The Rheology of Fiber-Reinforced Cement Paste Evaluated by a Parallel Plate Rheometer

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1 The Rheology of Fiber-Reinforced Cement Paste Evaluated by a Parallel Plate Rheometer Katherine G. Kuder, Nilufer Ozyurt, Bin Mu and S. P. Shah Center for Advanced Cement-Based Materials, Northwestern University, USA Abstract Fibers are often used as reinforcement in cementitious materials because they can improve hardened state properties, including strength, ductility and durability. However, fibers often make cementitious materials difficult to work with in the fresh state, which can compromise the hardened state properties. Rheological parameters can be used to describe these fresh state properties. By developing a better understanding of the rheology of fiber-reinforced cementitious materials, fibers can be incorporated more efficiently, so that the mechanical performance of the hardened materials is not adversely affected, and the material can be handled with ease in the fresh state. In this study, a parallel plate rheometer was designed and built to study stiff fiber-reinforced cementitious materials. Initially, yield stress and viscosity measurements from the parallel plate rheometer were verified to ensure that the rheometer yielded reasonable results. Next, the effect of steel fibers on the rheology of neat cement paste was studied. At the low fiber volumes tested, 1% and 2%, by volume, increasing fiber content caused a decrease in yield stress and did not affect viscosity. In this paper, the properties of the new parallel plate rheometer, the verification process and experimental work on fiberreinforced cement pastes are described and discussed. 1. Introduction Rheology is the study of the deformation and flow of materials under stress [1]. The first comprehensive investigation of the rheology of cementitious materials might be attributed to Tattersall and Banfill [2]. They found that the rheological behavior of cementitious materials can be modeled by simple constitutive equations. Several equations have been proposed to describe the flow behavior of cement-based materials. The most common of these is the Bingham equation, and is given as: τ = τ + µ γ (1) where, τ is the shear stress applied to the material, τ is the Bingham yield stress, µ is Bingham plastic viscosity and γ is the shear strain rate. Yield stress is typically defined as the force required to initiate flow and viscosity is the resistance to flow. Figure 1 shows the typical shear stress versus time behavior for a cementitious material being sheared at a constant shear rate. Both a peak and equilibrium stress are observed due to the KUDER, The Rheology of Fiber-Reinforced, 1/1 Fax: (847)

2 thixotropic nature of the material. Under a constant shear rate there is a reversible timedependent decrease in viscosity, which can be explained by the microstructural breakdown of the material [3]. Once the shear stress is removed, the microstructure rebuilds. Currently, measuring protocols are either based on the peak stress value, τ peak, or the equilibrium stress value, τ equilibrium [4]. Shear stress Peak value, τ peak Equilibrium value, τ equilibrium Time Figure 1. Peak and equilibrium values of shear stress at a constant shear rate. Rheometers are used to measure the yield stress and viscosity of cementitous materials. A variety of rheometer types exist due to the wide range of materials being tested - cement paste, mortar and concrete, with varying compositions including fibers, mineral additives and admixtures and aggregates. Depending on the stiffness, maximum particle size, fiber length and solid particle concentration of the material being tested, different rheometers are appropriate. Rheometers can be classified as either commercial rheometers, such as Haake, or as custom-designed and built rheometers, including the BML and CEMAGREF-IMG (coaxial type configuration) [, 6], BTRHEOM and a parallel plate configuration developed at the University of Illinois Urbana-Champaign [7, 8, 9] or IBB and Two-point [1, 11, 12]. Researchers have studied the rheology of cementitious materials, using a variety of rheometers, measuring protocols and materials. Unfortunately, the results from the different studies are not quantitatively comparable, although qualitative relationships can usually be found. Rheometer types, measuring protocols and materials all influence the results obtained. Plug flow, slip and sedimentation are problems often encountered with rheometers and can significantly influence rheological measurements. The extent to which these problems occur depends on the rheometer configuration used. Shear history also significantly affects the experimental results, due to the thixotropy of cement-based systems. Therefore, mixing and measuring protocols should be identical if repeatable test results are to be obtained. In this study, a parallel plate rheometer is designed and built, specifically for stiff fiberreinforced cementitious materials. Problems typically encountered in rheological testing, including plug flow, slip and maximum particle size limitations, were considered and their effects minimized. After the rheometer was built, tests were conducted to verify that it provided reasonable results. Then, the effect of steel fibers on the rheology of the stiff cement pastes was studied. 2. Rheometer design and verification A parallel plate configuration was selected as the most appropriate to test stiff cementitious materials, with and without fiber reinforcement. With this configuration, the shear rate varies KUDER, The Rheology of Fiber-Reinforced, 2/2 Fax: (847)

