Micro- and macroscale coefficients of friction of cementitious materials

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Micro- and macroscale coefficients of friction of cementitious materials

Gilson Lomboy a, Sriram Sundararajan b,⁎, Kejin Wang a

a Department of Civil, Construction, and Environmental Engineering, Iowa State University, Ames, IA 50011, United Statesb Department of Mechanical Engineering, Iowa State University, Ames, IA 50011, United States

a b s t r a c ta r t i c l e i n f o

Article history:Received 3 February 2012Accepted 7 August 2013

Keywords:Atomic force microscopyPortland cement [D]Fly ash [D]Granulated blast-furnace slag [D]

Millions of metric tons of cementitious materials are produced, transported and used in construction each year.The ease or difficulty of handling cementitious materials is greatly influenced by thematerial friction properties.In the present study, the coefficients of friction of cementitious materials were measured at the microscale andmacroscale. Thematerials testedwere commercially-available Portland cement, Class C fly ash, and ground gran-ulated blast furnace slag. At themicroscale, the coefficient of friction was determined from the interaction forcesbetween cementitious particles using an Atomic Force Microscope. At the macroscale, the coefficient of frictionwas determined from stresses on bulk cementitious materials under direct shear. The study indicated that themicroscale coefficient of friction ranged from 0.020 to 0.059, and the macroscale coefficient of friction rangedfrom 0.56 to 0.75. The fly ash studied had the highest microscale coefficient of friction and the lowestmacroscalecoefficient of friction.

© 2013 Elsevier Ltd. All rights reserved.

1. Introduction

Cementitious materials serve as binders for aggregates in concrete.Portland cement (PC) is the most widely used binder, while fly ash(FA) and ground granulated blast furnace slag (GGBFS), industrialby-products, are often used as supplementary cementitious materials(SCMs). Research has shown that in addition to cost reduction, theuse of SCMs in concrete can significantly improve concrete long-termstrength, permeability, and durability. Millions ofmetric tons of cemen-titious materials are produced, transported and used in constructioneach year [1–3].

Cementitious materials are transported to construction sites andbatching plants and stored in bags, barrels and silos. Pneumatic trans-port through pipe is commonly used formoving cementitiousmaterials.Like most dry powders, the ease or difficulty of handling cementitiousmaterials is greatly influenced by its friction properties [4]. Although alarge amount of cementitious materials are used each year, little isdocumented with regard to their bulk flow and storage properties.Many problems, such as bridging, ratholing, flooding or uncontrolledflow, and caking, have occurred, which negatively impact the materialproduction efficiency [5].

There is a strong correlation between the ease or difficulty of theflow of a dry powder and its macroscale coefficient of friction [6].Factors affecting macroscale coefficient of friction of a powder are theparticle characteristics of the transporting materials (such as the meanparticle size, size distribution, shape, surface texture, density), velocities

of the conveying gas or the transporting solid particles, the temperatureof conveying gas, bulk density, and the coefficient of friction of thepowder [7–9].

Different methods for measuring the above-mentioned bulk andparticle properties have been proposed, and their effects on thematerialtransport have been studied [6,9]. Research shows that wall andmaterial friction causes a pressure drop along the pipe during powdermaterial transport [10–12], and this friction can be influenced byother factors, such as particle degradation and inclination [13,14]. Theangle of repose, the measurement of the angle between the horizontaland the natural slope of a heap of the material, can give an indicationof the flowability of a material [9]. When the angle of repose of amaterial is low, it is considered ease to flow, and vice versa. For dryfine materials, a correlation exists between the angle of repose andthe bulk coefficient of friction, which was determined from a directshear test [15,16].

The coefficient of friction at the microscale is measured using anAtomic Force Microscope (AFM), which was first reported by Mateet al. [17] bymodifying an AFM tomeasure both the normal and frictionforces. Ruan and Bhushan [18] had presented calibration procedures forconverting measured data from a commercial AFM to normal andfriction forces. They had also compared microscale friction data forselected materials with Si3N4 tips with macroscale friction againstSi3N4 balls. They found that the microscale friction was significantlysmaller than macroscale friction of the tested materials. At the micro-and nanoscales, it has been observed that the frictional force measureddepends upon the contact area between the tested material and theapplied normal load. The frictional force does not vary linearly withnormal force in such situations [19]. The micro-scale friction plays avital role in understanding the flow behavior of bulk materials,

Cement and Concrete Research 54 (2013) 21–28

⁎ Corresponding author.E-mail address: [email protected] (S. Sundararajan).

