Comparison of different Constitutive Models for Concrete in ABAQUS/Explicit for Missile Impact ...

44 Pages·2010·2.62 MB·English

Comparison of different Constitutive

Models for Concrete in ABAQUS/Explicit

for Missile Impact Analyses

Oliver Martin

Safety of Present Nuclear Reactors Unit (SPNR)
Plant Operation Safety (POS)

EUR 24151EN -2010
The mission of the JRC-IE is to provide support to Community policies related to both nuclear
and non-nuclear energy in order to ensure sustainable, secure and efficient energy production,
distribution and use.

European Commission
Joint Research Centre
Institute for Energy

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Address: Oliver Martin, JRC-IE, Westerduinweg 3, NL-1755LE Petten
E-mail: [email protected]
Tel.: [phone]
Fax: [phone]

SPNR/POS/10 01 002

http://ie.jrc.ec.europa.eu/
http://www.jrc.ec.europa.eu/

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JRC 56256

EUR 24151 EN
ISBN 978-92-79-14988-7
ISSN 1018-5593
DOI 10.2790/19763

Luxembourg: Office for Official Publications of the European Communities

© European Communities, 2010

Reproduction is authorised provided the source is acknowledged

Printed in The Netherlands
Content

CONTENT..............................................................................................................................................................I
1 INTRODUCTION...............................................................................................................................................1
2 MISSILE IMPACT TESTS................................................................................................................................2
2.1 Large-Scale Missile Impact Tests....................................................................................2
2.2 Small-Scale Missile Impact Tests....................................................................................3
3 TYPICAL FAILURE MODES AND ENERGY BALANCE..........................................................................4
4 FE MODELS AND CONSTITUTIVE MODELS............................................................................................6
4.1 FE Models and basic Material Properties.........................................................................6
4.2 Brittle Cracking Model for Concrete................................................................................9
4.3 Concrete Damage Plasticity Model................................................................................10
4.4 Boundary Conditions and initial Missile Velocities.......................................................12
5 RESULTS OF FE ANALYSES........................................................................................................................12
5.1 Results with Concrete Cracking Model..........................................................................12
5.2 Results with Concrete Damaged Plasticity Model.........................................................15
5.2.1 Results with hard Missile........................................................................................15
5.2.2 Results with soft Missile.........................................................................................21
6 SUMMARY AND OUTLOOK........................................................................................................................30
7 REFERENCES..................................................................................................................................................31
APPENDIX: ABAQUS INPUT FILES..............................................................................................................32
ABAQUS Input File with Brittle Cracking Model..............................................................32
ABAQUS Input File with Concrete Damage Plasticity Model............................................35

I
1 Introduction

The issue of missile impacts on concrete containment buildings (CCBs) of nuclear power
plants (NPPs) was subject to intensive research for the first time in the 1970s and early 1980s.
During that period a number of missile impact tests, even on a large scale have been carried
out, most notably the Meppen Tests in Germany and the Tests at Sandia National Laboratory
in the USA. In both tests soft and hard missiles were impacted on large reinforced concrete
slabs resembling the CCBs of NPPs build at that time. In parallel quite a number of
computational analyses have been performed to predict the results of these tests. For these
analyses either empirical formulas or relatively coarse finite difference (FD) or finite element
(FE) models even with load curves were used. Due to the limitations of these models the
possibility to predict the outcome of missile impact tests was quite difficult. Today quite a
number of advanced computational methods and methodologies are available for impact
analyses and as a result the issue of missile impact testing has reached a significant level of
interest inside the nuclear community again.

The topic of missile impacts on CCBs of NPPs was subject of a panel discussion during the
previous SMiRT20 Conference, held in Espoo, Finland in August 2009 [1]. During this panel
discussion IRSN and OECD-NEA called for the benchmark project “Improving Robustness
Assessment Methodologies for Structures impacted by Missiles (IRIS)”. The objective of this
benchmark project is to issue recommendations for the modelling of mechanical effects of
missile impacts on concrete containment structures. The benchmark project will start in
January 2010 and will have a duration of one year. It runs under the subgroup on concrete of
the IAGE. Each participating party is requested to computationally model the new missile
impact tests by VTT/IRSN (performance in first half of 2010) and some of the Meppen Tests.
The participating organisations will present and exchange their results in a workshop in
December 2010 and will issue a state-of-the-art report on the subject in 2011 based on the
results of the participants. JRC-IE will participate in the benchmark project IRIS.

