Download Micromechanical behaviour of concrete interpreted by

Transactions on Modelling and Simulation vol 21, © 1999 WIT Press, www.witpress.com, ISSN 1743-355X
Micromechanical behaviour of concrete
interpreted by computer simulation
systems for material structure
P. Stroeven & M. Stroeven
Delft University of Technology, Delft, The Netherlands
Email: p. stroeven@ct. tudelft. nl
m. stroeven@ct. tudelft. nl
Abstract
Interest in material structure has been raised by upgrading of cementitious systems. Computer-simulation of material structure has been
pursued so far by using random generators. Such systems were successfully applied for estimating global properties. Realistic estimation
of structure-sensitive properties, however, requires a more appropriate simulation of material structure. The SPACE system has been
developed for that purpose. It incorporates particle interaction and
gravitational influences, which are typical for the 'natural' processes
undelying the formation of material structure in the production stage.
The capabilities are discussed of the two computer-simulation methods for generating structural information relevant for either structureinsensitive, or structure-sensitive properties in bulk and in the interfacial transition zone (ITZ). The structural information will deal with
composition and configuration of the material, respectively. The use
of random generator-based (KG) systems is demonstrated not justified when dealing with structure-sensitive problems.
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1 Introduction
A growing interest in material structure is resulting from efforts to
upgrade concrete materials. Such efforts involve the addition of silica fume and other (super-)fine mineral admixtures to concrete, the
blending of cements, or the increase in the range of particle sizes of
the aggregate. A realistic structure-simulation systems would offer
insight into the relevant features of the aggregation of particulate
matter, ultimately even setting the scene for systematic optimization
of such materials. Close to the mould, material structure on mesolevel
should deviate from that in bulk. Surfaces of aggregate particles will
similarly disturb the 'natural' processes of aggregation of matter on
microlevel. Mostly, experimental approaches focus on compositional
changes in the vicinity of interfaces. Structure-sensitive properties of
the material will depend, however, on material configuration.
Insight into material configuration is therefore a pre-requisite in
understanding mechanical behaviour of such composites. This holds
in particular for the post-peak range, where the non-uniformity of the
packing is of greater significance than any regular property. In 1927,
Brandzaeg* already stated: "The process of failure must necessarily be intimately connected with the properties of small parts of the
material, in particular those small parts where failure first begins to
develop. It would seem the individual rather than the average properties of the constituent parts of the material need to be considered."
The common way to simulate particulate composites is by using so called random generator (RG) systems. This approach was
proven successful for simulating structural features relevant for global
pre-peak concrete behaviour. However, it still has to be established
whether local structural characteristics, which are relevant for structure-sensitive properties like (meso)crack initiation, or (macro)crack
concentration in the post-peak region, can be realistically simulated
as well. Since major contributions to local strength in cementitous
materials are due to van der Waals binding forces, the spacing of
neighbouring particles will be of paramount importance. Moreover,
once bond cracks have been formed at particle-matrix interfaces, the
process of coalescence which ultimately will lead to fracture, will also
be governed by (particle) spacing. So, for the estimation of such
structure-sensitive phenomena, the nearest neighbour spacing should
Transactions on Modelling and Simulation vol 21, © 1999 WIT Press, www.witpress.com, ISSN 1743-355X
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573
be realistically simulated. Since this is expected to be impossible
by RG systems, recently a dynamic simulation system, SPACE, has
been developed. The differences in output of these two systems will
be discussed on the basis of implementations for structure-insensitive
('micro-hardness') and structure-sensitive properties ('bond'). The
particulate material will be modelled for that purpose as a multisized aggregate of spherical particles.
2 Static simulation by RG
system.
The non-homogeneous, or granular, nature of the internal material
structure is represented by a set of distinct elements. Each element
corresponds to a distinguishable, characteristic phase in the material.
For example, concrete is modelled as a set of elements representing
the aggregate particles. The elements are dispersed in a presumably
homogeneous mortar matrix moulded in a container. The parameters
describing the static conditions of the internal structure are the locations, orientations, and shapes of the various individual elements.
