CP620, Shock Compression of Condensed Matter - 2001
edited by M. D. Furnish, N. N. Thadhani, and Y. Horie
© 2002 American Institute of Physics 0-7354-0068-7/02/$ 19.00
THE DYNAMIC STRENGTH OF CEMENT PASTE UNDER SHOCK
COMPRESSION
K. Tsembelis, W. G. Proud and I.E. Field
PCS, Cavendish Laboratory, Madingley Road, Cambridge, CBS OHE. UK.
Abstract. A series of plate impact experiments on cement paste (grout) has been performed to assess the
dynamic strength of this material. Lateral stresses have been directly measured by means of embedded
manganin stress gauges. In combination with longitudinal stresses, measured previously [1], these results
have been used to obtain shear strength under shock loading. Results indicate that the material is
behaving in an inelastic manner with the shear strength increasing with increasing pressure.
INTRODUCTION
EXPERIMENTAL PROCEDURE
Considerable interest in characterising the
dynamic loading of concrete under impact
conditions exists because of its extensive use as a
structural material [2-5]. Concrete is a
heterogeneous material containing aggregates in a
cement matrix. Therefore, characterisation under
dynamic conditions is complicated compared to
homogeneous materials. For instance, impedance
differences inside the concrete emanating from its
different constituents lead to variations in the
particle velocities, longitudinal and lateral stresses.
One way to study this material is to average these
variations using a plate reverberation technique,
where a disc-shaped concrete specimen is mounted
on the projectile and undergoes planar impact on a
stationary target (PMMA, copper, tantalum) which
is fitted with diagnostics [2-5]. However, only the
Hugoniot curve (longitudinal behaviour) can be
found using this technique. For this reason, the
material understanding has been gradually built up
starting from studies of the matrix (cement paste)
and individual aggregates. In this paper, results are
presented on the lateral behaviour of the matrix
material, which are combined with published
longitudinal data under the same impact conditions
to determine the shear strength of the cement paste.
All the impact experiments were carried out in
the plate impact gun facility at the University of
Cambridge [6], which consists of a single stage 50mm bore, light gas gun. The gun is capable of
achieving velocities up to 1200 ms"1. The impactor
materials consisted of Polymethylmethacrylate
(PMMA), aluminium, or copper. Impact velocities
were measured to an accuracy of 0.5% using a
sequential pin-shorting method and tilt was fixed to
be less than 1 mrad by means of an adjustable
specimen mount. The cement paste specimen were
20 mm thick by 50 mm x 50 mm.
Yr&asvwse
stress
Target
Figure 1. Target configuration
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Backing plate
(target material or
FMMA)
9TCu and lOTCu respectively (for impact
conditions, see Table 1). The solid trace
corresponds to the longitudinal stress while the
dotted trace corresponds to the lateral stress as
obtained in [1]. It can be seen that the longitudinal
stresses have higher values than the lateral ones and
their difference leads to the shear stress inside the
material according to equation 1.
Each sample was sectioned in two, and commercial
stress gauges (MicroMeasurements type J2M-SS580SF-025) were introduced at fixed distances
between 2 mm and 7 mm from the impact surface of
the sample. Samples were then assembled using a
low viscosity epoxy with a curing time of
approximately 24 hours. Lateral gauge data was
reduced using the analysis of Rosenberg and Partom
[7]. The gauge mounting positions and sample
configurations are shown in figure 1. The shear
strength ( ) of a material under one-dimensional
shock loading can be calculated from knowledge of
the longitudinal (ax) and lateral stresses (ay)
through the relation,
(1)
Our method of determining the shear stress has the
advantage over previous calculations of being direct
since no computation of the hydrostat is required.
0
0.1
0.2
0.3
0.4
0.5
0.6
0.7
Particle Velocity (mm ps1)
MATERIAL DATA
Figure 2. Cement Paste Hugoniot
Cement paste tested in this study was prepared
and supplied by Concrete Structures Section (CSS),
Department of Civil & Environmental Engineering,
Imperial College, London, UK. The paste had a
water-to-cement ratio of 0.35 by weight. Specimens
were cured for 21 days in a water-bath at 20 °C.
Density and ultrasonic measurements were
performed after grinding samples from different
batches. The density was 2.0 ± 0.2 g cm"3, while the
longitudinal and shear elastic wave velocities, were
3.7 ± 0.2 and 2.2 ± 0.2 km s"1, respectively. Density
variations resulted from different initial porosity.
The density variations were in agreement with
independent measurements performed by CSS.
0.
o
Time (ps)
Figure 3. Stress Wave Profiles for experiment
9TCu.