This EUR report describes the first own missile impact analyses performed at JRC-IE in order
to get familiar with the topic and as a preparation for the benchmark project IRIS. The
analyses are performed with the FE solver ABAQUS/Explicit [2] and traditional Lagrangian
formulations for both the missile and reinforced concrete slabs are used. Two different build-
in constitutive models for concrete in ABAQUS/Explicit, the Brittle Cracking Model and the
Concrete Damaged Plasticity Model [2], are used and their suitability and limitations for
missile impact analyses are explored. A hard and a soft missile are used for both constitutive
models and sensitivity studies related to the initial missile velocity are performed.

Comparison of different Constitutive Models for Concrete in ABAQUS 1
2 Missile Impact Tests
2.1 Large-Scale Missile Impact Tests

As mentioned in the introduction already the Meppen Tests and the Tests at Sandia National
Laboratory represent two series of large scale missile impact tests to assess the strength of
CCB designs of NPPs against air plane crashes. The Meppen Tests were performed in the late
1970s and early 1980s near the German town of Meppen (this is where their name originates
from) by the German construction company HOCHTIEF and the German electrical &
electronics company SIEMENS to test the CCB design of German NPPs against the impact of
small military aircrafts [3,4,5]. Two series of tests were carried out. In the first tests series,
which was entirely performed by HOCHTIEF, highly deformable missiles were impacted
against rigid targets. The purpose of the first test series was to investigate the generated load
time curves [3,4,5]. In the second test series the same missiles were impacted on reinforced
concrete slabs, which resembled the concrete hull of a typical NPP build at that time. The
missiles used in the Meppen Tests were made of mild steel (mild steel St 37), had an outer
diameter of 600 mm and a total length of approximately 6 m. Thus they resembled the body of
a typical military aircraft. The wall thickness of the missile varied between 7 mm in the front
to 10 mm in the rear [3]. The reinforced concrete slabs used in the Meppen Tests were
rectangular in shape with the dimensions 6.5 m × 6 m and had a thickness from 50 mm to 90
mm. The velocities of the missiles varied from 172.2 m/s to 257.6 m/s.

The missile impact tests of Sandia National Laboratories involved small scale, intermediate
scale and full scale tests using reinforced concrete slabs of dimensions 1.5 m × 1.5 m, 2.5 m ×
2.5 m and 7 m × 7 m respectively [6]. The thicknesses of the slabs varied between 60 mm to
350 mm, 350 mm to 600 mm and 900 mm to 1600 mm respectively [6]. Test series with rigid
and deformable missiles were performed for each of the three reinforced concrete slabs. The
deformable missiles were cylindrical tubes with a diameter of 101 mm and a length of 317
mm for the small-scale tests, cylindrical tubes with a diameter of 300 mm and a length of 983
mm for the intermediate-scale tests and cylindrical tubes with a diameter of 760 mm and a
length of 2378 mm for the large-scale tests [6]. The rigid missiles were massive
steel/aluminium cylinders with a diameter of 101 mm and a length of 110 mm for the small-
scale tests. For the intermediate-scale tests cylindrically shaped steel tubes with a massive
thick front plate were used for the rigid missiles. They were 300 mm in diameter and had a
length varying between 351 mm and 498 mm. For the large-scale tests real aircraft engines,
i.e. a GE-J79 engine, were used as rigid missiles [6]. The velocities of the missiles varied
between 83 m/s and 217 m/s for the small-scale tests, 99 m/s and 251 m/s for the
intermediate-scale tests and 205 m/s and 215 m/s for the large-scale tests [6].