Since the elements represent real physical phases in the material,
physical properties can be assigned to each element along with its
shape and size, at least in principle. The most difficult task, however, is the derivation of the location and the orientation of these
non-overlapping elements.
In a static simulation system, the particles will be sequentially located inside a container. Each location is governed by randomly generated coordinates. 'Overlap' with earlier generated particles will result in rejection, whereupon the generation process is continued. The
number of rejections will increase dramatically at high volume fractions, making the process of generation very time-consuming. Also,
simulation of a multi-size particle composite requires starting with
the largest particles in the mix. But maximum particle densities cannot be realized even under such conditions. The system obviously
excludes the mechanism of particle interaction, which is so characteristic for the production stage of cementitious materials. Finally, a
natural phenomenon as clustering will be under-estimated, resulting
in a biased nearest neighbour distribution of particles, as will be
demonstrated later. Three of the more popular systems in this category were developed by Roelfstra^, by Diekkamper^, and at NIST^.
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3 Dynamic simulation by SPACE system.
The SPACE system (Software Package for the Assessment of Compositional Evolution) is based on a dynamic concept of simulating
the production process of composite material, i.e., in case of concrete: mixing of aggregates and paste, or cement and water. The
details of the generation system have been published by this authors
elsewhere^. To be able to simulate effects such as clustering and
to reach high volume densities, element motion and inter-element
collision^ are modelled, leading to effective ingredient mixing. This
stage is referred to as the dynamic stage.
The general simulation concept can be described as follows:
• Initially, a structured or random 3-D dilute distribution of elements with pre-defined shape and size distribution (such as the
grading curve) is generated within the boundaries of a container.
This stage can be similar to that of a RG system. Fig. la presents
an example of the starting situation of a multi-sized 'dilute' mixture of spherical particles inside a cubic container (Vy w 0.2).
Fig. 1. Development of participate structure in SPACE system
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Next, random linear and rotational velocity vectors are assigned
to each element.
• The second step, the actual dynamic stage, is an iterative procedure where location and orientation of all elements are changed
at each time step according to a Newtonian motion model. This
motion model relates the element's linear and angular displacement to a set of conditions enforced on the element (e.g., gravity,
friction, etc.). When elements meet during this time interval, a
contact model defines the effect of contact on the motion/rotation
update. Inter-particle influences - one of the requirements for
achieving a more versatile system - are incorporated in the contact
model. Additionally, electrical or chemical inter-particle forces
may be added to the motion model. Higher densities are obtained
by a gradual reduction in the size of the container (compacting
the structure), or under the action of a gravity force.
• Finally, the iteration stops when certain conditions are reached.
As an example, Fig. Ib shows the multi-sized particle system of
Fig. la , which was compacted to its maximum density (in this
case, Vv ~ 0.72), and thereupon magnified for visual purposes.
The final distribution state can incorporate effects due to gravity
and to inter-particle influences. Simple physical laws may be used
to define the inter-particle relationships, by introducing parameters
such as specific mass and energy dissipation. High packing densities
can be obtained, representing dense random packing states, typical
of aggregate and binder particles in cementitious materials.
4 Structure-insensitive approach
The first example concerns a study of the packing density of multisized, spherical cement grains in the neighbourhood of a rigid boundary. Hence, this study deals with the compositional discontinuity
in the packing of binder particle in the so called interfacial transition zone (ITZ). The particle size distribution of Portland cement
particles is taken in accordance with the Rosin-Rammler cumulative
particle size distribution function, G(d) = 1 - exp(-W). A mixture
was simulated by both systems (RG and SPACE) representing a water to cement ratio of 0.5. Note that simulation by the RG system
of more densely packed aggregates will be very complicated. 30,000
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particles between 1 and 20 /mi were considered for parameter settings
of n= 1.003 and 6=0.0288. Total volume fraction of the cement particles is plotted as function of the distance to the interface in Fig. 2.