The results are presented in Figure 5. The shear
stress data calculated from equation 1 are plotted
against longitudinal stress. As a comparison, the
data are also fitted to the assumed elastic behaviour
given by equation,
RESULTS AND DISCUSSION
Table 1 summarises the impact conditions and
lateral stresses as obtained from the gauges. In
addition, the corresponding longitudinal stresses
(Hugoniot curve) taken from [1] are also given and
illustrated in Figure 2. Figures 3 and 4 illustrate
some typical stress wave profiles for experiments
0 = - a
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x
,
(2a)
Table 1. Experimental Parameters, Lateral Stresses and corresponding Hugoniot Data
Shot no.
Impactor material and
thickness (mm)
Impact Velocity (m s"1)
Lateral Stress (GPa)
1TA1
2TA1
3TA1
4TA1
5TA1
6TCu
7TCu
8TA1
9TCu
lOTCu
11TPMMA
12TCu
lOmmAl
lOmmAl
lOmmAl
lOmmAl
lOmmAl
lOmmCu
lOmmCu
lOmmAl
lOmmCu
6 mmCu
lOmmPMMA
lOmmCu
352
1.00 ±0.03
2.00 ± 0.06
0.52 ±0.02
1.39 ±0.04
1.35 ±0.03
2.28 ±0.05
2.66 ± 0.08
1.64 ±0.14
2.94 ±0.1 5
3.75 ±0.15
0.09 ±0.01
4.69 ± 0.40
512
261
438
440
499
569
514
635
724
229
846
Corresponding
Longitudinal Stress
(GPa)
1.34 ±0.06
2.25 ±0.12
0.84 ±0.04
1.92 ±0.06
1.92 ±0.06
2.64 ±0.1 6
3.30 ±0.20
2.25 ±0.12
4.05 ±0.20
5.00±0.15
0.47 ±0.01
6.20 ±0.19
1-2V
———
1-v
(2b)
where is the Poisson's ratio of the material (0.23).
It can be seen that, within the data scatter due to the
nature of the cement paste, the material behaviour
deviates from the purely elastic behaviour around
the HEL, which has previously [1] been measured to
be 0.30 ± 0.05 GPa. In addition, the shear stress
increases with increasing impact stress. Therefore,
there must be some process such as fracture, or pore
collapse, which reduces the strength, while the shear
stress exhibits pressure dependence, which is
indicative of the brittle nature of the material.
Similar behaviour has also been observed in certain
filled glasses [8] where the shear stress of the
damaged material deviates from the elastic loading
line and also increases with pressure.
Time (MS)
Figure 4. Stress Wave Profiles for experiment
lOTCu.
o.
o
CONCLUSIONS
2
3
4
Plate impact experiments have been presented
to assess the shear behaviour of the cement paste. It
is observed that above its HEL the material behaves
inelastically indicating a process such as fracture or
pore collapse reducing the strength. In addition, the
shear stress increases with increasing pressure.
5
Longitudinal Stress (GPa)
Figure 5. Cement Paste Shear Response
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8.Radford, D.D., Proud, W.G. and Field, I.E., To
appear in: Proc. Of SHOCK 2001 - APS 12th
Topical Conference on Shock Compression of
Condensed Matter, Atlanta, 24-29 June, 2001.
ACKNOWLEDGEMENTS
The Defence and Evaluation Research Agency,
UK has sponsored this work, under contract
WSS/U3257. Dr. A. Pullen from Imperial College
provided the cement samples. Dr J. Sheridan, C.
O'Carroll, I.G. Cullis and P.D. Church are thanked
for their interest. Finally, we thank D.L.A. Cross
and R. Flaxman for technical support.
REFERENCES
1.Tsembelis, K, Millett, J.C.F., Proud, W.G. and
Field, J.E.. "The Shock Hugoniot Properties of
Cement Paste up to 5 GPa",. in Shock
Compression of Condensed Matter - 1999,
(Edited by M.D. Furnish, L.C. Chhabildas and
R.S. Hixson), pp. 1267-1270.
2. Grady, D. E., "Impact Compression Properties of
Concrete", in Proceedings of the Sixth
International Symposium on Interaction of
Nonnuclear Munitions with Structures, Panama
City Beach, Florida, pp. 172-175, May 3-7
(1993)
3.Hall, C. A., Chhabildas, L. C., and Reinhart, W.
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from 3 to 23 GPa," in Shock Compression in
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et al., AIP Conference Proceedings 429, New
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Mechanics
Publications,
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5.Kipp, M. E., Chhabildas, L. C., and Reinhart, W.
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