Proceedings of the IMPLAST 2010 Conference
October 12-14 2010 Providence, Rhode Island USA
© 2010 Society for Experimental Mechanics, Inc.
Stress Wave Propagation in a Composite Beam Subjected to Transverse
Impact
Bo Song, Helena Jin, Wei-Yang Lu
Sandia National Laboratories, Livermore, CA 94551-0969, USA
Composite materials, particularly fiber reinforced plastic composites, have been extensively utilized in
many military and industrial applications. As an important structural component in these applications, the
composites are often subjected to external impact loading. It is desirable to understand the mechanical response
of the composites under impact loading for performance evaluation in the applications. Even though many
material models for the composites have been developed, experimental investigation is still needed to validate
and verify the models. It is essential to investigate the intrinsic material response. However, it becomes more
applicable to determine the structural response of composites, such as a composite beam.
The composites are usually subjected to out-of-plane loading in applications. When a composite beam is
subjected to a sudden transverse impact, two different kinds of stress waves, longitudinal and transverse waves,
are generated and propagate in the beam. The longitudinal stress wave propagates through the thickness
direction; whereas, the propagation of the transverse stress wave is in-plane directions. The longitudinal stress
wave speed is usually considered as a material constant determined by the material density and Young’s
modulus, regardless of the loading rate. By contrast, the transverse wave speed is related to structural
parameters. In ballistic mechanics, the transverse wave plays a key role to absorb external impact energy [1].
The faster the transverse wave speed, the more impact energy dissipated. Since the transverse wave speed is
not a material constant, it is not possible to be calculated from stress-wave theory. One can place several
transducers to track the transverse wave propagation. An alternative but more efficient method is to apply digital
image correlation (DIC) to visualize the transverse wave propagation. In this study, we applied three-pointbending (TPB) technique to Kolsky compression bar to facilitate dynamic transverse loading on a glass
fiber/epoxy composite beam. The high-speed DIC technique was employed to study the transverse wave
propagation.
Fig. 1 Schematic of the testing section.
Fig. 2 Displacement history at the impact wedge end.
The dynamic TPB experiments were conducted with the Kolsky compression bar at Sandia National
Laboratories, California. Figure 1 shows the schematic of the testing section. A random pattern was painted on
the composite surface for the purpose of applying DIC technique. The high-rate deformation of the composite
beam was photographed with a Cordin 550 high speed digital camera. The stain gage signals on the pressure
bars provide a velocity/displacement boundary transversally loaded on the composite beam. In this case, the
transmitted signal is nearly negligible in comparison to the incident pulse. The displacement boundary on the
span side can be considered stationary. The displacement history at the wedge end are calculated with
X = C0 ³ (ε I (τ ) − ε R (τ ))dτ ≈ 2C0 ³ ε I (τ )dτ
t
t
0
0
(1)
and is shown in Fig. 2. The impact speed is measured as 9.0 m/s.
When the stress wave in the incident bar travels to the composite beam, a longitudinal stress wave is
generated and then propagates through the thickness direction. When the longitudinal stress wave arrives at the
free back side of the composite beam, it reflects back and doubles the particle velocity. Due to the fast
longitudinal stress wave speed and relatively small thickness in the composite beam, it takes only a few
microseconds to achieve a nearly equilibrated state in displacement. In other words, the displacement gradient
through the thickness direction can be neglected after a few microseconds. However, along the beam direction,
there exists a significant gradient in displacement due to the propagation of transverse wave. The DIC results
shown in Fig. 3 confirm the transverse wave propagation.
0
t
Y
Fig. 3 Propagation of transverse wave (time interval: 5 microseconds)
Figure 4 illustrates the displacement histories at different locations. When the transverse wave arrives at
a particular location, the displacement is initiated. For example, at the time, T=10 ȝs, the particle at the location
Y=-9.70 mm starts moving indicated by the initiated jump in displacement. This means, at this time, the
transverse wave front arrives at this location. Recording the location and time of displacement initiations can
track the transverse wave propagation, as shown in Fig. 5. The slop of the linear fit of the data indicates that
transverse wave speed is approximately 580 m/s in response to the transverse impact speed of 9.0 m/s.
Fig. 4 Displacement histories at different locations
Fig. 5 Transverse wave front propagation
We also examined the displacement history at
a specific location, such as at Y=-20 mm in Fig. 4. The
displacements for the first 25 ȝs were plotted in Fig. 6,
showing the particle movement speed at this cross
section is 8.9 m/s along thickness direction. Ideally, the
particle movement speed should have a maximum
value of 9.0 m/s (Fig. 2) in the middle (the wedge
location), and a minimum value of nearly 0 m/s at the
span locations of the composite beam. The speed of
8.9 m/s at the location of 5 mm from the middle is
therefore reasonable.
In this study, the high speed DIC technique has
been found efficient to investigate the stress wave
propagation in the composite beam under high rate
loading. The relationship between the transverse wave
speed and the transverse impact speed is thus able to
be determined with the DIC technique. The quantitative
experimental determination of the dynamic transverse
response of the composite beam may be used for
validating and verifying material models. It also helps
precise data interpretation in dynamic ENF testing of
composites [2].
Fig. 6 Particle displacement at the location
Y=5mm from the wedge.
ACKNOWLEDGEMENTS
Sandia is a multiprogram laboratory operated by Sandia Corporation, a Lockheed Martin Company, for
the United States Department of Energy under Contract DE-AC04-94AL85000.
REFERENCES
1. Wang, L.-L., Foundations of stress waves, Elsevier, 2007.
2. Lu, W.-Y., Song, B., and Jin, H., 2010, “A revisit to high-rate mode-II fracture characterization of
composites with Kolsky bar techniques,” In: Proceedings of 2010 SEM Annual Conference and Exposition
on Experimental and Applied Mechanics, June 7-10, 2010, Indianapolis, IN.