The extent of the discontinuity in volume fraction is slightly different for both systems. The compositional differences between the two
systems are not dramatic.
0.45
__ 0.4
^0.35
1
0-3
"So.25
• rH
|
0.2
| 0.15
^ 0.1
RG
experimental
SPACE
0.05
0
0
2
4
6
8
10
12
Distance to the interface in [fim]
14
Fig. 2. Total volume fraction changes in the ITZ of multi-sized
cement particle mixture.
A popular way to study packing density differences in the ITZ
is by microhardness measurements. If it is assumed for the present
purpose that 'hardness' is similar for all cement particles, then outcomes of microhardness tests can be associated with volume fraction
of particles^. It should be emphasized that the Knoop indentor 'averages' over its width, b in a direction perpendicular to the interface.
With the high hardness value of the aggregate particle influencing the
outcomes for small distances to the interface, r < 6/2, a through-type
of micro-hardness curve can be derived from the simulation data of
Fig. 2. Such microhardness characteristics are also reported in the lit-
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577
erature for the ITZ™. So, either one of the systems can be employed
for estimating structure-insensitive properties, such a micro-hardness.
5 Structure-sensitive approach
The particle fractions underlying Fig. 2 have been demonstrated
by Stroeven & Stroeven? to reveal a size-dependentfluctuatingbehaviour away from the interface, causing a long-range discontinuity
in grading. This will also hold for material configuration underlying
structure-sensitive problems. The volume fraction curve in Fig. 2,
which is the common way of presenting computer-simulation data,
gives as a consequence a misleading impression of structural variation relevant for structure-sensitive properties.
The most relevant configuration parameter is probably the nearest neighbour distance. This parameter allows the assessment of the
respective capabilities of the two structural simulation systems when
studying structure-sensitive properties, such as crack initiation. Initiation of cracking will be mainly at interfaces between aggregate
particles in concrete. It will be the result of stresses exceeding local
(physical) bond capacity. Van der Waals bonding forces will be governed by surface-to-surface spacing of cement particles, or of the cement particles and the aggregrate grain interface. The nearest neighbour distance is intimately related to surface spacing, so it can be
used for the present purpose. A common analytical approach in case
of finite particle sizes is to reject particle 'overlap'**. Hence, this is
the same procedure as used by RG systems. This leads to more evenly
distributed particles than met in nature, and an under-representation
of the natural process of particle 'clustering'. Conclusive evidence for
these statements can be found in different fields of science. Supporting experimental data in the field of concrete are given in Stroeven^,
in which the nearest neigbour distance distribution is derived from
quantitative image measurements in serial sections. Fig. 3 convincingly demonstrates the growing gap between the two structural simulation concepts (i.e. dynamic particle interference versus overlap
rejection) when estimating the nearest neighbour distance distribution at increasing volume densities up to only moderate values of
volume fraction.
Data confirming the capability of the SPACE system to simulate
the natural process of particle clustering is presented Fig. 4. A mix-
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• SPACE
RG (analytical)
3.1 3.2 33
3.5 3.6 3.73.8
Fig. 3. Comparison between simulations by analytical, random
generator-based approach, and by SPACE system on the basis
of the shape of the nearest neighbour distance distribution for
particulate aggregates with volume fraction of 1% and 30%.
ture of three different particle sizes (di=3, 6^=5 mm and d^—l mm)
is generated by the SPACE system for increasing total volume fractions, W, of the aggregate. A strong tendency for particle clustering
when particle density increases is reflected by the distinct peaks in the
nearest neighbour distance distribution curve for the highest density
case (35%). The peaks correspond to zero surface-to-surface spacings
of the different combinations of particle sizes. Thus, only the SPACE
system is able to simulate particle configuration in agreement with
experimental findings. Even for moderate particle densities, the RG
systems will erroneously simulate nearest neighbour spacing.
