 

0 500 1000 1500 2000 0

0.02

0.04

0.06

0.08

Center 

Deflection

(in) 

Number of Elements

Figure 7: Finite Element Convergence Study

terial. Split Hopkinson pressure bar test results for the rate dependence

of SC-15, a thermoset polymer matrix material, were used as a guide for

an ”initial guess” of the rate-dependent properties. SC-15 epoxy is a lowviscosity, two-phased toughened epoxy resin system consisting of phase A

(resin mixture of diglycidylether epoxy toughener) and phase B (hardener

mixture of cycloaliphaic amine poluoxylalkylamine) [13]. The assumed

rate dependence for SC-15 is plotted as a solid line in figure 8, where the

circles represent the experimental data.

Due to the complexity of the constitutive model many parameters need

to be determined; these are, modulus, yield stress ratio, power law exponent, and material damping. The known inputs can be seen in table 2. In a

brittle epoxy sample, a test that subjects the panel to failure provides very

little information about the yield and plasticity parameters. From such a

test, about all that can be determined are the initial modulus and failure

strength. Therefore, if a panel test is conducted at a suitable burst pressure below the plate to fracture level, the resulting oscillatory out-of-plane

panel response provides information that can be used to determine several

of the material parameters.

Through the use of inverse modeling the following parameters for the

NASA/TM—2010-216941 11
 

 

 

 

 

0 1000 2000 3000 4000 0

0.5

1.0

1.5

2.0

R

Strain Rate (s−1)

Figure 8:  ̇ vs. σ

σ0

for SC-15 Matrix

Table 2: Sample Test Known Parameters

Thickness 0.242 in.

Density 1.14e − 4

lbs

in3

epoxy material have been determined (see table 3), by matching the time

history of events. With the use of the parameters shown in table 3, a comparison between experiment and simulation for the panel out-of-plane deflection can be made and is shown in figure 9. A consistent error between

the computed and measured displacement amplitude history is seen, even

though the frequency of response is matched almost exactly. Reviewing

the hardware configuration of the DIC system, it becomes apparent that

an inherent error was inadvertently introduced into the system. Figure

10 shows that the optical path can shift, due to any shift in the position

of the lexan panel window, causing a parallax error. When the system

was initially calibrated the containment chamber was a distance ’d’ away

from the mount. However when the tests were run ’d’ became zero as the

system was clamped together. The cameras remained at the same fixed

NASA/TM—2010-216941 12
 

 

 

0 0.25 0.50 0.75 1.0

0

0.025

0.050

0.075

0.100

Center 

Deflection

(in) 

Time (ms)

DIC

FE model

Figure 9: Finite Element Results vs. DIC results

distance from the point where the specimen is mounted. This shift will

cause a change in the DIC systems measurements since the optical path

shift introduces a systematic error into the initial image calibration. When

the DIC system is initially calibrated, the distance ’d’ must be held at the

same value to be used later during the actual tests. Additional error could

have been introduced if the assumed material properties from the SC-15

data were inaccurate, since only one run was used to curve fit many different properties.

Table 3: Sample Test Parameters

Modulus 350, 000 lbs

in2

σy 3, 250 lbs

in2

D 4880

n 2.883

In addition to displacements, the strain histories are also compared.

Since strains are based on displacement data there will again be a mismatch due to the parallax error in terms of magnitude however, the general trend and contours should be the same. The results compare a section

line through the center in the DIC results, which are seen in figures 11

and 12. There is an excellent agreement between the FE predicted result

and the DIC extracted result. The values of xx show nearly identical conNASA/TM—2010-216941 13
d

Figure 10: Difference in optical paths from movement of lexan panel.

tour maps which is due to very little out-of-plane displacement 0.06in.

occurred relative to the overall size of the specimen 3in. therefore, the calculations for strains becomes more reliant on the 2D motion, which can

be captured accurately with 1 camera. The DIC results show that there is

some localized strain effects, which could be caused by imperfections in

the material.

