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10th International Conference on Fracture Mechanics of Concrete and Concrete Structures
FraMCoS-X
G. Pijaudier-Cabot, P. Grassl and C. La Borderie (Eds)
1
IMPACT RESPONSE OF UHPC AND UHPFRC: EXPERIMENTAL STUDY
AND NUMERICAL SIMULATION
C. PONTIROLI AND B. ERZAR*
* CEA, DAM, CEA-GRAMAT
F-46500 Gramat, FRANCE
e-mail: christophe.pontiroli@cea.fr
Key words: Ballistic impact, Fiber Reinforced Concrete, Modeling, Simulation
Abstract: When a projectile hits a concrete target, several specific mechanisms are activated.
Craters forms on front and rear faces of the target mainly due to shear and tensile damage. In the
vicinity of the projectile nose, the concrete material is subjected to intense pressures (several
hundreds of MPa), increasing its apparent ductility. Ultra-high performance concrete (UHPC) and
ultra-high performance fiber reinforced concrete (UHPFRC) represent new opportunities to design
protective structures. The compressive strength of these materials is commonly five times the one of
standard concrete. Compared to usual concrete, the tensile behaviour of UHPC is also different: the
composition is optimized to reduce the porosity and fibers can be included in the formulation
(UHPFRC). To study the impact response of this kind of materials, penetration tests are conducted
in Gramat on Ductal®FM targets using a steel projectile. Perforation experiments allowed
investigating the influence of steel fibers on the impact craters and exit velocities. To simulate
impact event on UHPFRC, the Pontiroli-Rouquand-Mazars (PRM) model developed in CEA-
Gramat is modified based on characterization tests performed on material specimens. Hydrostatic
loading, triaxial tests and shock experiments are done to study the compressive response of UHPC
under high confining pressures. Quasi-static bending tests and spalling experiments are useful to
investigate the tensile response and the influence of fibers on the fracture energy. This modified
version of the PRM model is used to simulate the impact response of UHPC and UHPFRC.
1 INTRODUCTION
In the last decades, the possibilities offered
by ultra-high performance concrete (UHPC)
have been exploited by engineers and
architects to design structural elements with
unusual thin shapes. These families of material
constitute interesting candidates for protective
structures or structural elements. Indeed, the
high compressive strength and the high-energy
dissipation capacity due to the presence of
steel fibers (UHPFRC) allow designing
effective protection towards blast and ballistic
threats.
Penetration tests carried out in the past 20
years have showed that increasing concrete
compressive strength resulted in decreasing
penetration depths or residual velocities of the
projectile after perforating concrete slabs [0-
0]. It was found also that adding steel fibers
was the most effective method in reducing
spalling and scabbing crater dimensions of
both impacted and rear faces of the targets [0-
0]. Twelve years ago, CEG-DGA has
conducted penetration tests on standard and
ultra-high strength concrete (Ductal-FM®)
targets using a steel penetrator [0]. For impact
velocities ranging from 250 to 450 m/s, the
penetration depths have been found to be 1.4
times less for a UHPFRC with a compressive
https://doi.org/10.21012/FC10.236361
C. Pontiroli and B. Erzar
2
strength of 200 MPa than in a standard
concrete (fc = 40 MPa). Blast experiments and
ballistic impact experiments with small-calibre
bullet and fragment simulating projectile have
been carried out on Ductal® targets by Cavill
[0]. The ability of such concrete material to be
used as protective elements has been
confirmed.
Nowadays, the CEA Gramat makes
constant efforts to develop and to validate
models describing accurately the dynamic
behaviour of concrete under extreme
conditions. The numerical simulation
represents a versatile tool to assess the damage
and the residual load capacity of a structure
subjected to blast loading or projectile impact.
However, the ability of a simulation to be
predictive is closely linked to the consistency
of the material model. The modeling approach
should to take into account the main physical
phenomena activated in dynamic conditions
and it must be identified with reliable
experimental data. This is of primary
importance in the case of high amplitude
loading under high strain rates, a specific
loading regime associated to high velocity
impact or contact detonation. Unfortunately
only few experimental data under high
pressure and high strain rates are available
today in the literature for UHPC.
In this work, the modeling approach
developed in CEA Gramat for standard
concrete is first described. Then, several
characterization experiments at the material
scale are presented as well as corresponding
calibration of PRM model for UHPC. Then,
experimental results of ballistic impacts on
Ductal are reported and compared to similar
tests carried out on a standard concrete.
Finally, numerical simulations of perforation
tests have been conducted and confronted to
experimental data.