In summary deformable missiles representing the body of a typical military aircraft and/or
extremely stiff missiles representing the engine of an aircraft are used for large-scale missile
impact tests. They are impacted on reinforced concrete slabs with velocities, which resemble
typical velocities of aircrafts.
Comparison of different Constitutive Models for Concrete in ABAQUS 2
2.2 Small-Scale Missile Impact Tests

Normally large-scale missile impact tests are expensive to perform, so the number of these
tests performed so far is quite limited. Additionally often strike forces are the initiators of
such tests and so their results are often not publically available. Instead smaller tests on
laboratory scale are carried out. Both the reinforced concrete slab and the missile are
considerably scaled down in their dimensions. One example for these lab scale tests are the
missile impact tests by Hanchak et al. [7]. For these tests rectangular shaped reinforced
concrete slabs of the dimensions 610 mm × 610 mm × 178 mm are used. The slabs contain
three layers of steel reinforcement in thickness direction with a distance of 76.2 mm from
each other in both horizontal directions (see Figure 1). The diameter of the steel bars is 5.69
mm. Figure 2 shows the missile Hanchak et al. were using for their tests. It is a 25.4 mm
massive calibre steel projectile with an ogive nose and a total length of 143.7 mm.

Fig 1: Reinforced concrete slabs used in the missile impact tests of Hanchak et al. [7].

Fig. 2: Massive calibre steel projectile used by Hanchak et al. [7].

The tests of Hanchak et al. are typical for lab-scale missile impact tests both concerning the
dimensions of the reinforced concrete slab and also with regards to the size and material of the
missile. The computational analyses described in this report are based on the tests of Hanchak.
Additionally to the hard missile in Figure 2 also FE analyses with a soft missile are performed
(see Chapter 4).

Comparison of different Constitutive Models for Concrete in ABAQUS 3
3 Typical Failure Modes and Energy Balance

There are in principal two overall response failure modes for reinforced concrete walls or
buildings impacted by a missile: Flexural failure or punching shear failure. Both failure modes
are caused by the elastic-plastic response of the reinforced concrete structure. They are
displayed in Figure 3.

a) b)

Fig. 3: a) Flexural failure and b) punching shear failure.

At the flexural failure mode the reinforced concrete slab bends strongly due to the impact of
the missile. The front side of the reinforced concrete slab, where the missile impacted on, is
compression loaded. The back side is subject to tension loading, which leads to the formation
of cracks in thickness direction of the reinforced concrete slab. In the worst case the cracks go
through the entire thickness of the reinforced concrete slab leading eventually to complete
perforation. At the punching shear failure mode a shear cone forms inside the reinforced
concrete slab as indicated in Figure 3b. In the worst case the shear cone is punched out of the
reinforced concrete slab. In contrast to flexural failure, where the concrete slab fails due to
excessive tension stresses, at punching shear failure the concrete slab fails due to excessive
shear stresses.

The likelihood if flexural failure or punching shear failure is more likely depends upon the
kind and velocity of the missile and the strength of the reinforcement inside the concrete slab.
For a strong reinforcement flexural failure is more likely, for a weaker one punching shear
failure. In case of a soft missile flexural failure of the reinforced concrete slab is more likely
and in case of a hard missile (with an ogive nose) punching shear failure becomes more likely.
For lower impact velocities flexural failure is more likely, for high impact velocities punching
shear failure becomes more likely.

Beside the two overall response failure modes four local damage failure modes exist, which
are displayed in Figure 4. They are caused by stress wave response and usually always occur
in conjunction with the two overall response failure modes. At surface failure concrete falls
off the impacted wall or structure at and around the impact zone. The penetration depth of the
missile is low. When spalling occurs the missile penetrates deeper into the concrete wall or
structure and significantly more material falls off compared to surface failure. In case of
Comparison of different Constitutive Models for Concrete in ABAQUS 4
scabbing additionally concrete particles spall off the backside of the impacted wall or
structure. Perforation represents the worst case. The missile moves through the impacted wall
or structure. Perforation is normally always accompanied by spalling and scabbing.

a) b) c) d)

Fig. 4: Local damage failure modes: a) Surface failure, b) spalling, c) scabbing and d) perforation.