3 along both the radius and the gap of the plates, reducing the occurrence of plug flow. Square grooves were machined onto the two plate surfaces to minimize slip. A motor with a high torque capacity was used, to enable the testing of stiff materials. The gap between the two plates can be adjusted based on the maximum particle size, offering greater design flexibility. A wall was included to prevent the material from flowing away. This wall will affect the rheological measurements. To reduce the effect of the wall, a large diameter to gap ratio was used, which, theoretically, means that a linear distribution of the shear rate along the gap direction can be obtained. 2.1 Rheometer design. Without a wall, the shear rate, γ (s -1 ), between the two plates, is a function of the radius, r (m), and gap height, h (m):. rω γ = (2) h where ω is the rotation of the top plate (rad/s). For a Bingham material, this relationship can be described as a function of rheometer geometry, rotations speed and torque: T 3 R = τ + ( ω) µ (3) h πr 3 where T is the resistant torque (N*m) and R is the radius of the plates (m) [13]. If a cylindrical wall is attached to the stationary bottom plate, it will be remain static during the test. From a microscopic viewpoint, there will be an interfacial layer between the wall and the measured material. Various authors have proposed the following model to describe this phenomenon [14]: τ = τ, i + η vg (4) where τ is the shear stress (Pa), τ,i is the interfacial yield stress (Pa), η is the interfacial viscous constant (Pa*s/m) and v g the sliding velocity (m/s). Then, the total torque required should be a summation of the resistant torque by the measured material, which is the same as Equation (2), and the resistant torque by the cylindrical wall (v g is assumed to be linearly distributed along the gap).: 2 T 3h 3 R 2η h = ( τ + τ,i ) + ( ω )( µ + ) () 2 3 R 4 h R πr 3 From the torque - rotation relationship, the Bingham parameters, τ and µ can be obtained, if the boundary conditions of the wall are known. Equation () suggests that the wall effect is more significant as the gap height increases. Figure 2 shows the newly designed and built parallel plate rheometer. The two steel plates have a diameter of 24 mm with square grooves measuring 6.3 mm x 6.3 mm x 2.4 mm. The gap is adjustable and is much smaller than the diameter. The maximum shear rate is approximately s -1 and the maximum torque is around 2 N*m. KUDER, The Rheology of Fiber-Reinforced, 3/3 Fax: (847)

4 R h X Top plate Bottom plate Z ω ωr Y (c) Figure 2. The parallel plate rheometer designed for the study rheometer plates and wall c) velocity distributions. 2.2 Rheometer verification To demonstrate that the parallel plate rheometer worked properly, yield stress and viscosity measurements were verified. Initially, this verification was to be done by comparing the parallel plate rheometer measurements to the results from a commercial rheometer, a Haake Rheostress 1, using the concentric cylinder configuration. Neat cement pastes, with water/cement ratios (w/c) =.3 and.3, were tested with both rheometers using the equilibrium method discussed previously. The results, however, were not comparable, with the parallel plate rheometer providing yield stress and viscosity values that were significantly higher than the results obtained by the Haake rheometer. It is suspected that this discrepancy is due to the problems of plug flow and slip that are often encountered when using the concentric cylinder geometry [1, 16]. The vane geometry, shown in Figure 3, was selected for the Haake rheometer since it eliminates slip and plug flow [13, 17, 18]. Saak et al compared yield stress values obtained using the concentric cylinder geometry and the vane [16]. For identical cement pastes, a % increase in yield stress values was observed due to the elimination of slip and plug flow. With the vane, only a thin layer of unknown thickness, is sheared. Consequently, only rotation rates are known, not shear rates. For this reason, the vane can only be used to measure yield stress, not viscosity. KUDER, The Rheology of Fiber-Reinforced, 4/4 Fax: (847)

