JOURNAL DE PHYSIQUE 1V

Colloque C8, supplkment au Journal de Physique III, Volume 4, septembre 1994 C8-113

Study of the true tensile stress-strain diagram of plain concrete with real
size aggregate; need for and design of a large Hopkinson bar bundle
C. Albertini and M. Montagnani
Commission of the European Communities, Joint Research Centre, Institute of Safety Technology,
2 1020 Ispra (Varese),Italy

Resume: L'idCe est discutCe d'employer deux grands faisceaux de barres &Hopkinson,
disposCes de fason spkculaire, pour l'observation de la distribution instantanee de la
contrainte et de la deformation sur la section rCsistante des grandes Cprouvettes de bCton,
chargkes en dynamique rapide.

Abstract: The idea is discussed of using two specular bundles of Hopkinson's bars for the
experimental observation of the instantaneous distribution of stress and strain over the
cross-section of large concrete specimens with real size aggregate, subjected to high
loading rates.

1. INTRODUCTION

The true stress-strain diagram at high loading rate of plain concrete is of basic importance for the
assessment of the resistance of civil engineering structures against accidental loadings like those
provoked by earthquakes and explosions.
Normally, Hopkinson bars for steel have a diameter of 10-20 mm, [I] [2], which is sufficient to
load small specimens representative of fine-grained materials like steel. In the last decade, two
research groups (Kormeling et al., [3]), (Malvern et al., [4] increased the bar diameter to 60 and
75 mrn, respectively, in order to load representative plain concrete specimens having an aggregate
of 8-10 mm size; we have also heard of a 100 mm diameter bar used in the USA by Ross.
The Hopkinson bar system developed in our research differs from the two systems mentioned
above in two ways:
- the mechanical pulse is generated by the elastic energy stored in a prestressed bar (not by an
impacting projectile) [ S ] ;
the bar shape is a square of 6x6 cm instead of being round, of small transverse dimension in
comparison with the wavelength of the applied stress pulse (200 cm). The propagation
dispersion of stress pulses in square bars is similar to that of cylindrical bars [6].

2. EXPERIMENTAL EQUIPMENT

The Hopkinson bar developed in our laboratory for tensile tests of plain concrete is sketched in
Figure 1. As a first operation, a hydraulic actuator prestresses only the steel bar up to its elastic

Article published online by EDP Sciences and available at http://dx.doi.org/10.1051/jp4:1994817

C8-114 JOURNAL DE PHYSIQUE IV

limit because of the frictional action of a blocking device. The successive operation is the
controlled rupture of a brittle intermediate piece of the blocking device, which gives rise to a
tensile mechanical pulse of rectangular shape, propagating along the first aluminium bar,
specimen and the second aluminium bar; the generated tensile mechanical pulse has a constant
-
amplitude and a duration of 920 10-6s because the prestressed bar has a length of 2300 mm.
The plain concrete specimen has the same cross-section (6x6 cm) as the aluminium bars, to which
it is glued with an epoxy resin. Aluminium was chosen as the bar material because of its
transverse modulus, which is not far from that of plain concrete. This last fact, together with some
fine longitudinal cuts on the ends of the aluminium bars glued to the specimen, minimizes the
constraint to transverse deformation of the concrete specimen. A first strain gauge station on the
incident bar measures the incident pulse €1 and the reflected pulse CR. A second strain gauge
station on the transmitted bar measures the pulse e~ transmitted through the specimen. The
distance of both the strain gauge stations from the specimen is 700mm; therefore after
- 280 10-6s the strain gauge station on the incident bar gives a measurement of the reflected
pulse r~ obtained from the difference between the amplitude of the incident pulse measured
before the time of 280 10-6s, and the actual measurement of the strain gauge. From Figure 2 it
can be seen that before the time of 280 10-6s the amplitude of the incident pulse shows very
small oscillations, of the order of + 2 percent, and therefore the reflected pulse is measured with
an accuracy of the same order. The average instantaneous values of the stress and strain of the
concrete, assuming uniaxial wave propagation and homogeneous stress distribution in the
specimen, are obtained by the following equations:

0 (t) = AEET(~)
A0
where: A = cross-section of the aluminium bar,
A, = cross-section of the concrete specimen,
E = Young modulus of aluminium
t = time

and:

2C
(t) = - q(t)dt
Lo 0

where: C = elastic wave speed in aluminium,

Lo = length of the concrete specimen,
The strain of the concrete specimen is also measured by strain gauges directly glued on the
specimen (Figure 1). A record of the measurements given by the strain gauges glued on the bars
and on the specimens is given in Figure 2.