2 PRM MODEL
2.1 Damage model
The PRM model has been developed to
simulate the behaviour of concrete under
severe loading [0]. This macroscopic model,
based on the Mazars damage model proposed
in 1984 [0], includes two scalar damage
variables Dt and Dc that give respectively the
loss of stiffness under pure tensile loading and
pure compressive loading. In this generalized
version of the damage model, t evolves
between 0 and 1 (see Equation 1):
D =
t Dt + (1-
t) Dc
(1)
The general 3D constitutive relations
relating stress and strain tensors are given by
Equation 2, where 0 and 0 are the Lamé
constants defining the initial elastic stiffness of
the material.
= (1-D)0 tr I+ 2 0 )
(2)
A problem of mesh size dependency is
often observed for damage models. In order to
limit this effect, the Hillerborg regularization
model has been included [12]. In this method,
the energy consumed by a crack to propagate
through a band of finite elements is no more
dependent of the mesh size thanks to a fixed
characteristic length Lc. In fact, the method
consists in modifying the softening part of the
stress-strain relation in order to get the same
fracture energy whatever the mesh size. To do
so, a new variable is introduced:
if ε ε (3)
if ε ε (4)
where p = t pt + (1-t) pc with pt and pc
respectively the peak strain in tension and
compression. a(Rt) is a corrective function
dependent of the dynamic increase factor Rt.
This variable is included into the damage
formula (Eq. 5) to adapt the damage kinetic,
taking into account the characteristic length Lc
of the material and the finite element
characteristic length Le:
ωω ε (5)
In the precedent relations, 0t, 0c, At, Ac, Bt
and Bc are material parameters and the
equivalent strain is defined by Eq. 6. In this
relation, Xi corresponds to the positive
principal strain components.
ε ²
(6) ( (6)
First A. Author, Second B. Author and Third C. Coauthor
3
As proposed by Hillerborg [12], the
characteristic length Lc is assumed to be
directly linked to the fracture energy Gf and
the static tensile strength ft of the considered
material:
(7)
For compressive loading at high strain-
rates, no dynamic increase factor has been
considered because the apparent increase of
compressive strength is certainly due to
inertial auto-confinement or non-homogeneous
lateral deformation of concrete specimens
during dynamic compressive tests [0], [0], [0].
2.2 Strain-rate sensitivity of tensile strength
For dynamic regime, one has to take into
account the strain-rate sensitivity of concrete.
Indeed, the ultimate tensile stress reached by
concrete at 100 s-1 is usually 4 to 5 times
higher than its quasi-static strength [18].
Authors are agreed to consider this effect like
an intrinsic material phenomena. This aspect
of the behaviour is accounted for by replacing
the parameter d0t (initial deformation for
damage in tension) by its dynamic equivalent
d0t computed thanks to the dynamic increase
factor Rt :
Rt
d0t / 0t = 1 + at
(8)
This power model has already been
identified for standard concrete using quasi-
static direct tension experiments and spalling
tests conducted with a Hopkinson bar device
[18], and with ultra-high strain-rate uniaxial
deformation tests carried out with a pulsed
power generator named GEPI [19]. The strain-
rate sensitivity of UHPC and UHPFRC has
been investigated with the same devices.
Experimental results are showed on Figure 1.
No differences are observed between concrete
with or without fibers. Tensile strength
depends essentially on cement paste
behaviour. The main difference lies in the
post-peak tensile behaviour. The comparison
of the velocity profiles during spalling tests for
UHPC and UHPFRC (with 2% steel fibers
volume) allows to identify clearly the
influence of fibers: the presence of fibers
induces additional residual strength and the
residual velocity for this specimen is below the
signal measured for a UHPC specimen which
appears more brittle (see Figure 2).
Figure 1: Strain rate effects on the dynamic tensile
strength obtained on dried concrete and mortar, and
on UHPC with and without fibers
Figure 2 : Typical signals of spalling tests conducted
on a UHPC and a UHPFRC specimens
2.3 Fibers influence on tensile behaviour
Besides the compressive strength, the main
difference between standard concrete and
UHPFRC lies in the post-peak tensile behavior
(see Figure 2). Indeed, the presence of fibers
offers a pronounced ductility to UHPFRC.
Disseminated in the microstructure, steel fibers
play a major role during the fracture process,
bridging the cracks and retaining fragments.