5 Applied Rotational Speed D=11 mm L L=16 (16 mm) Figure 3. Vane configuration. Verification of the newly-built parallel plate rheometer was accomplished by comparing yield stress measurements of the neat cement paste obtained by the parallel plate rheometer, the Haake rheometer, with the vane configuration, and the experimental values reported in the literature. Due to the aforementioned problems of plug flow and slip typically encountered with commercial rheometers using the concentric cylinder geometry, verification of neat cement paste viscosity either with the Haake rheometer, or with the literature, was not possible. Instead, viscosity measurements were verified using a known-viscosity oil with the parallel plate rheometer Yield stress verification The same materials and the mixing procedure were used for both the parallel plate and the Haake rheometer. Samples were mixed in a Hobart mixer. LaFarge Type I cement was used. The mixing procedure was as follows: First, the cement was placed in the mixing bowl. Water was added, followed by a 3 second rest. Next, the material was mixed for 3 seconds on the lowest speed. Then, the mixer was stopped and there was a 3 second rest, during which the bowl was scraped to collect any undistributed material. Finally, the material was mixed for 1 minute at the medium speed. Three gap heights were tested, to observe the effect of the wall. Equation predicts a linear increase in yield stress as the gap height is increased. However, a linear increase was not observed. Instead, yield stress values remained approximately constant with increasing gap height. This observation is discussed further in Section 3.2. Yield stress measurements using the vane configuration were obtained by rotating the vane at a number of extremely slow rotational speeds and observing the shear stress as a function of time for each. At very slow rotational speeds, the shear stress increased at a slow rate and the time until the peak shear stress was reached was long. Conversely, at higher rotational speeds, the shear stress increased more rapidly and the peak shear stress was reached sooner. At slower rotation rates, the rebuilding of the network was dominant. In other words, the network was able withstand higher shear strain because it had enough time to rebuild and reorient. At higher rotational rates, the structural breakdown of the material dominated because the microstructure did not have enough time to rebuild. The minimum peak yield stress was defined as the true yield stress of the material, since it is at this rotation rate that neither the rebuilding nor the structural breakdown of the material were dominant. The vane configuration provided both the peak and the equilibrium yield stress values for each rotation rate. KUDER, The Rheology of Fiber-Reinforced, / Fax: (847)

6 Figure 4 presents the results from the vane tests. For w/c =.3, a peak yield stress plateau of 18 Pa was found, indicating that, at the rotation rates tested, the rebuilding and reorientation process did not dominate. For w/c =.3, a peak yield stress of 13 Pa was obtained. After the peak yield stress is reached for each rotation rate, the shear stress approaches an equilibrium value. For the neat paste with a w/c =.3, presented in Figure 4a, the equilibrium values are different for each rotational speeds. This difference may be because the breakdown and rebuilding processes are coupled and are functions of rotation rates, or shear rates. For the neat paste with w/c =.3, shown in Figure 4b, the equilibrium value is approximately the same for each rotation rate tested. Shear stress (Pa) /s.2 1/s. 1/s.1 1/s.1 1/s.3 1/s Peak yield plateau Shear stress (Pa) Peak yield stress.1 1/s. 1/s.1 1/s.1 1/s.3 1/s equlibrium yield stress Time (s) equilibrium yield stress Time (s) Figure 4. Shear stress versus time for a vane rheometer w/c=.3, w/c=.3. The parallel plate rheometer can be used to obtain either equilibrium or peak shear stress values. Equilibrium shear stress values were obtained using the measuring procedure shown in Figure. This measuring protocol was similar to the one proposed by Geiker et. al [4]. At each shear rate, torque measurements were recorded at,1, 1 and 2 seconds. The torque at each shear rate was then obtained by averaging the values at 1, 1 and 2 seconds, which corresponds to the equilibrium region. To ensure that a steady-state condition was reached, the data from the highest rotation rate was neglected. Torque and rotation speed were converted to shear stress and shear rate. The equilibrium yield stress was determined from the resultant shear stress versus shear rate data for the slowest two shear rates, since the yield stress corresponds to the shear stress at a shear rate of zero. In addition, peak yield stress values were obtained by shearing the material at a low shear rate, approximately 1 s -1, and recording the maximum torque reached. This peak torque value was converted to shear stress and was considered as the peak shear stress. Since the current parallel plate configuration does not include a data acquisition system, obtaining peak yield stress values at varying rotation rates, as was done with the vane configuration, was too cumbersome. The intention is only to give an indication of the range of yield stress values that may be expected from the parallel plate rheometer for a given material, so that comparisons with the vane configuration may be made. KUDER, The Rheology of Fiber-Reinforced, 6/6 Fax: (847)