3. PLAIN CONCRETE COMPOSITION AND SPECIMENS

The plain concrete composition was the following:

- water/cement ratio 0.5 - cement type R425
- % sand (0.3 mm) 60 - % gravel (3-10 mm) 40
- aggregate quantity 1700 Kg/ m3 - cement quantity 375 Kg/m3
- maximum aggregate size 10 mm
NIELONGIRiDIN4l

PRESTRESSED WUPAULIC

WNCRRESPECIMEN
60 mm SIOE PIECE
0 125 250 378 500
TIME (PSI

Figure 1: Hopkinson bar for dynamic Figure 2: Record of a tensile test on a

tension testing of plain concrete. concrete specimen by a modified
Hopkinson bar.

The specimens had a square cross-section of 6x6 cm and the following lengths: 3, 5, 7, 10, 12 and
15 cm. The plain concrete with this aggregate size is normally defined as "micro concrete" because
the aggregate size normally used in real civil structures is larger (> 25 mrn).

4. RESULTS AND DISCUSSION OF MICROCONCRETE TESTING

The stress strain curves in tension of plain concrete at strain rates of 6x10-7 and 2.5 s-l (loading
rate 106N/mrn2s) were determined following two methods:
a) using the Hopkinson bar formulae (1) and (2) giving the stress and strain values at each instant
of the test from the records of transmitted and reflected pulses, respectively;
b) using the Hopkinson bar formula (1) to calculate the stress and the direct measurement of the
strain on the specimen by means of the glued electrical strain gauge.
The two measurement methods gave results which are in good agreement as far as the rising
branch of the stress strain curve is concerned (Figure 3), while the falling branch of the curve
could be measured only by the Hopkinson bar formulae (method a) because the strain gauge on
the specimen broke when the highest strength was reached in the specimen. The results obtained
at low and high strain rate with specimens of different lengths are shown in Figure 4, where we
observe that:
- at high strain rate the ultimate tensile strength is about 2.5 times the strength at low strain rate;
- at high strain rate the strain at the ultimate tensile strength is about twice as large as that at
low strain rate.
The explanation of the two phenomena may be based on the fact that, in dynamics, the increase of
the load is so fast that all the components of the mix contribute to the resistance against the
external load because there is not sufficient time for the external load to follow the path of
highest weakness through the mix. In fact, observation of the fracture surfaces of the specimens
loaded in dynamic conditions, which were usually normal to the load direction, showed a large
amount of fractured coarse aggregate, as was also observed by Kormeling et al. [3].
Observing the records of the incident, reflected and transmitted pulses versus time of Figure 2, we
can distinguish three phases:
1st) transmitted pulse rising with a roughly constant slope and reflected pulse also increasing
with a constant slope;
2nd) further nonlinear increase of the transmitted pulse up to its maximum; change in slope of
the reflected pulse;
3rd) sharp decrease of the transmitted pulse and increase of the reflected pulse with the same
constant slope - sharper than during phase 1.
C8-116 JOURNAL DE PHYSIQUE IV

SPECIMEN LENGW -1
SIRAIN RAE 2.5 D'

ENG. STRAIN ( p slrain) ENG. STRAIN ( CL strain)

Figure 3: Stress strain curves of micro concrete Figure 4: Stress strain curves by Hopkinson
by Hopkinson bar measurements and bar measurements of micro concrete
by strain gauge measurement. specimens of different lengths.

The transmitted and reflected pulses of the first phase give rise to the nearly linear part of the
stress strain diagram of Figure 4, where the material could be considered elastic. The transmitted
and reflected pulses of the second phase give the highly nonlinear upper part of the stress strain
diagram of Figure 4; during this phase, microcracks probably develop and coalesce (see also
Kormeling et al., [3]). The descending branch of the stress strain diagram of Figure 4 is obtained
from the third phase, transmitted and reflected pulses. During this phase it is assumed that
macrocracks propagate through the whole thickness of the specimen.
We have observed that the duration of the third phase has a nearly constant value of about 30 ps,
resulting in a high crack propagation speed. Therefore, the simplification of using the initial cross-
section and the initial gauge length is too rough for the calculation of the stress and strain of the
descending part of the diagrams of Figure 4.
From the observation of the stress-strain diagrams of microconcrete (Figure 4) it follows that:
- the main differences in the stress-strain diagrams concern the softening branch characterized
by crack propagation which is strongly influenced by aggregate size;
- a correct estimate of the softening branch needs a measurement of the true resisting cross-
section and of the strain of the material volume bearing the load during crack propagation;
- the loading gradient over the specimen gauge length increasing up to 150 rnm was of minor
importance (see Figure 2).