0008-8846/$ – see front matter © 2013 Elsevier Ltd. All rights reserved.http://dx.doi.org/10.1016/j.cemconres.2013.08.006

Contents lists available at ScienceDirect

Cement and Concrete Research

j ourna l homepage: ht tp : / /ees .e lsev ie r .com/CEMCON/defau l t .asp


including grinding and wearing of materials, where particle contacts,plastic deformation, and micro-friction are treated separately [20,21].

The present work is to investigate the macro- and microfrictionproperties of cementitious materials in its dry or unhydrated state.The results will help further understand the flow behavior of cementi-tious materials and benefit proper transport and storage of thesematerials. The cementitious materials studied are Portland cement(PC), fly ash (FA) and ground granulated blast furnace slag (GGBFS).The macro- and microscale coefficient of friction of plain materials andbetween different materials is measured and analyzed.

2. Material and methods

The cementitious materials studied were Portland cement (PC),Class C fly ash (FA) and ground granulated blast furnace slag (GGBFS).The specific gravity [22] and fineness [23] of these cementitious mate-rials are given in Table 1. PC has the highest specific gravity amongthe materials studied, and fly ash has the lowest. The fineness of PCand GGBBS is similar, both of which higher than the fineness of fly ash.

The scanning electron microscope (SEM)micrographs of the cemen-titiousmaterials are shown in Fig. 1. PC andGGBFS have angular particlesdue to the grinding during their production, while FA has sphericalshaped particles, which are formed by fusing in suspension of exhaustgases.

2.1. Microscale friction

Dry cementitious materials flow by pneumatic transport throughpipes. It may also flow by gravity through outlets when dischargedfrom silos. At the microscale, flowing particles will collide. Collisionforce has a normal and/or tangential component. The tangential compo-nent of a collision force involves the friction forces resulting from theparticles that slide against each other. The amount of the friction force(f) is proportional on the normal force (N) and the coefficient of friction(μ) between the particles.

f ¼ μN: ð1Þ

The normal force between particles depends on the momentum ofthe particles and the weight of the particles for dense flows. The coeffi-cient of friction depends on the properties of the material contactsurfaces. To quantify the friction force, the coefficient of friction of theinterested material needs to be determined.

2.1.1. Coefficient of friction determinationThe test method introduced by Ruan and Bushan [18] using friction

force microscopy is employed to determine the coefficient of frictionbetween two cementitious materials at the microscale in the presentstudy. To measure the friction force using an AFM, the probe is lowereddown gradually until the tip comes to contact with the sample and thecantilever deflects to apply a normal force (N0) between the twocontacting materials. The normal force is given by N0 = cantileververtical deflection H0 × normal spring constant k.

The AFM is engaged in a scanningmotionwhere the probe is movedparallel to the cantilever's long axis. The cantilever deflects due to thesample surface topography and also due to the friction force betweenthe probe and the sample surface. The friction force acts in the oppositedirection of the probemotion (Fig. 2a and c). Tomaintain the deflectionof the cantilever to a given value or set-point, the AFM piezo adjusts byretracting or extending, thus decreasing or increasing the normal loadby ΔN1 or ΔN2, respectively (Fig. 2b and d). The change in normal loadis given by ΔN1 = piezo retraction ΔH1 × k or ΔN2 = piezo extensionΔH2 × k.

To calculate for the coefficient of friction (μ), it isfirst recognized thatsince the cantilever deflection in Fig. 2b and d is the same, then, thesums of the moments acting about the root of the cantilever at point Pare equal [18], i.e.

