Image Anal Stereol 2000;19:85-90Original Research Paper

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ASSESSMENT OF PARTICLE PACKING CHARACTERISTICS ATINTERFACES BY SPACE SYSTEM

PIET STROEVEN AND MARTIJN STROEVEN

Faculty of Civil Engineering and Geosciences, Stevinweg 1, 2600 GA, Delft, Netherlands(Accepted April 19, 2000)

ABSTRACT

Interest in material structure has been raised by upgrading of cementitious systems. Computer-simulation ofmaterial structure has been pursued so far by using random generators. Such systems were successfullyapplied for estimating global properties. Realistic estimation of structure-sensitive properties, howeverrequires a more appropriate simulation of material structure. The SPACE (Software Package for theAssessment of Compositional Evolution) system has been developed for that purpose. It incorporatesparticle interaction and gravitational influences, which are typical for the ‘natural’ processes underlying theformation of material structure in the production stage. The capabilities are discussed of the two computer-simulation methods for generating structural information relevant for either structure-insensitive, orstructure-sensitive properties in bulk and in the interfacial transition zone (ITZ). The structural informationwill deal with composition and configuration of the material, respectively. The use of random generator-based (RG) systems is demonstrated not justified when dealing with structure-sensitive problems.

Keywords: bond, computer simulation, interface, particle packing, random generator, SPACE system.

INTRODUCTION

A growing interest in material structure isresulting from efforts to upgrade concrete materials.Such efforts involve the addition of silica fume andother (super-)fine mineral admixtures to concrete, theblending of cements, or the increase in the range ofparticle sizes .of the aggregate. A realistic structure-simulation system would offer insight into therelevant features of the aggregation of particulatematter, ultimately even setting the scene forsystematic optimization of such materials. Close tothe mould, material structure on mesolevel shoulddeviate from that in bulk. Surfaces of aggregateparticles will similarly disturb the ‘natural’ processesof aggregation of matter on microlevel. Mostly,experimental approaches focus on compositionalchanges in the vicinity of interfaces. Structure-sensitive properties of the material will depend,however, on material configuration.

Insight into material configuration is therefore apre-requisite in understanding mechanical behaviourof such composites. This holds in particular for thepost-peak range, where the non-uniformity of thepacking is of greater significance than any regularproperty. The common way to simulate particulatecomposites is by using so called random generator(RG) systems. This approach was proven successful

for simulating structural features relevant for globalpre-peak concrete behaviour. Since major contributionsto local strength in cementitous materials are due tovan der Waals binding forces, the spacing ofneighbouring particles will be of paramountimportance. Moreover, once bond cracks have beenformed at particle-matrix interfaces, the process ofcoalescence which ultimately will lead to fracture,will also be governed by (particle) spacing. So, forthe estimation of such structure-sensitive phenomena,the nearest neighbour spacing should be realisticallysimulated. The differences in output of such a ‘classical’approach and one by the recently developed ‘dynamic’SPACE (Software Package for the Assessment ofCompositional Evolution) system pursued in this paper

COMPUTER SIMULATION OFGRANULAR MATERIALS

The granular material structure is represented inboth computer simulation approaches by a set ofdistinct elements. Each element corresponds to adistinguishable, characteristic phase in the material.For example, concrete is modelled as a set ofelements representing the aggregate particles. Theelements are dispersed in a presumably homogeneousmortar matrix moulded in a container. The parameters

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describing the static conditions of the internalstructure are the locations, orientations, and shapes ofthe various individual elements. Since the elementsrepresent real physical phases in the material,physical properties can be assigned to each elementalong with its shape and size, at least in principle.The most difficult task, however, is the derivation ofthe location and the orientation of these non-overlapping elements.

In a static simulation system, the particles aresequentially located inside a container. Each locationis governed by randomly generated coordinates.‘Overlap’ with earlier generated particles will resultin rejection, whereupon the generation process iscontinued. The number of rejections will alreadyincrease dramatically at moderate volume fractions,making the process of generation very time-consuming. Also, simulation of a multi-size particlecomposite requires starting with the largest particlesin the mix. But maximum particle densities met inconcrete technology (volume contents of 70% orhigher) cannot be realized even under suchconditions. The system obviously excludes themechanism of particle interaction, which is socharacteristic for the production stage of cementitiousmaterials. Three of the more popular systems in thiscategory were developed by Roelfstra (1989), byDiekkamper (1984), and by Bentz et al. (1993).