During a missile impact on a structure there is always a huge transfer of mechanical energies
involved. So in order to evaluate the results of numerical missile impact analyses correctly a
look at the energy balance should always be the first step. The missile and the concrete slab
together can be seen as one mechanical system. In the beginning before the impact there is
only the kinetic energy of the missile. While the missile impacts into the concrete structure it
is usually slowed down significantly, i.e. it looses huge portions of its kinetic energy. Most of
the lost kinetic energy is absorbed as strain energy (elastic and plastic strain energy) in the
reinforced concrete slab and in the missile. This is visible as deformation of slab and missile
after the impact. Normally also parts of the concrete slab are destroyed, so part of the kinetic
energy of the missile is transformed into damage energy. A smaller part of the kinetic energy
of the missile is transferred to the concrete slab as kinetic energy. This is visible as vibrations
of the concrete slab that typically occur as a result of a missile impact. Then normally also
part of the initial kinetic energy of the missile will dissipate due to viscous damping inside the
missile and the reinforced concrete slab. So the energy balance of a missile impact on a
concrete slab can be written as follows:

EM = EM +EM +ES +ES +ES +E , (3.1)
kin0 kin1 str1 kin1 str1 dam1 vis

with EM = kinetic energy of missile before impact
kin0
EM = kinetic energy of missile after impact
kin1
EM = strain energy of missile after impact
str1
ES = kinetic energy of concrete slab after impact
kin1
ES = strain energy of concrete slab after impact
str1
ES = energy dissipating due to damage of concrete
dam
E = energy dissipating due to viscous damping
vis

The way how the initial kinetic energy of the missile is allocated among the different forms of
energy in equation (3.1) after the impact depends upon the type of the missile (hard or soft),
its velocity and the reinforcement of the concrete slab. When e.g. a concrete structure with a
strong reinforcement is subject to an impact of a soft missile with a high velocity most of the
Comparison of different Constitutive Models for Concrete in ABAQUS 5
initial kinetic energy of the missile will end up as strain (deformation) energy of the missile.

Beside the real physical energies artificial energies might occur during a numerical analysis.
When a numerical analysis, i.e. FE analysis, is carried out where individual finite elements are
likely to be heavily distorted (deformed) so that they might end up having no volume
anymore, FE solvers usually add an artificial stiffness to these finite elements in order to
avoid excessive distortions and compression of elements. These artificial stiffnesses are
visible in the results of FE analyses as artificial energies. They are not real physical energies,
but can build-up during FE analyses to amounts comparable to real physical energies. So the
results of FE analyses where heavy distortion or compression of individual finite elements is
likely should be critically reviewed. In order to account for the artificial energies E equation
art
(3.1) has to be rewritten as

EM = EM +EM +ES +ES +ES +E +E . (3.2)
kin0 kin1 str1 kin1 str1 dam vis art

4 FE Models and Constitutive Models
4.1 FE Models and basic Material Properties

Figure 5 shows the FE model with the hard missile and Figure 6 the one with the soft missile.
The mesh for the concrete slab is the same in both cases and standard linear solid elements
(HEX8, ABAQUS elements C3D8/C3D8R, Lagrangian formulation) are used. The solid
elements have a dimension of approximately 6 mm in all three directions in space, making the
mesh of the concrete slab extremely fine.

Fig. 5: FE model with hard missile.

Comparison of different Constitutive Models for Concrete in ABAQUS 6
Fig. 6: FE model with soft missile.

The reinforcement of the concrete slab is modelled with truss elements as displayed in Figure
7 (ABAQUS elements T3D2). The truss elements are coupled with the HEX elements of the
concrete slab with the *EMBEDDED ELEMENTS function of ABAQUS [2]. With this
function the nodes of a truss element are kinematically constrained to the nodes of the solid
element in which it is located. This means that the displacement of the node of the truss
element is an average value of the displacements of the neighbouring nodes of the solid
element in which the truss element is embedded.

Fig. 7: Modelling of reinforcement in concrete slab.

Figure 8 shows the FE models of the hard and soft missile. The hard missile is modelled as a
rigid body, in order to avoid excessive simulation times caused by heavy distortion of the
elements at the projectile nose. The soft missile is modelled with standard shell elements
(ABAQUS elements S3R and S4R) with 3 mm thickness.
Comparison of different Constitutive Models for Concrete in ABAQUS 7