N0−ΔN1ð ÞLþ fð Þ lð Þ ¼ N0 þ ΔN2ð ÞL− fð Þ lð Þ:

The friction force can be solved as

f ¼ ΔN1 þ ΔN2ð ÞL2l

: ð2Þ

The coefficient of friction can be solved with Eq. (1) as

μ ¼ fN

¼ ΔN1 þ ΔN2ð ÞN0

L2l

: ð3Þ

L and l are the functions of the distance of the probe tip to the root ofthe cantilever Lc and the height of the tip ht, making

L ¼ Lc cosθl ¼ Lc sinθþ ht cosθ

ð4Þ

where θ is the angle between the cantilevers and the sliding surface,taken as 11°.

2.1.2. AFM probes and sample preparationTests were conducted to determine the coefficient of friction

between PC/FA and PC/FA/GGBFS. Two sets of AFM probes were pre-pared, one having cantilevers attached with a PC particle and anotherattached with a FA particle. Fig. 3a and b shows two AFM probesattached with a PC particle and a FA particle on their tips, respectively.The normal stiffness of the cantilever used ranged from 0.17 to0.39 N/m, which was determined using the reference cantilever

Table 1Specific gravity and fineness (m2/kg).

Material

PC FA GGBFS

Specific gravity 3.14 2.52 2.95Fineness (m2/kg) 452.7 419.6 455

PC FA GGBFS

Fig. 1. SEMmicrograph of cementitious powders.

22 G. Lomboy et al. / Cement and Concrete Research 54 (2013) 21–28


method proposed by Torii et al. [24]. As the probe tips are slid againstthe sample on the microscope slide, they may degrade, and the wornmaterial may transfer between the tip and the sample. Therefore, im-ages of the probes used were taken with an SEM before and after thefriction tests to check for the tip wearing or deterioration. There wasno deterioration observed in the before and after images of the tipsused. Fresh tips were used for each test to avoidmaterial contaminationdue to material transfer during testing.

Three sets of microscope slide samples were prepared, and a layer ofPC, FA and GGBFS particles was affixed on a set of the slides, respective-ly. As described in Reference [25], the PC and GGBFS were mixed withfast setting epoxy, adhered on glass slides, and then polished to makea flat surface, while FA is adhered to a glass slide with a thin film ofUV cured epoxy. The AFM scans of the sample surfaces are shown in

Fig. 4. The scan sizes were 5 × 5 μm and the average RMS roughnessis from five particles.

2.1.3. Test set-up and friction measurementTo begin the friction force measurement, the geometry of the probe

Lc and ht in Eq. (4) was first determined. Lc wasmeasured with an opti-cal microscope while ht was measured using an SEM. For the frictiontests, the probe and sample were mounted in the AFM and the AFMchamber was closed and purged with N2 gas until it had a RH ≤ 10%.The probe then was brought down to the sample until the tip contactedthe sample, as shown in Fig. 5. The zero deflection set-point and thepull-off deflection [26] was then determined. When the tip is pressedby the cantilever against the slide sample, the normal force will be thesum of the force exerted by the cantilever and the adhesion force

L

lf

N0

Sliding directionof probe

Sliding directionof probe

P

y

L

lf

N0

P

y

a) Additional deflection is caused by friction force as the probe slides in the positive y

direction

c) Additional deflection is caused by frictionforce as the probe slides in the negative y

direction

L

lf

N0 1−Δ

Pθ

L

lf Pθ

d) The effect is cancelled by extending thepiezo, thus increasing the normal force

b) The effect is cancelled by retracting thepiezo, thus reducing the normal force

N

N0 2ΔN+

Fig. 2. Schematic showing additional bending of cantilever due to friction force when the probe slides in the positive y and negative y directions and subsequent piezo adjustment tomaintain an initial cantilever deflection.

a) PC tip viewed from end of cantilever

b) FA tip viewed from top of cantilever

Fig. 3. SEM images of PC and FA particles attached to the end rectangular AFM cantilevers.

23G. Lomboy et al. / Cement and Concrete Research 54 (2013) 21–28


between the tip and the sample. The zero deflection set-point will havea normal force that is only due to adhesion. The pull-off deflection is theamount the AFM cantilever deflects before the tip of the cantileverseparates from the sample on the slide as the AFM probe is withdrawnaway from the sample. It measures the adhesive force acting between

the probe tip and the sample, which is computed from the cantileverpull-off deflection multiplied with the cantilever stiffness [25].