With a focus on strain rate dependent material properties, a representative point in the center of the panel is examined. The center of the panel

produces a biaxial stress state, which implies that both xx and yy are the

same value for an isotropic material. The strain-time history for the center

point can be seen in figure 13. As can be seen there is very good agreement

between the two results. From the strain-time histories, the strain rates are

computed and shown in figure 14. As can be seen in figure 13, there is a

considerable amount of noise in the DIC data. The data was filtered, using

a ninth order polynomial curve fit, to eliminate much of the noise so that

one can observe a general trend. There is an initial peak followed by a spiral pattern as the plate oscillates. To better see this, the strain components

at the center, as predicted from the finite element simulation, are shown

in figure 15. This plot shows that we have attained a medium strain rate

(50-200 1

s

, see figure 14) for the material. We have not achieved an ultraNASA/TM—2010-216941 14
(a) Finite Element (b) DIC

 

 

 

 

 

0 1 2 3 −2

-1

0

1

2

ε (%)

Position (in.)

FE

DIC

(c) Section Line

Figure 11: Comparison of xx results at max displacement.

NASA/TM—2010-216941 15
(a) Finite Element (b) DIC

 

 

 

0 1 2 3 0

1

2

ε (%)

Position (in.)

FE

DIC

(c) Section Line

Figure 12: Comparison of yy results at max displacement.

NASA/TM—2010-216941 16
 

 

 

 

0 250 500 750 1000 0

0.5

1.0

1.5

ε (%)

time (μ s)

ε

xx

 FE

ε

xx

 DIC

Figure 13: Strain time history of center point comparing FE vs. DIC

 

 

 

 

0 0.5 1.0 1.5 −100

0

100

200

2 ̇ (1/s)

ε (%)

ε

xx

 FE

ε

xx

 DIC Figure 14: Strain rate vs. strain history at the crown of the panel; comparison between the FE model and DIC results, which have been filtered.

high rate (2000-3000 1

s

, see figure 8) as seen in the Hopkinson bar. The

material will have ranges of constant strain rate and also oscillate about

this strain rate. Figure 14 shows how the material will respond to a strain

rate of 100 1

s

staying relatively constant until it reaches a maximum strain,

reversing and going to a strain rate of −75 1

s

, and then as the oscillations

continue it will return to 75 1

s

and shift to −75 1

s

as the deflection decreases.

From figure 15 it is observed that the shear strain is negligible, since its

values and contributions are less than 1% of x and y.

The remaining test results (where the panel fractured) were used to determine the stress level when failure occurred. Since this material is very

brittle at high strain rates, there is minimal yielding. The test results were

NASA/TM—2010-216941 17
 

 

 

 

0 0.5 1.0 1.5 −100

0

100

200

2 ̇ (1/s)

ε (%)

ε

xx

ε

yy

ε

xy

Figure 15: Strain rate vs. strain history at the crown of the panel from FE

model.

compared to properties determined by the FE simulation model and used

to back out the failure stress, based on the time that failure was recorded

with the Photron cameras. It should be noted that the model is based

on SHPB data from a separate material, along with the fact that the data

was collected at much higher strain rates. Additionally, the different thickness of materials may have different material properties, based upon slight

processing variations. Therefore, the model should only be used to note

trends.

A summary of the computed failure stresses, and the out-of-plane deflections, as a function of panel thickness, is provided in table 4. Here the

failure stress is produced from the FE model and the displacement and

failure time are obtained from the DIC software. It is seen that at the very

high rates, panel failure occurs in the brittle-elastic regime, as was evident

in the failure mode of the material and the small amount of plasticity measured in the model.

5 Conclusion

A methodology has been developed to determine the mechanical response

of materials subjected to pressure pulse loading. Using high speed cameras, the out-of-plane deflection time history has been measured using the

DIC method. This result, in conjunction with a finite element model and

Hopkinson bar data can be used to inverse model the panel response and

NASA/TM—2010-216941 18
Table 4: Failure Stress

Thickness (in.) Failure Stress (psi) Time (μs) Z-Disp (in.)