7 Shear rate (1/s) s 4s Measuring time (s) Figure. Measuring protocol for parallel plate rheometer. A comparison of the yield stresses measured with the parallel plate rheometer (peak and equilibrium) and the vane (peak), and by the other researchers (peak and equilibrium) is presented in Figure 6. Yield stress values from other researchers represent the range reported in literature, demonstrating the influence of varying materials, rheometer geometries and measuring procedures on rheological findings. Despite the large range seen, the results obtained by the parallel plate rheometer are comparable. Yield stress (Pa) Literature (19) (2,21) Roy & Asaga (28) Asaga & Roy (29) our study (22) Jones & Taylor (3) Present Work Vane Parallel plate Saak (19) Others Vane (peak) Vane (equilibrium) Parallel plate (peak) Parallel plate (equilibrium) Yield stress (Pa) Literature Ivanov (23) & Zacharieva (32) our study Banfill (24)(31) (2,21) Roy & Asaga (28) Asaga & Roy (29) (24) Banfill (31) (22) Jones & Taylor (3) Vane our study Present Work our study Parallel plate Others Vane (peak) Vane Parallel plate Parallel plate (equilibrium) (peak) (equilibrium) Figure 6. A comparison between the yield stresses by the parallel plate rheometer and other research w/c=.3 w/c= Viscosity verification Viscosity measurements obtained using the parallel plate rheometer were verified with a standardized known-viscosity oil (Cannon N1 viscosity standard: 66 Pa*s at 2 o C). The measuring protocol used was the same as described in Section Three gap heights were tested. The results are presented in Figure 7. As predicted, the viscosity increases with increasing gap height, due to the wall effect. Based on Equation, a second order polynomial curve is fit to the data. By obtaining the viscosity at a gap height of zero, the wall effect is theoretically eliminated. Experimentally, the value of the polynomial curve at a gap height of zero, minimizes the effect of the wall. Here, the polynomial curve fits the data well and predicts a viscosity of 62 Pa*s, with an error of only 6%. KUDER, The Rheology of Fiber-Reinforced, 7/7 Fax: (847)

8 3 Viscosity (Pa*s) µ = 197,83.33h known viscosity = 66 Pa*s Gap height, h, (m) Figure 7. Minimization of wall effect by polynomial curve fitting. 3. Rheology of neat and fiber-reinforced cement pastes Once the parallel plate rheometer measurements were verified, the rheology of neat cement paste and fiber-reinforced cement paste was studied. To begin, a testing procedure that yielded consistent results with reasonable variation was developed with the neat paste. Then, the effect of the volume of steel fibers on the rheology of neat cement paste was studied. The measuring protocol described in Section 2 was used to obtain torque values at the prescribed rotation speeds. These values were converted to shear stress and shear rate. Shear stress was plotted as a function of shear rate to obtain the Bingham parameters. The Bingham yield stress was determined by the method presented in Section The Bingham viscosity was calculated from all of the data points, except for the highest shear rate, which is not included to ensure that a steady-state condition has been reached, as discussed previously. Type I cement was used. Short steel fibers, with a length of 6 mm and a diameter of.16 mm, were provided by Bekaert. Two w/c,.3 and.3, with two fiber volume ratios, 1% and 2%, were studied. 3.1 Sample preparation without vibration (neat cement paste) The mixing procedure was the same as described in Section 2. After mixing, the fresh cement paste was put into the rheometer with a scraper and then leveled by hand. Three gap heights were considered and two repetitions were made for each gap height. Figures 8 and 9 show the yield stresses and viscosities for w/c =.3 and.3, respectively. Large variations were found for both parameters. Due to the stiffness of the matrices, the surface of the fresh cement paste was uneven, making it difficult to ensure that the top rheometer plate came in complete contact with the material. In addition, differences in void contents from sample to sample might have been large. To investigate the significance of these factors, and to try to reduce measurement variations, the testing procedure was modified. KUDER, The Rheology of Fiber-Reinforced, 8/8 Fax: (847)