The SPACE system is based on a dynamicconcept of simulating the production process of acomposite material; i.e., in case of concrete: mixingof aggregates and paste, or cement and water. Thedetails of the generation system have been publishedby the Stroeven and Stroeven (1996). To be able tosimulate effects such as clustering and to reach highvolume densities, element motion and inter-elementcollision are modelled, leading to effective ingredientmixing. This stage is referred to as the dynamic stage.The final distribution state can incorporate effects dueto gravity and to inter-particle influences. Simplephysical laws may be used to define the inter-particlerelationships, by introducing parameters such asspecific mass and energy dissipation. High packingdensities can be obtained, representing dense randompacking states, typical of aggregate and binderparticles in cementitious materials.

ESTIMATION OF MATERIALBEHAVIOUR

The first illustrative example concerns a study ofthe packing density of multi-sized, spherical cement

grains in the neighbourhood of a rigid boundary.Hence, this study deals with the compositionaldiscontinnity in the packing of binder particle in theso called interfacial transition zone (ITZ). Such datacould underly estimates of structucre-insensitiveproperties. The particle size distribution of Portlandcement particles is taken in accordance with theRosin-Rammler cumulative particle size distributionfunction, G(d) = 1 – exp(– bdn). A mixture wassimulated by both systems (RG and SPACE)representing a water to cement ratio of 0.5. Resultsdemonstrated clearly that the compositionaldifferences between the two systems were notdramatic. 30,000 particles between 1 and 20 µm wereconsidered for parameter settings of n = 1.003 andb = 0.0288. Fig. 1 shows an additional simulation at awater to cement ratios of 0.17 by SPACE. Simulationby the RG system of such densely packed cementgrains systems would be very complicated. Totalvolume fraction of the 1-20 µm cement particles isplotted as function of the distance to the interface.

A popular way to study effects of packing densitydifferences in the ITZ on mechanical properties is bymicrohardness measurements. If it is assumed for thepresent purpose that ‘hardness’ is similar for allcement particles, then outcomes of microhardnesstests can be associated with volume fraction ofparticles. It should be emphasized that the Knoopindentor yields an average value over its width, b, ina direction perpendicular to the interface. With thehigh hardness value of the aggregate particleinfluencing the outcomes for small distances to theinterface, r ≤ b/2, a through-type of micro-hardnesscurve can be derived from both sets of simulationdata of Fig. 1. Such microhardness characteristics arereported in the relevant literature (e.g. Wang, 1988).Generalizing, either one of the systems can beemployed for estimating structure-insensitiveproperties, such a micro-hardness. It must be obvious,though, that the averaging character of theexperimental data on microhardness will lead tobiased (too large) estimates for the thickness of theITZ. In comparing simulation results andexperimental data it should be recognized, moreover,that experimental measurements performed on a setof serial sections will always be biased (too large).When µ is the average measured thickness of theITZ, and t the real thickness, it can easily be seen that

1·sin 2t /µ α π−= = . Here, 2α is the angle at theparticle's center under which the circular sectionplane can be viewed. This holds for a practical rangeof aggregate grain sizes, whereby t !" d (d = grain

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size). Finally, it should be noted that a conventionalcement will contain a measurable quantity of 80 µmgrains, while the example of Fig. 1 is limited to the 1-20 µm range. When all those factors are considered,it could be concluded that experimental observationsof the ITZ's thickness would satisfactorily match thesimulated ones, which are solely based on the socalled packing phenomenon. Of course, estimates andexperiments should focus on properties of similarstructure-sensitivity.