A line scan was then performed on the sample. The sliding distancefor the tip was 5 μm. The H0 and (ΔH1 + ΔH2) at given deflectionset-points were recorded. Five readings were recorded per deflectionset-point. H0, ΔH1 and ΔH2 were in units of volts. It was converted tonanometer with the AFM z-scan sensitivity. The deflection set-pointwas varied for an increasing normal load, from a set-point less thanzero (adhesion regime) to ~100 nN exerted by the cantilever. Fig. 6shows the increase in normal load with increasing set-point. Fig. 7shows the increase (ΔN1 + ΔN2) with increasing set-point due toincreasing normal load and friction force. It can be observed that near

a) PC, RMSave = 11.2nm b) GGBFS, RMSave =19.8nm

c) FA, RMSave =28.3nm

0.3

0.0

0.3

0.3

0.0

0.3

1.0

0.0

1.0

1.02.0

3.04.0

μm

1.02.0

3.04.0

μm

1.0

2.0

3.0

4.0μm

Fig. 4. AFM scanned image of the sample surfaces, along with RMS roughness.

Fig. 5. Schematic of set-up for friction measurement using AFM.

R² = 1.000

-10

0

10

20

30

40

50

60

70

80

-2.0 -1.0 0.0 1.0

N0

(nN

)

Set-point (V)

ΔN20

ΔSet-point

Fig. 6. Normal force due to cantilever deflection with increasing deflection set-point.



the adhesion regime, there is a non-linear increase in (ΔN1 + ΔN2).This is due to the large change in contact area at very low normalloads. To compare the results with macroscale coefficient of friction,only the linear part of the curve was used in the calculation of thecoefficient of friction.

To calculate the coefficient of friction with Eq. (3), the slope of thecurve in Fig. 6 (ΔN/Δset-point) and the slope of the curve in Fig. 7(Δ(ΔN1 + ΔN2)/Δset-point ) are used. Eq. (3) then becomes

μ ¼ fN

¼ Δ ΔN1 þ ΔN2ð ÞΔset‐point

Δset‐pointΔN0

L2l

: ð5Þ

2.2. Macroscale friction

The macroscale coefficient of friction was measured with the directshear setup shown in Fig. 8. The shear box was 100 × 100 × 50 mm.The lower half of the box moved forward at a rate of 1 mm per minute,while the upper half remained stationary. The shearing force was mea-sured with a load cell and the vertical and horizontal displacementswere measured with LVDTs. The normal load was applied through ahanger.

The samples with a total mass of 600 g were blended manually in amixing bowl with a rubber spatula until the materials were uniformlydistributed. The samples were placed in the shear box in three layers.Each layer was consolidated with a pressure of 4.1 kPa and vibratedwhile maintaining the pressure. Normal loads were applied on thesamples before shearing. The normal loads for three shear tests of asample were 6.9, 19.8 and 45.6 kPa. Displacements and shear force

readings were taken every 15 s. The shearing was stopped when thelower portion of the box had moved 12.5 mm.

The typical stress vs. displacement andheight change vs. displacementcurves are shown in Figs. 9 and 10, respectively. The trends of thecurves are typical of loosely consolidated material [27]. For the stresscurve, the stress gradually increases to an ultimate shear stress. Thedecrease in height is due to the effects of cementitious particlesrolling about and falling into voids of an initially loose arrangement.The change in sample height εhwas expressed in terms of the changein height Δh and the original height h0 of the sample. h0 was theheight after the placement of the normal stress, before the applicationof the shearing stress.

εh ¼ Δh=h0: ð6Þ

Themacroscale coefficient of friction was computed by first plottingthe ultimate shear stress τu at the displacement of 12.5 mm against itscorresponding normal stress (N) as shown in Fig. 11. The macroscalecoefficient of friction μ is the slope of the regression line along thethree points.

μ ¼ dτudN

: ð7Þ

3. Results

3.1. Microscale friction

The microscale coefficient of friction for different cementitiousmaterial combinations is given in Fig. 13. The first material in the labels

R² = 0.992

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

1.6

-2.0 -1.0 0.0 1.0

ΔN1+

ΔN2

(nN

)

Set-point (V)

Δ(ΔN1+ΔN2)

ΔSet-point

Fig. 7.Normal force changeswhenprobe is traveling parallelwith the probe long axiswithincreasing deflection set-point.