To model their influence, the fracture energy
due to fibers has been introduced directly in
the evolution of the tensile damage variable
Dt, depending on Lf the fiber length and on the
volume fraction of fibers Vf actually
participating into the resistance to crack
1.0
10.0
100.0
1.E-07 1.E-05 1.E-03 1.E-01 1.E+01 1.E+03 1.E+05
Tensile strength (MPa)
Strain rate (1/s)
UHPFRC
UHPC
Dry concrete (R30A7)
Dry mortar (MR30A7)
0
5
10
15
20
25
30
35
40
3.E-06 4.E-06 5.E-06 6.E-06 7.E-06 8.E-06 9.E-06 1.E-05
Velocity (m/s)
Time (s)
UHPC (no fibre)
UHPFRC
C. Pontiroli and B. Erzar
4
opening. We can rewrite equations (3) and (4)
by:
if ε ε (9)
if ε ε (10)
where a(Rt, Vf) and b(Vf) are functions
dependent of the dynamic increase factor Rt
and of the volume fraction of fibers Vf.
2.4 Plasticity and compaction modelling
The PRM damage model is efficient to
simulate the dynamic response of concrete
under very low confinement. However, an
elastic-plastic model is more appropriate for
simulating the impact of a steel projectile in a
concrete slab at about 300 m/s. Indeed, in this
case, pressure level of several hundreds of
MPa can be observed in the vicinity of the
projectile nose. Specific phenomena such as
pore collapse or increase of shear strength
have to be considered to model accurately the
dynamic response of concrete.
To do so, the PRM damage model has been
coupled with a simple plasticity model
proposed by Krieg, Swenson and Taylor [20],
[21].
On the one hand, in this elastic-plastic
model, a parabolic relation describes the
pressure-dependency of the yield stress q:
(11)
where p is the pressure and a0, a1 and a2 are
material parameters. q is the yield stress in the
sense of Von Mises plasticity:
(12)
being the deviatoric stress tensor defined as
. The increase of q with pressure can
be limited by a saturation value qmax. This is
particularly important for standard concrete
which presents a saturation value linked to its
water saturation level [22], [23].
On the other hand, the pore-collapse
phenomenon occurring at high pressure is
described by a piecewise-linear compaction
curve. The elastic behaviour becomes more
and more non-linear up to the full
consolidation of concrete: at this point, the
pore collapse phenomenon is achieved and the
material is considered fully compacted.
To identified PRM material parameters,
two kinds of experiments have been carried
out on the UHPC with the load cell of CEA
Gramat (Figure 3a). The first test is dedicated
to the determination of the compaction curve:
a hydrostatic experiment is conducted by
increasing the fluid pressure pf in the load cell
(Figure 3b). This test has been used to identify
the response of UHPC (pressure vs volumetric
strain) up to nearly 1 GPa (Figure 4a). It
should be noted that at 900 MPa, only 6% of
volumetric strain is observed. This value, very
low in comparison to a standard concrete, is
the consequence of the optimization of the
composition to fill the pores at every scale.
The second type of experiment is the
triaxial test. It begins with a hydrostatic
loading due to fluid pressure. Then, an axial
loading is applied to increase the deviatoric
stress in the concrete specimen. Four tests with
increasing fluid pressure of pf = 200, 300, 400
and 600 MPa have been conducted. The Figure
4b presents the results through q-p plot where
the stress difference q and the average stress p
are defined by:
fz pq
(1)
fz pp 2
3
1
(2)
where z is the axial compression stress
amplitude, counted as positive. It can be
pointed out that q corresponds to the
equivalent stress defined by Von Mises and
Tresca in this particular case.
First A. Author, Second B. Author and Third C. Coauthor
5
Figure 3. (a) High capacity load cell in CEA Gramat
and (b) experiments in confined compression conducted
on UHPC specimens.
(a)
(b)
Figure 4. Compaction curve of UHPC (without steel
fibers) obtained through a purely hydrostatic test (a),
and shear failure from different triaxial tests (b)
Even if the data gathered in the quasi-static
experimental configuration are necessary to
assess the pressure dependency of the
deviatoric strength, the characterization is
limited to pressures lower than 1 GPa.
However, the stress level reached locally in a
concrete target near an explosive charge or in
front of a penetrating fragment may be notably
higher. Consequently, the dataset has been
completed in the shock regime response up to
6 GPa by means of plate impact experiments
[24].
These plasticity and compaction models are
complementary to the PRM damage model.
The fully coupled PRM model includes all
these mechanisms with a perfect continuity
between the compressive damage definition
and the plasticity model. It has been
implemented in a classical finite elements code
(Abaqus/Explicit [25]) through a VUMAT
subroutine. This choice allows conducting
numerical simulations from the material scale
up to the structural response.
3 PERFORATION EXPERIMENTS
To translate the experimental results from
the material scale to the structure scale,
perforation tests have been performed at CEA-
Gramat on UHPC and UHPRFC concrete
(Ductal®FM with a compressive strength of
180-200 MPa). A 98 mm caliber gas gun has
been used for impact tests (Figure 5).