The particle fractions underlying the total volumecurve in Fig. 1 reveal a typical size-dependentbehaviour away from the interface, causing a long-range discontinuity in grading. The fines concentratenear the interface. They govern primarily the steepincrease in total volume of particles near theinterface. The fraction of the largest particles has itspeak in volume density at a distance correlated withparticle size. With a higher water to cement ratio - as

in the present case - this distance is close to theaverage particle radius, but for the lower water tocement ratios used in high performace concretes, thisdistance increases: particles seem to be pushedfurther inwards (Stroeven, 1999). So, when thethickness of the ITZ is based on gradinghomogeneity, it will significantly exceed that basedon composition. The same will hold for thehomogeneity in medium structure-sensitive propertiesdepending on grading. This is visualized in Fig. 2,where the mean free path λ, as introduced by Fullman(1953), is used. The plotted parameter, λ-3, can beinterpreted as proportional to an overal bondingcapacity relying on van der Waals forces (Wittmann,1971). Characteristic differences between the twosystems were visualized at lower w/c ratios, but theRG systems fail in simulating interface packingsituations in such high performance concrete mixes.

Fig. l. Changes in volume fraction of distinct size ranges and in total volume fraction of cement particles in theITZ in concrete.

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Fig. 2. Normalized global inter-particle bond capacity in the ITZ, expressed by λ-3, as function of the distanceto the interface. Dashed lines indicate size range of particles. For w/c = 0.17 the ITZ extends to 20 µm,approximately.

Fig. 3. Nearest neighbour distance distributions for aggregate mixture composed of three particle sizes and atotal volume content of 5, 15 and 35%, respectively.

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The most relevant configuration parameter isprobably the nearest neighbour distance. Thisparameter allows the assessment of the respectivecapabilities of the two structural simulation systemswhen studying structure-sensitive properties likecrack initiation. Initiation of cracking will be mainlyat interfaces between aggregate particles in concrete.It will be the result of stresses exceeding local(physical) bond capacity. Van der Waals bondingforces will be governed by surface-to-surface spacingof cement particles, or of the cement particles and theaggregrate grain interface. The nearest neighbourdistance is intimately related to surface spacing, so itcan be used for the present purpose. The rejection ofparticle ‘overlap’ leads in the RG-based simulationsto more evenly distributed particles than met innature, inevitably revealing a natural phenomenon asparticle clustering to be suppressed. Conclusiveevidence for these statements Fig. 3 in Stroeven andStroeven (1996) convincingly demonstrates the fastlygrowing gap between the two structural simulationconcepts in estimating the nearest neighbour distancedistribution at increasing volume densities. Dataconfirming the capability of the SPACE system tosimulate the natural process of particle clustering ispresented Fig. 3. A mixture of three different particlesizes (d1 = 3, d2 = 5 mm and d3 = 7 mm) is generatedby the SPACE system for increasing total volumefractions, VV, of the aggregate. A strong tendency forparticle clustering when particle density increases isreflected by the distinct peaks in the nearestneighbour distance distribution curve for the highestdensity case (35%). The peaks correspond to zerosurface-to-surface spacings of the differentcombinations of particle sizes. The proper way in whichthe SPACE system realistically generates small nearestneighbour distances (thereby revealing particleclustering) is a prerequisite for developing reliablyestimates for structure-sensitive properties (such asinterparticle bond and aggregate-cement bonding).

CONCLUSIONS

Computer-simulation allows for accurateassessment of compositional parameters characterizingparticulate structures in cementitious materials, eitheron mesolevel where aggregate grains are packed in acontainer, or on microlevel where (blended) Portlandcement particles are dispersed in pockets between theseaggregate grains. Bulk properties, or discontinuitiesnear boundaries, can be studied in this way.Compositional parameters such as volume percentageof particles, or porosity should be used in connection

with structure-insensitive properties. The paperindicates that microhardness properties in the ITZcould be estimated properly, at least qualitatively, inthis way. Such compositional problem can beapproached by random generator-based systems andby the SPACE system alike.

RG-based systems generate more evenlydistributed particles, thereby under-estimating thenatural phenomenon of particle clustering. Thenearest neighbour distance distribution in moderatelyto densely packed particulate structures (as met incementitious materials) simulated by RG systems,will be significantly biased, as a result. Hence,material configuration in such dense randompackings will be poorly represented by RG-basedsimulation data. Structure-sensitive properties basedon particle packing, like van der Waals bond betweendensely packed hydrated Portland cement particles, orbetween such particles and the interface, can beexpected only properly simulated on the basis ofSPACE-generated particulate structures.

A preliminary report of some of the data waspresented at the Xth International Congress forStereology, Melbourne, Australia, 1-4 November1999.

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