Fig. 8. Direct shear test setup of cementitious materials.

Fig. 9. Shear stress vs. displacement curve at different normal loads.



is the particle at theAFM tip and the other is the sample on the slide. Thecoefficient of friction ranges from 0.020 to 0.059. It can be observed thatcoefficient of friction involving FA is high. FA against FA has the highestcoefficient of friction among the material combinations tested. Aschematic drawing of how the surface conditions and asperities of PCand FA tips interact with PC, FA and GGBFS particles on slides isshown in Fig. 12. The surface features of the interacting particle affectsthe frictional resistance of the particle to sliding. PC and GGBFS particleson a slide were polished flat, thus had small asperities. This surfacefeature offers little resistance to sliding with a PC tip as shown inFig. 12a. In Fig. 12b, the asperities on the surface of FA particles tendto hinder sliding because of their hill-like shape, thus resulting in ahigh coefficient of friction. The additional frictional resistance wasattributed in [28] as the ratchet mechanism of friction and collision

force on the asperities. In the case of FA sliding against PC or GGBFS,Fig. 12c, the asperities of FA particles collide with the small asperitiesof PC or GGBFS causing a resistance to sliding greater than PC–PC orPC–GGBFS, but less than FA–FA.

The coefficient of friction is plotted against the pull-off force [26]between the tested materials (Fig. 14). It can be observed that thepull-off forces are significantly higher for the PC–GGBFS. The pull-offforce for the PC–GGBFS ranged from 64.2 to 161.4 nN, while the rangeof pull-off forces for the other cementitious materials was from 5.9 to40.5 nN. The pull-off force measures the adhesion force between thetested materials. This force will be present during the coefficient offriction measurement. As observed by Bhushan and Sundararajan [29],the measured coefficient of friction may be reduced due to highadhesion forces, which may result in the observed low coefficient offriction for PC–GGBFS.

3.2. Macroscale friction

The macroscale coefficient of friction for different cementitious ma-terial combinations is given in Fig. 15. The coefficient of friction rangesfrom 0.56 to 0.75. The coefficient of friction of materials containing FAis lower than the coefficient of friction of PC–PC and PC–GGBFS, withplain FA having the lowest coefficient of friction. This may be attributedto the spherical shape of FA particles. The angular shape of PC andGGBFS particles would make the particles susceptible to interlocking,while the spherical shape of FA would make the particles roll againsteach other creating less stress and resistance to shearing.

The change in height of the samples during shearing is given inFig. 16. The change in the height of PC–PC, FA–FA and FA–GGBFStends to decrease with increasing normal load, while the change inheight tends to increase with increasing normal loads for PC–GGBFSand FA–PC.

Fig. 10. Change in height vs. displacement curve at different normal loads.

0

5

10

15

20

25

30

0 10 20 30 40 50 60

She

ar S

tres

s (k

Pa)

Normal Stress (kPa)

d τu

dNN2,τu2

N3,τu3

N1,τu1

Fig. 11. Peak shear stress vs. normal stress of cementitious sample.

Fig. 12. Schematic of AFM particle tip sliding against sample on slide; a) PC–PC and PC–GGBFS, b) FA–FA, c) FA–PC and FA–GGBFS.

0.02

0

0.02

8

0.04

6

0.05

0

0.05

9

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

PC-GGBFS PC-PC PC-FA FA-GGBFS FA-FA

Coe

ffici

ent o

f Fric

tion

Fig. 13.Microscale coefficient of friction of cementitious materials.



Based on their macroscale coefficient of friction, PC will have theleast dry powder flowability, while FA would be the most flowable.Well blended FA with other cementitious materials may improve bulkmaterial handling and transportation. Other factors that may the affectpre-blending process and flow are specific gravity and fineness.