5. THE HOPKINSON BAR BUNDLE EQUIPMENT

From these observations, it was decided to test large concrete specimens (cube with 20 cm side)
with real size aggregate, developing special equipment for the correct characterization of the
softening branch of the stress-strain diagram which is very important for the evaluation of the
energy absorption capability of the real material used in civil engineering structures.
The special equipment is sketched in Figure 5 and consists of:
- a hydropneumatic head, a prestressed steel bar and a blocking device;
- input and output Hopkinson's bars subdivided into two specular bundles of elementary
Hopkinson's bars.
The equipment can be used in a very large range of loading rates, typical of static, earthquake and
impact loadings, obtained by a specific loading application mode.
The static and low loading rates can be realized by the direct action of the hydropneumatic head
on the specimen, excluding the blocking device.
The medium and high loading rates will be realized by using the device as a Hopkinson's bar. In
this case elastic energy is stored in the steel bar by prestressing it with the hydropneumatic head.
Before beginning the test, the load is supported by the blocking device.
 STRAIN GAUGES FOR

Figure Bundle Hopkinson Bar for dynamic tension testing of plain concrete.

Figure 6 - Tension test of large concrete specimens with crack propagation measurement.

The test begins by deactivation of the blocking device, which gives rise to a pulse with high
loading rate propagating along the bundle of the input bars, the specimen and the bundle of the
output bars.
During the crack propagation phase each pair of specular bars of the Hopkinson's bar bundles,
which is individually instrumented with strain gauges (Figure 5), measures the incident, reflected
and transmitted pulses €1, ER,ET,concerning only the portion of the specimen cross-section facing
the cross-section of the pair of bars of the bundle.
In more detail, during the fracturing process each pair of specular bars of the bundles will be in
one of the following physical situations:
1. Facing an uncracked portion of the specimen cross-section, therefore measuring a small
reflected pulse ERand a large transmitted pulse ET.
2. Facing a cracked portion of the specimen cross-section, therefore measuring a reflected pulse
f R of equal amplitude and of opposite sign to the incident pulse 61, while the correlated
transmitted pulse decreases to ET = 0.
(23-118 JOURNAL DE PHYSIQUE IV

3. Facing a semi-cracked portion of the specimen cross-section, therefore in a measurement

situation of r R and ET in between situations 1and 2.
By means of the Hopkinson's bar bundle it is therefore possible to measure moment by moment:
- the true resisting cross-section;
- the true material volume under strain;
- the crack propagation path;
- the crack propagation speed.
These parameters allow a reconstruction of the true stress strain diagram of the material up to
complete separation of the specimen into two halves.
The Hopkinson's bar bundles were constructed using two square aluminium bars of 20 cm side
subdivided by electroerosion into 25 pairs of specular bars individually instrumented with strain
gauge stations; the two bundles have been installed in the Large Dynamic Testing Facility [7] of
the Joint Research Centre as shown in Figure 6, which generates and sends a loading pulse
linearly increasing up to a maximum of 2.5 MN into the bundle equipment for the testing of 20 cm
side cubic specimens of plain concrete with real size aggregate (25-40 rnm size).

ACKNOWLEDGEMENTS

The authors are grateful to Professor Luigi Cedolin of Milan Polytechnic for helpful discussions
and the preparation of the specimens, and to the LDTF staff of JRC (Mrs. E. Blery, A. del
Grande, C. Delzano, M. Murarotto, E. Pizzinato, G.L. Prosdocimi, A. Rodis and W. Schnabel).

REFERENCES

[I] Davies, R.M., A Critical Study of the Hopkinson Pressure Bar, Phil. Trans. Roy. Soc.,
London, Ser. A, (1948) 240-375.
[2] Lindholm, U.S., High Strain Rate Tests, Technique of Metals Research (J. Wiley, 1971),
Vol. 5, Part. 1.
[3] Kormeling, H.A., Zielinski, A.J., Reinhardt, H.W., Report No. 5-80-3, Delft University of
Technology, Stevin Laboratory (1980).
[4] Malvern, L.E., Tang, T., Jenkins, D.A., Gong, J.C., Dynamic Compressive Strength of
Cementitious Materials, Materials Research Society Symposium, (1986) Vol. 64, 119-138.
[5] Albertini, C., Montagnani, M., Testing Techniques Based on the Split Hopkinson Bar
(Institute of Physics, London, 1974) Cod. Ser. No. 21,22-31.
[6] Kolsky, H., Stress Waves in Solids (Clarendon Press, 1953) 74-75.
[7] Albertini, C., Montagnani, M., Testing Techniques in Dynamic Biaxial Loading, (Institute of
Physics, London, 1979). Conf. Ser. No. 47,2534.