Figure 5. Gas launcher
The conical nose projectile has a total
length of 240 mm and 40 mm in diameter. The
total mass is 1.6 kg. The body is made of high
strength steel 35NCD16. The targets were 150
cm squared slabs of concrete. The thickness
was either 10 and 30 cm. As concrete is a
highly fibered material (2% steel fiber volume
ratio), no additional rebar was needed, only
single rebar were added closest to the target
C. Pontiroli and B. Erzar
6
boundaries. The experiments considered
different impact velocities and angles of
obliquity 0°, 15 and 30°. Yaw and pitch angles
have been verified to be negligible.
Figure 6 shows projectile and experiment
configuration for impact tests.
Table 1Table 2 give perforation results in
terms of exit velocity function on impact
velocity, obliquity angle and concrete
thickness. Fibers affect exit velocities
especially for thick slabs. Figure 7 allows
comparing crater dimensions on the front face
with or without fiber. Brittle fracture mode can
be observed on concrete without fiber while
with fiber cratering is driven by ductile
behaviour.
Figure 6. Projectile and experiment configuration
Table 1 : Experimental results for 10 cm in thickness
Obliquity
angle
0
15°
30°
Concrete
no
fiber
fiber
no
fiber
fiber
no
fiber
fiber
Vimpact
(m/s)
320
331,5
300
321,7
331,2
345
Vexit
(m/s)
236
238
215
204
234
226,5
Table 2 : Experimental results for 30 cm thickness
Obliquity
angle
0
30°
Concrete
no
fiber
fiber
no
fiber
fiber
Vimpact
(m/s)
700
702/703
716
702/704
Vexit
(m/s)
-
368/357
364
168/136
Figure 7 : Cratering with or without fiber
4. NUMERICAL SIMULATIONS
The capabilities of the PRM model have
been analyzed with ABAQUS/explicit code
(v2018) by the restitution of experiments
conducted on projectile perforation in concrete
structures.
We have used 3D solid finite elements and
the projectile has been assumed to behave as a
rigid body (no deformation has been observed
on projectile after experimental tests and we
neglect slight erosion induced on the projectile
nose). For concrete without fiber, PRM model
has been used. For UHPFRC two modeling
approaches have been tested:
a macroscopic approach using PRM
model by considering an homogenized
material,
a mesoscopic approach with a separate
discrete modeling for cement paste and
fiber. 3D solid finite elements are used
for mortar and steel fibers are
introduced in volumic model using
embedded two-node beam finite
elements.
Some technical problems and limitations
with Abaqus/Explicit have obligated to used
mesoscopic approach only for perforation
target with 10 cm in thickness. Furthermore, to
reduce finite element model size only the
projectile penetration zone is modeling with
this approach (a cylindrical zone with 30 cm in
diameter and 10 cm in thickness). From the
fiber content Vf and the geometrical properties
of both the steel fiber Lf and concrete
specimen, a cloud of fibers is generated using
uniform random distribution. Single segments
are sufficient for generating straight fibers.
Due to the cast and target thickness, fiber
orientation is not random but has a bias
First A. Author, Second B. Author and Third C. Coauthor
7
towards a preferential direction parallel to the
target surface. For target with 10 cm in
thickness, algorithm code has generated about
1.8 millions beam elements for modeling steel
fibers. About 7 millions 3D finite elements are
used to discretize concrete material.
PRM model is chosen for plain concrete
and a one-dimensional elastoplastic
constitutive model is using for steel fiber.
Using embedded method for steel fiber, a
perfect adherence is assumed with concrete 3D
finite element.
Figure 8 : FE model of UHPFRC target under impact
Perforation simulations have been
performed with Abaqus/Explicit code.
Comparisons between experimental and
numerical results are presented in Table 3
andTable 4 in terms of exit velocities obtained
for 10 and 30 cm thickness targets. As said
previously, mesoscopic approach could be
only applied for thin wall.
For concrete with 10 cm in thickness, a
good correlation has been obtained between
experimental tests and the two numerical
approaches proposed in this study. Figure 9
shows numerical damage on front and rear
UHPC target faces during projectile
perforation simulation.
The most significant difference between
numerical and experimental result is observed
for the incident impact on thick UHPFRC slab.
Further investigations and mesoscopic
simulations had to be performed to understand
this gap.
Table 3 : Experimental/numerical comparisons for 10
cm in thickness
Obliquity
angle
0
15°
30°
Concrete
no
fiber
fiber
no
fiber
fiber
no
fiber
fiber
Vimpact
(m/s)
320
331,5
300
321,7
331,2
345
Vexitexp
(m/s)
236
238
215
204
234
226,5
Macro.
