these cases, therefore, only a portion of the flaw could be suc-
cessfully scanned, resulting in an underestimation of flaw size.
Further work should be devoted to adapting the sensing
probe to enable scanning on curved surfaces, which could
be accomplished using either conformable wedges or fully
stretchable and flexible transducer arrays, as recently demon-
strated by one of the authors and collaborators (Hu et al. 2018).
This is an area of open research.
While the primary goal of the present research is to
improve current hand verification techniques for rail flaws,
the fast SAF technique introduced here could also be imple-
mented in motion. Possibilities for in-motion imaging could be
a walking-stick wheel or even an inspecting hi-railer vehicle,
although important issues such as fast image data interpreta-
tion and full rail coverage (probably requiring multiple arrays
simultaneously) would have to be addressed.
ACKNOWLEDGMENTS
This research was funded by the US Federal Railroad Administration under
contract no. 693JJ619C000008 (Dr. Robert Wilson, Program Manager).
The authors acknowledge the technical feedback provided by Dr. Wilson
throughout this project. The authors also acknowledge the support of
the former Transportation Technology Center (now MxV Rail) in Pueblo,
Colorado, and especially Dr. Anish Poudel, for providing the rail test
sections utilized in the validation tests and the ground truth information,
as well as assisting with the evaluation of the results. Finally, the authors
would like to acknowledge Mr. Gavin Dao of Advanced OEM Solutions
(West Chester, OH) for providing technical advice on SAF hardware
solutions and valuable insights over the use of the multiplexer currently
adopted in the prototype.
REFERENCES
Drinkwater, B. W., and P. D. Wilcox. 2006. “Ultrasonic arrays for
non-destructive evaluation: A review.” NDT &E International 39 (7):
525–41. https://doi.org/10.1016/j.ndteint.2006.03.006.
Flaherty, J. J., K. R. Erikson, and V. M. Lund. 1967. Synthetic aperture
ultrasonic imaging systems. U.S. Patent 3,548,642, filed 2 March 1967, and
issued 22 December 1970.
Frazier, C. H., and W. D. O’Brien. 1998. “Synthetic aperture tech-
niques with a virtual source element.” IEEE Transactions on Ultra-
sonics, Ferroelectrics, and Frequency Control 45 (1): 196–207. https://doi.
org/10.1109/58.646925.
Hu, H., X. Zhu, C. Wang, L. Zhang, X. Li, S. Lee, Z. Huang, et al. 2018.
“Stretchable ultrasonic transducer arrays for three-dimensional imaging
on complex surfaces.” Science Advances 4 (3): eaar3979. https://doi.
org/10.1126/sciadv.aar3979.
Huang, C., and F. Lanza di Scalea. 2022. “High Resolution Real Time
Synthetic Aperture Imaging in Solids Using Virtual Elements,” Proceed-
ings of the ASME 2022 International Mechanical Engineering Congress
and Exposition. Volume 9: Mechanics of Solids, Structures, and Fluids
Micro- and Nano-Systems Engineering and Packaging Safety Engineering,
Risk, and Reliability Analysis Research Posters. https://doi.org/10.1115/
IMECE2022-94445.
Jensen, J. A., S. I. Nikolov, K. L. Gammelmark, and M. H. Pedersen. 2006.
“Synthetic aperture ultrasound imaging.” Ultrasonics 44 (Suppl. 1): e5–15.
https://doi.org/10.1016/j.ultras.2006.07.017.
Karaman, M., P. -C. Li, and M. O’Donnell. 1995. “Synthetic aperture
imaging for small scale systems.” IEEE Transactions on Ultrasonics,
Ferroelectrics, and Frequency Control 42 (3): 429–42. https://doi.
org/10.1109/58.384453.
Lockwood, G. R., J. R. Talman, and S. S. Brunke. 1998. “Real-time 3-D
ultrasound imaging using sparse synthetic aperture beamforming.” IEEE
Transactions on Ultrasonics, Ferroelectrics, and Frequency Control 45 (4):
980–88. https://doi.org/10.1109/58.710573.
Lanza di Scalea, F., 2007, “Ultrasonic testing applications in the railroad
industry,” Chapter 15: Special Applications of Ultrasonic Testing, in
Non-destructive Testing Handbook, 3rd edition, P.O. Moore, ed., American
Society for Nondestructive Testing, pp. 535-552.
Lanza di Scalea, F., S. Sternini, and T. V. Nguyen. 2017. “Ultrasonic imaging
in solids using wave mode beamforming.” IEEE Transactions on Ultra-
sonics, Ferroelectrics, and Frequency Control 64 (3): 602–16. https://doi.
org/10.1109/TUFFC.2016.2637299.
Martin-Arguedas, C. J., D. Romero-Laorden, O. Martinez-Graullera, M.