9 Yield stress (Pa) Viscosity (Pa*s) Gap,h, (m) Gap, h, (m) Figure 8. Neat paste (w/c=.3) without vibration yield stress viscosity. Yield stress (Pa) Viscosity (Pa*s) Gap,h, (m) Gap, h, (m) Figure 9. Neat paste (w/c=.3) without vibration yield stress viscosity. 3.2 Sample preparation with 1-second vibration plus normal compression (neat and fiber-reinforced cement pastes) Experimental variations were reduced by employing a new mixing procedure and compacting the material. The new mixing procedure was as follows: First, the cement and fibers (if applicable) were placed in a Hobart mixer and mixed for 1 minute at the low speed. Next, water was added and the material mixed for 1 minute at the low speed and then there was a 3 second rest. Finally, the materials were mixed for 2 minutes at the high speed. This procedure was selected because it was found to disperse the fibers well. After mixing, the fresh sample was poured into the rheometer container, consisting of the bottom stationary plate and the wall. A 1-second vibration was applied with a normal compression force of 2.36 kg applied on the top of the sample to make the surface more smooth and the sample more dense. Three gap heights were tested and three replications were made for each height. Figures 1 and 11 present the yield stresses and viscosities for neat cement pastes with w/c =.3 and.3. Compared with Figures 8 and 9, where no compaction was used, the variation is KUDER, The Rheology of Fiber-Reinforced, 9/9 Fax: (847)

10 significantly decreased, suggesting that repeatability can be improved by making the matrix surface more smooth and the material more consistent. de Larrard also uses a previbration before conducting tests with the BTRHEOM, another parallel plate configuration [2]. This testing procedure was used for the rest of the rheology measurements. Yield stress (Pa) Polynomial fit Viscosity (Pa*s) Polynomial fit Gap, h, (m) Gap, h, (m) Figure 1. Neat paste (w/c=.3) with 1 s vibration plus compression yield stress viscosity. Yield stress (Pa) Polynomial fit Viscosity (Pa*s) Polynomial fit Gap, h, (m) Gap, h, (m) Figure 11. Neat paste (w/c=.3) with 1 s vibration plus compression yield stress viscosity. The effect of the wall height on the Bingham parameters is seen in Figures 1 and 11. As predicted by Equation, the larger the gap, the more the influence of the wall on the viscosity. However, the gap height does not significantly affect the yield stress. One possible explanation for this phenomenon is due to the fact that the yield stress is the stress required to initiate flow. Since no movement has yet occurred, the friction effect caused by the wall may be small. Other researchers have also reported a change in viscosity with increasing wall height, but no effect on the yield stress [8, 2]. KUDER, The Rheology of Fiber-Reinforced, 1/1 Fax: (847)