Vexitnum
(m/s)
232
230
213
218
240
228
Meso.
Vexitnum
(m/s)
-
227
-
217
-
229
Table 4 : Experimental/numerical comparisons for 30
cm thickness
Obliquity
angle
0
30°
Concrete
no
fiber
fiber
no
fiber
fiber
Vimpact
(m/s)
700
702/703
716
702/704
Vexitexp
(m/s)
-
368/357
364
168/136
Macro.
Vexitnum
(m/s)
350
324
346
241
(a) (b)
Figure 9 : Front (a) and rear (b) UHPC target faces
during penetration obtained by numerical simulation
Damage patterns can be also assessed and
C. Pontiroli and B. Erzar
8
compared with experimental results. Figure 10
and Figure 11 compare experimental cracks
zones and numerical damage patterns for
normal incidence perforation and with an
obliquity angle of 30° for impact on UHPC
target. Crater dimensions due to scabbing
spalling phenomena on front and rear faces of
concrete slabs are similar between
experimental and numerical results. PRM
model is able to reproduce correctly the brittle
behaviour of plain concrete.
(a)
(b)
Figure 10 : Comparison of damage pattern on front (a)
and rear (b) faces for UHPC normal perforation with
320 m/s impact velocity
(a)
(b)
Figure 11 : Comparison of damage pattern on front (a)
and rear (b) faces for UHPC perforation with AOI = 30°
and 331.2 m/s impact velocity
Figure 12 shows comparisons between
experimental and, macroscopic and
mesoscopic numerical approaches for
UHPFRC normal incidence perforation.
Numerical simulations using PRM model with
homogenized behaviour (concrete + steel
fibers) or using separate discretization of steel
fibers and cement paste give together similar
damage pattern compare to experimental
facies. Numerical model can reproduce
correctly the ductility behaviour of UHPFRC
due to steel fibers presence.
(a) (b)
(c) (d)
(e) (f)
Figure 12 : Comparison of damage pattern on front (a),
(c), (e) and rear (b), (d), (f) faces for UHPFRC normal
perforation with 331.5 m/s impact velocity – using
macroscopic approach (c), (d) and mesocospic approach
(e), (f)
Figure 13 give comparison between
experiment and simulation of bridge effect due
to fibers. Fibers prevent the crack opening on
cement paste. Erosion method is used on
numerical simulations to remove 3D finite
elements with large deformations which could
be slowed down or sometimes stopped
calculation.
First A. Author, Second B. Author and Third C. Coauthor
9
(a) (b)
Figure 13 : Experimental (a) and numerical (b)
comparison of fiber effect to bridge cracks
12 CONCLUSIONS
The design of new protective structures
exposed to blast loads or high velocity impact
using UHPFRC can be undertaken through
numerical simulations. However, the
constitutive and damage models have to be
accurate and validated with reliable data. Thus,
considering the relatively recent knowledge
concerning mechanical response of this class
of materials, extensive mechanical
characterization is still necessary.
In this work, quasi-static and dynamic
mechanical tests have been conducted on
UHPC and UHPFRC to identify the main
characteristics of the UHPFRC response in
tension and in confined compression. Then, a
new material parameters dataset has been
calibrated for fully coupled PRM model. This
sophisticated concrete model consists in a
phenomenological modeling approach
including the main mechanisms activated
under high strain rate and high confining
pressure, coupling damage to plasticity and
compaction. The influence of steel fibers
disseminated in the concrete has been included
in the model: the damage kinetic has been
modified to improve the description of the
fiber influence on the dynamic tensile fracture
of UHPFRC.
The modeling approach has been validated
step by step using characterization data. The
final evaluation of the PRM model consists in
simulating perforation problems in UHPC and
UHPFRC targets. Two numerical approaches
for modeling cement paste and steel fibers
have been proposed, one using the
macroscopic and homogenized PRM model,
the other using a discrete representation of
fibers independently of cement paste material.
Projectile residual velocities and damage
patterns in the concrete block allowed
comparing qualitatively the numerical
predictions with experimental results. First
perforation simulations show the capacities of
the two numerical methods to reproduce the
UHPC brittle and the UHPFRC ductile
behaviours. Further works and others
numerical comparisons with experimental
tests, as closest detonation near UHPFRC
slabs, had to be continued to validate and
improve PRM model.
ACKNOWLEDGEMENTS
This work was supported by DGA (French
General Delegation for Armament, Ministry of
Defence). The authors are also grateful to P.
Forquin (3SR Laboratory, Grenoble Alpes
University, France) for his technical
contribution to this project.
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