In another example, the mean free path, A, is determined for
the same mixture as used for Fig. 2. The mean free path is the average of all unobstucted distances between a particle and all of its
neighbours in an aggregate of finite size particles. This parameter
was proposed by Pullman*\ and employed by Stroeven for experimental assessment of particle packing characteristics in concrete^.
A global notion of inter-particle 'bond capacity' might be based for
the present purpose on this structural parameter. Dependence of
this approach on particle configuration is only moderate. The parameter A is selected, because it can be determined by stereological
(i.e. quantitative microscopy) measurements in sections parallel to
the interface, i.e. A - 4(1 - Vy)/Sv, in which Vy and 6y denote
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1
0.9
R=2.5mm V:
= I : 4.6 : 12.6
0.8
0.7
0.6
Vw=35%
0.5
0.4
0.3
0.2 0.1 -
0
10
12
14
16 mm
Fig. 4. Nearest neighbour distance distributions for aggregate
mixture composed of three particle sizes and a total volume content of 5, 15 and 35%, respectively.
the volume fraction and the specific surface area of the particles, respectively. The global bond capacity is taken proportional to A~^
in conformity with a van der Waals concept**. Fig. 5 presents this
normalized inter-particle bond capacity as a function of distance to
the interface. Characteristic differences between the two systems are
reflected, despite the only moderate volume density required by the
RG system.
As stated earlier, the fines concentrate near the interface^. Because of their large specific surface area, global inter-particle bond
capacity is rising steeply over thefirstpart of the curve. Random generators increase, however, the degree of inter-particle 'order', because
clustering is suppressed. This is reflected by the dramatic underrepresentation of close nearest neighbours among particles in Fig. 3,
and between particles and interface in Fig. 2. The mean free spacing
is reduced, as a result, in the zone of high particle density. Consequently, the RG system seriously under-estimates the global interparticle bond capacity in the vicinity of the interface, as depicted by
Transactions on Modelling and Simulation vol 21, © 1999 WIT Press, www.witpress.com, ISSN 1743-355X
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0.45
0.4
0.35
0.3
0.25
0.2
RG
0.15
0.1
experimental
SPACE
0.05
0
0
2
4
6
8
10
12
Distance to the interface in [|itm]
14
Fig. 5. Normalized global inter-particle bond capacity in the
ITZ, expressed by A~^, as function of the distance to the interface.
Fig. 5. Because of the same reason, the bond between particles and
interface layer will be seriously under-estimated by the RG systems
(not shown in Fig. 5). The long-range fluctuating grading characteristics with distance to the interface, presented in \ are reflected by
the post-peak curve of the SPACE system. So, even for this weakly
structure-sensitive approach, RG systems would yield biased information. Additional experimental data should be generated to further
validate this statement.
Conclusions
Computer-simulation allows for accurate assessment of compositional
parameters characterizing particulate structures in cementitious materials, either on mesolevel where aggregate grains are packed in a
container, or on microlevel where (blended) Portland cement particles are dispersed in pockets between these aggregate grains. Bulk
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properties, or discontinuities near boundaries, can be studied in this
way. Compositional parameters should be used in connection with
structure-insensitive properties, such as volume percentage of particles, or porosity. The paper shows how microhardness measurements
in the ITZ can be estimated properly, at least qualitatively, in this
way. Such compositional problem can be approached by random
generator-based systems and by the SPACE system alike.
RG-based systems generate more evenly distributed particles,
thereby under-estimating the natural phenomenon of particle clustering. Inter-particle distances are affected by the rejection mechanism
following 'overlap' during generation. The nearest neighbour distance
distribution in moderately to densely packed particulate structures
(as met in cementitious materials) simulated by RG systems, will
be significantly biased, as a result. Hence, material configuration
in such dense random packings is poorly represented by RG-based
systems. Structure-sensitive properties, like van der Waals bond between densely packed hydrated Portland cement particles, or between
such particles and the interface, can only be properly simulated by
the SPACE system.
References
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