0.060 7,635 120 0.152

0.125 6,860 120 0.131

0.192 6,599 130 0.0874

0.242 5,421 130 0.0587

validate the rate-dependent properties of the panel. The pressure-time

history is used as an input to the finite element simulation. It has been

shown that the pressure transducer closest to the panel on the driven tube

provides information regarding the loading of the specimen. In the shock

tube tests, it is beneficial to stop the testing prior to failure, rather than having an oscillatory panel response, since that allows the determination of a

larger number of material parameters. Tests to failure provide additional

information on rate-dependent material strength and mode of failure.

References

[1] M. Stoffel. Measurement technique for shock wave-loaded structures and its applications. Experimental Mechanics, 46:47–55, 2006.

[2] H.W. Liepmann and A. Roshko. Elements of Gasdynamics. Wiley, 1957.

[3] J.D. Anderson. Modern Compressible Flow. McGraw-Hill, 3rd edition, 2002.

[4] J. LeBlanc, A. Shukla, C. Rousseau, and A. Bogdanovich. Shock loading of threedimensional woven composite materials. Composite Structures, 79:344–355, 2007.

[5] M. Herbert, C.E. Rousseau, and A. Shukla. Shock loading and drop weight impact

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[6] S.A. Tekalur, A. Shukla, and K. Shivakumar. Blast resistance of polyurea based layered composite materials. Composite Structures, 84:271–281, 2008.

[7] S.A. Tekalur, K. Shivakumar, and A. Shukla. Mechanical behavior and damage

evolution in e-glass vinyl ester and carbon composites subjected to static and blast

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[9] Q. Li, D. Liu, D. Templeton, and B. Raju. A shock tube-based facility for impact

testing. Experimental Techniques, (25–28), 2007.

[10] M. Stoffel. Experimental validation of anisotropic ductile damage and failure of

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[11] M. Stoffel, R. Schmidt, and D. Weichert. Shock wave-loaded plates. International

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[13] Y. Zhou, F. Pervin, M.A. Biswas, V.K. Rangari, and S. Jeelani. Fabrication and characterization of montmorillonite clay-filled sc-15 epoxy. Materials letters, 60:869–873,

2006.

NASA/TM—2010-216941 20
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Blast Loading of Epoxy Panels Using a Shock Tube 

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6. AUTHOR(S)

Pankow, Mark; Waas, Anthony, M.; Bednarcyk, Brett 

5d. PROJECT NUMBER

5e. TASK NUMBER

5f. WORK UNIT NUMBER

WBS 698259.02.07.03 

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

National Aeronautics and Space Administration 

John H. Glenn Research Center at Lewis Field 

Cleveland, Ohio 44135-3191 

8. PERFORMING ORGANIZATION

 REPORT NUMBER

E-17545 

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

National Aeronautics and Space Administration 

Washington, DC 20546-0001 

10. SPONSORING/MONITOR'S

 ACRONYM(S)

NASA 

11. SPONSORING/MONITORING

 REPORT NUMBER

NASA/TM-2010-216941 

12. DISTRIBUTION/AVAILABILITY STATEMENT

Unclassified-Unlimited 

Subject Category: 39 

Available electronically at http://gltrs.grc.nasa.gov 

This publication is available from the NASA Center for AeroSpace Information, 443-757-5802

13. SUPPLEMENTARY NOTES

14. ABSTRACT

The high strain rate mechanical response of thin polymer plates has been studied using a modified shock tube. Diagnostics include the 

pressure-time history of the incident and reflected pulses and the use of digital image correlation (DIC) techniques to extract the time-history 

of the out-of-plane displacement distribution. Additionally, finite element models have been developed to understand the plate response and 

to validate and modify plate material constitutive models that have been proposed.

15. SUBJECT TERMS

Strain rate; Thin plates; Shock tubes; Imaging techniques; Displacement; Finite element method; Characterization 

16. SECURITY CLASSIFICATION OF: 17. LIMITATION OF

 ABSTRACT

UU 

18. NUMBER

 OF 

 PAGES

26 

19a. NAME OF RESPONSIBLE PERSON

STI Help Desk (email:help@sti.nasa.gov) 

a. REPORT

U 

b. ABSTRACT

U 

c. THIS 

PAGE

U 

19b. TELEPHONE NUMBER (include area code)

443-757-5802 

Standard Form 298 (Rev. 8-98)

Prescribed by ANSI Std. Z39-18