11 Figure 12 shows the effect of steel fiber volume on the yield stress and viscosity of neat pastes with w/c =.3 and.3, respectively. The yield stresses for both neat pastes are similar, while the viscosities are much different. This result might imply that viscosity is more sensitive to the w/c than the yield stress, at least when using the equilibrium shear stress values. For peak shear stress measurements, the yield stress is sensitive to the w/c, as was shown in Figure (vane method). Figure 12 also shows that the yield stress decreases with increasing fiber volume, while the viscosity is not significantly affected Yield stress (Pa) Fiber volume, V f, (%) Viscosity (Pa*s) Fiber Volume, V f, (%) Figure 12. A comparison of the rheology between the neat paste and fiber-reinforced paste: yield stress viscosity. Generally, it is expected that adding fibers will increase the yield stress and viscosity of cementitious materials. However, little research has been done on the rheology of fiberreinforced cementitious materials and most of the work has been done on concrete or mortar, not on cement paste. The stiffness of the steel fibers might explain the observed decrease in yield stress and the unaffected viscosity. These fibers might increase the amount structural breakdown that occurs during mixing, thus reducing the yield stress of the material. However, once flow is initiated, the thickness of the matrix layer will influence the viscosity. According to Bui and colleagues, the lubricating matrix layer of cementitious materials decreases with increasing fiber volume [26]. When the shear thinning and lubricating effect are coupled, the viscosities become unchanged with the increase of the fiber volume ratio. In addition, it is possible that a critical fiber volume ratio exists, after which the rheological parameters will increase with increasing fiber volume ratio, and that this fiber volume ratio was not yet reached in these experiments. Future work will include increasing the fiber volume of the steel fiber-reinforced neat paste to see if a critical fiber volume exists. Polypropylene fiber-reinforced paste will also be tested to see the effect of a different fiber type on the rheological parameters. 4. Conclusion KUDER, The Rheology of Fiber-Reinforced, 11/11 Fax: (847)

12 The rheology of neat cement pastes and fiber-reinforced cement pastes was investigated using a newly-designed and built parallel plate rheometer. From the study, the following conclusions can be drawn: The parallel plate rheometer provides reasonable yield stress and viscosity measurements. High variations in yield stress and viscosity measurements are seen when vibration is not applied, due to the uneven surfaces of the samples and the differing void contents. Repeatability can be improved by applying vibration with normal compression to the sample before testing. Both neat cement paste and fiber-reinforced cement paste follow the Bingham constitutive equation. Yield stress does not appear to be affected by the wall height. However, viscosity does increase with increasing wall height. Polynomial curve fitting can be used to minimize the influence of the wall. Viscosity is more sensitive to the w/c than the yield stress, when the equilibrium shear stress is used. However, with the peak shear stress measurements, the yield stress is sensitive to the w/c. For the steel fibers investigated, the yield stress decreases with increasing fiber content (at the V f tested), while the viscosity is almost unchanged with the increase of the fiber volume ratio. This observation may be explained by the shear thinning effect of the cement paste reinforced with stiff steel fibers and the lubricating effect of cement paste around fibers.. References 1. Mindess, S., Young, J.F., Concrete, (Prentice-Hall, Inc., Englewood Cliffs, NJ, 1981). 2. Tattersall, G. H. and Banfill, P. F. G., The Rheology of Fresh Concrete, (Pitman, London, 1983). 3. Hackley, V.A., Ferraris, C.F., Guide to rheological nomenclature: measurements in ceramic particulate systems, NIST Special Publication 946, US. Department of Commerce, (21). 4. Geiker, M. R., Brandl, M., Thrane, L. N., Bager, D. H., and Wallevik, O., The Effect of Measuring Procedure on the Apparent Rheological Properties of Self-Compacting Concrete, Cement and Concrete Research, 32 (22) Wallevik O. H. and Gjorv, O. E., Development of Coaxial Cylinder Viscometer for Fresh Concrete, Properties of Concrete, Proceeding of the RILEM Colloquium, Chapman & Hall, Hanover, 199, Coussor, P., Rheologie des boues et laves torrentielles Etudes de dispersions et suspensions concentrees, These de doctorat de l institut National Polytechnique de Grenoble, et Etudes du Cemagref, serie Montagne n, 418, de Larrard, F., Hu, C., Sedran, T., Szitkar, J. C., Joly, M., Claux, F., and Derkx, F., A New Rheometer for Soft-to-Fluid Fresh Concrete, ACI Materials Journal, 94 (3) (1997) Hu, C., de Larrard, Dedran, T., Boulay, C., Bosc, F., and Deflorenne, F., Validation of BTRHEOM, the New Rheometer for Soft-to-fluid Concrete, Materials and Structures, 29 (1996) Struble, L. J., Puri, U., and Ji, X., Concrete Rheometer, Advances in Cement Research, 13 (2) (21) KUDER, The Rheology of Fiber-Reinforced, 12/12 Fax: (847)

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