Comparing the microscale coefficient of friction obtained by AFMgiven in Fig. 13 and the macroscale coefficient of friction obtained bydirect shear of bulk cementitious material given in Fig. 15, the micro-scale coefficients of friction are an order of magnitude smaller thanthe macroscale coefficients of friction, shown in Fig. 17 with resultstabulated in Table 2. At the macroscale, contributing factors to thebulk coefficient of friction are particle interlock and the interfacialshear of sliding particles. Sliding of bulk materials occurs when particleinterlocks are overcome by material yield at the points of contact ofparticles [30]. The yield stress of a material may be approximated byits indentation hardness [31]. Nanoindentation of Portland cementphases indicates hardness values of 8–10.8 GPa [32]. Thus, for a directshear test with a normal stress of 13.1 kPa, the true contact areabetween particles may be as little as 1.2 × 10−6 of the superficial area.With the small contact areas and very low loads in the AFM microscalecoefficient of friction measurements, contact stresses do not exceedsample hardness, minimizing plastic deformation [29]. The lack ofplastic deformation greatly reduces frictional force, making the micro-scale coefficient of friction much lower than the macroscale coefficientof friction. It was shown in [29] that at contact stresses exceeding the

material hardness, the coefficient of friction increases towards valuescomparable to those of macroscale measurements.

It can also be observed that FA–FA macroscale coefficient of frictionis lower than the PC–PC macroscale coefficient of friction, while themicroscale coefficient of friction of PC–PC is lower than microscaleFA–FA. This may be attributed to the shape of the particles, where FAare spherical andwillflowmucheasierwhen sheared as a bulkmaterial.In rheology or friction of bulk materials that are modeled by particlebehavior, the microscale coefficient of friction should be used becauseparticle shape and stiffness have separate contributions to the overallmacrodeformations and stresses [33].

4. Conclusions

The microscale and macroscale coefficients of friction of cementi-tious materials were determined using atomic force microscopy anddirect shear test, respectively. The results indicate that:

(1) Atomic forcemicroscopy can be used for determining the micro-scale friction commercially available cementitious materials. Themicroscale coefficient of friction of tested cementitious materialsranges from 0.020 to 0.059. PC–GGBFS had the lowestmicroscalecoefficient of friction, while FA–FA had the highest.

(2) The microscale surface properties of cementitious materials mayaffect the microscale coefficient of friction as demonstrated bythe surface properties of FA particles. The microscale coefficientof friction of FA with other cementitious materials is higherthan the microscale coefficient of friction of cementitious mate-rials without FA.

0.00

0.01

0.02

0.03

0.04

0.05

0.06

0.07

0.08

0 25 50 75 100 125 150 175

Coe

ffici

ent o

f Fric

tion

Pull-off Force, nN

PC-PC PC-GGBFS

PC-FA FA-GGBFS

FA-FA

Fig. 14. Effect of pull-off forces on microscale coefficient of friction of cementitiousmaterials.

Fig. 15. Macroscale coefficient of friction of cementitious materials.

Fig. 16. Height changes of sheared samples at different normal loads.

Fig. 17.Micro- and macroscale coefficients of friction of cementitious materials.



(3) The macroscale coefficient of friction of tested cementitiousmaterials ranges from 0.56 to 0.75. PC–PC has the highestmacro-scale coefficient of friction and FA–FA has the lowest. Particleshape plays a significant contribution to the macroscalecoefficient of friction.

(4) The microscale coefficients of friction of tested cementitiousmaterials are lower than the macroscale coefficients of friction.When themacroscale rheology ismodeled by interacting particles,the microscale coefficient of friction should be used into the parti-cle properties because themacroscale coefficient of friction is fromthe sum of several factors such as particle shape, stiffness andinterparticle friction.

Acknowledgment

This research is sponsored by the National Science Foundation(Grant No. 0927660). The assistance from Mr. Robert Steffes in the di-rect shear test setup is greatly appreciated.

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Table 2Friction coefficients at micro- and macroscales and height changes during macroscaleshearing.

Material Coefficient offriction

Height change εh (×1000) at differentnormal loads

Micro Macro 13.1 kPa 26.0 kPa 51.8 kPa

PC–GGBFS 0.020 0.699 45.3 54.9 55.2PC–PC 0.028 0.749 64.9 54.6 47.9PC–FA 0.046 0.629 43.1 54.9 56.2FA–GGBFS 0.050 0.653 57.1 53.2 46.7FA–FA 0.059 0.559 47.4 43.4 39.5


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Micro- and macroscale coefficients of friction of cementitious materials