Perez-Lopez, and L. Gomez-Ullate. 2012. “An ultrasonic imaging system
based on a new SAFT approach and a GPU beamformer.” IEEE Transac-
tions on Ultrasonics, Ferroelectrics, and Frequency Control 59 (7): 1402–12.
https://doi.org/10.1109/TUFFC.2012.2341.
Sternini, S., A. Y. Liang, and F. Lanza di Scalea. 2019a. “Ultrasonic
synthetic aperture imaging with interposed transducer–medium coupling
path.” Structural Health Monitoring 18 (5-6): 1543–56. https://doi.
org/10.1177/1475921718805514.
Sternini, S., A. Y. Liang, and F. Lanza di Scalea. 2019b. “Rail Defect Imaging
by Improved Ultrasonic Synthetic Aperture Focus Techniques.” Materials
Evaluation 77 (7): 931–40.
Witte, M., and A. Poudel. 2016. “High-speed rail flaw detection using
phased array ultrasonics.” Technology Digest TD16-030.
J A N U A R Y 2 0 2 4 • M A T E R I A L S E V A L U A T I O N 59
2401 ME January.indd 59 12/20/23 8:01 AM

ABSTR ACT
Continuously welded rails are connected without
stress relief joints and, thus, thermally induced rail
movement is constrained, which can result in the
development of excessive axial stress and risk of
rail failure. Nondestructive testing (NDT) methods
that estimate in-place rail stress state or rail neutral
temperature are desired. Some methods have been
developed, but none satisfy the requirements for ideal
monitoring in practice. We propose an NDT technique
based on impulse-generated vibration, seeking high-
frequency rail vibration resonances whose frequency
maintains a consistent correlation with rail axial
stress/strain across different temperatures, stress
states, and rail support conditions. Rail temperature,
axial strain, and vibration data were collected
from an active Class 1 commercial rail line over a
period of nearly two years. The frequencies of four
consistent and clear resonance modes of the rail were
monitored. One of the identified modes demonstrates
a unique linear relation with axial strain across a
range of temperatures and stress states at each of the
two measurement locations. The developed linear
relations were used to predict in-place strain and rail
neutral temperature with acceptable accuracy across
all the measurement data, although each test location
exhibits a unique relation.
KEYWORDS: acoustic sensing, NDT, rail neutral temperature,
rail buckling, spectral analysis
Introduction
Continuously welded rail (CWR) is the prevailing type of
railroad track structure in the United States. CWR comprises
long sections of continuous rail steel that are welded together
at the ends. The CWR structure also contains rail fastener
and foundational components such as rail crossties, clips,
and anchors and thus represents a mechanically constrained
system without stress-relief joints. Although CWR offers
advantages such as smooth transit at high speed, it constrains
the free thermal expansion of the rail and therefore tends to
build up high levels of axial stress when the rail experiences
temperature extremes. In particular, high levels of axial com-
pression build up at high rail temperatures, which can cause
rail buckling events. According to a report from the Federal
Railroad Association (FRA), “track alignment irregularities
(buckled/sun kink)” is among the leading track-related factors
that cause train accidents (US DOT n.d.). Rail buckling is also
associated with a high risk of large-scale train derailment
(Wang et al. 2020), which entails rail operation suspension,
damage, and even casualties. Therefore, monitoring thermally
induced axial stress state in CWR is important for railway oper-
ations and safety.
The parameter rail neutral temperature (RNT) is broadly
used by track engineers to characterize the stress state of CWR.
RNT represents the rail temperature at which the rail is totally
free of axial stress, and it provides a quick sense of the load
level by comparing the present rail temperature to RNT. Larger
differences between the present rail temperature and RNT
indicates higher levels of load in constrained systems, follow-
ing the relationship derived from linear thermal expansion: ​ ​
(1)​ ​ P
AE​
=​ ε​x​​ =α(T ​ − RNT)​​,
where
P is the thermally induced axial force,
E is the Young’s modulus of the rail steel,
A is the cross-sectional area of the rail, ​ ​
ε​x​​​ is the equivalent axial strain, ​
α​ is the coefficient of linear thermal expansion of the rail
steel, and
T is the in situ rail temperature.
The RNT of a track structure is set at the time of rail instal-
lation, but it can vary over the short term (for example, owing
PREDICTING AXIAL STRESS STATE IN
CONTINUOUSLY WELDED RAIL USING
IMPULSE-GENERATED VIBRATION
MEASUREMENTS
CHI-LUEN HUANG* AND JOHN S. POPOVICS*†
*Department of Civil and Environmental Engineering, University of Illinois at
Urbana-Champaign, Urbana, IL 61801
† johnpop@illinois.edu
Materials Evaluation 82 (1): 60–66
https://doi.org/10.32548/2024.me-04377
©2024 American Society for Nondestructive Testing
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