Example of an amplitude (strain or stress) oscillation test (test performed with Rheometer AR2000Ex from TA Instruments equipped with Vane geometry).
The stress growth procedure consists of the application of a very low shear rate in the range of 10
−3 s
−1–10
−2 s
−1, depending on the rheometer sensitivity. In fact, the yield stress corresponds to the minimum stress required to initiate flow. Theoretically, it corresponds to the shear stress at rest, i.e., for a shear rate equal to 0. Since rheometers cannot apply a shear rate of zero, this shear rate must be as low as possible. The correct measurement of the yield stress consists of the application of a strong pre-shearing phase, followed by a sufficient resting time to allow the structure to be rebuilt
[23][31][32][33][34][23,33,34,35,36]. Then, a very low shear rate in the range of 10
−3 s
−1–10
−2 s
−1 is applied to the cement paste during a sufficient time to reach the steady state flow. This time has to be greater than the characteristic time of flocculation, which is of the order of 10 s
[23]. Vane geometry appears to be the most suitable for such a test.
3. Rheological Behavior of Cement Paste
3.1. Flow Behavior
The cementitious suspensions generally display a shear-thinning behavior with a continuous decrease in viscosity with the shear rate. This behavior, characteristic of flocculated suspensions, describes the deflocculation under shearing. For simplification, the rheological behavior of cement paste is often assimilated to a Binghamian behavior under certain conditions. In addition, cement pastes (without dispersant) exhibit a yield stress that has to be overcome to initiate flow. Viscoplastic models such as the Herschel–Bulkley model or Bingham model seem to be relevant and are widely used to describe the flow behavior of cement pastes. The flow curve obtained by a stress (or shear rate) sweep is fitted with such models to determine the dynamic yield stress at a very low shear rate.
The effect of several parameters such as the properties of cement, water-to-cement ratio (w/c), admixtures, and supplementary cementitious materials (SCMs) on the flow behavior has been widely studied
[15][23][35][36][37][38][39][40][41][42][15,23,32,39,40,41,42,43,44,45]. The effect of w/c on rheological parameters can be described by the dependence on the solid volume fraction through the Krieger–Dougherty law for viscosity
[43][46] or yield stress
[44][47] or by the yield stress model (YODEL) developed by Flatt and Bowen
[45][48]. The effect of admixtures (especially superplasticizers) and SCMs has been the subject of a large number of publications.
Although it is often assumed, by simplification, that cement pastes behave like a Bingham fluid, it turns out that many experimental results reveal behaviors marked by nonlinear flow curves, especially with shear-thinning behavior. However, cement pastes can also display a shear-thickening behavior, particularly in the presence of superplasticizers and/or certain mineral additions
[15][46][47][15,49,50]. The shear-thickening behavior refers to the abrupt or continuous increase in viscosity with the shear rate.
By carrying out dynamic simulations, Bossis and Brady
[48][51] proposed a mechanism based on particle clustering to explain the shear thickening. The cluster formation results from the lubrication forces. In a suspension with short-range repulsive interparticle forces (electro-steric effect; Brownian motion) such as cement paste with a superplasticizer, the cluster formation could be avoided, especially at low or moderate shear rates. With an increasing shear rate, the hydrodynamic forces increase until their intensity exceeds that of the repulsive forces, thus inducing the formation of particle clusters.
Another mechanism based on the order–disorder transition has been proposed to explain the shear thickening
[15][49][50][51][15,52,53,54]. According to this theory, the shear-thickening behavior would be the consequence of the transition from a layered flow, where the particles are ordered in successive layers, to a locally disordered state, where the particles are dislodged from the layer structure. In fact, the hydrodynamic forces cause this instability, which breaks up the layered flow. This local instability induces particle jamming, which probably involves cluster formation, leading to an increase in viscosity.
3.2. Linear Visco-Elastic Domain
The linear visco-elastic domain (LVED) can be determined by oscillation rheology. In this domain, the storage and loss moduli remain constant. Generally, fresh cement pastes (without a superplasticizer) exhibit a solid-like behavior in this domain with a storage modulus greater than the loss modulus (G′ > G″). The end of this domain is associated with a shear strain of the order of 10
−2%. This shear strain can be attributed to the breakage of the links between particles due to early hydrates nucleation
[23] and/or the attractive colloidal forces
[28][35][29,32]. It has to be kept in mind that this critical strain remains identical from fresh cement paste to hardened cement paste
[28][29].
The effect of several factors (w/c ratio, SP dosage, SCMs …) on the LVED of fresh cement paste has been investigated, but the number of studies remains relatively limited
[17][19][26][28][52][53][17,19,27,29,55,56]. Recently, an interesting study dealing with the effect of the w/c ratio and superplasticizer (SP) on the viscoelastic properties of fresh cement pastes has been carried out
[17].
Furthermore, it appears that the critical strain at the end of the LVED is strongly affected by the superplasticizer dosage, while the effect of the w/c ratio is less significant. Only a high w/c ratio leads to an increase in this critical strain
[17]. The effect of the SP dosage thus appears to be more significant than that of the w/c ratio (
Figure 46). The interpretation of this phenomenon remains complex, and some ambiguities remain in the literature. First, the critical strain at the end of the LVED is attributed to the breakage of C-S-H bridges between cement particles
[17][23][17,23].
Figure 46.
Effect of water-to-cement ratio (w/c) and superplasticizer dosage on the critical strain (data from [17]).
Concerning the effect of w/c on the critical strain, Jiao and De Schutter
[17] explain it by the increase in the dissolution rate, leading to the increase in early hydrates formation. In addition, these early hydrates could be more fragile when w/c increases. The effect of the superplasticizer on the critical strain is explained by the entanglement of superplasticizer molecules with each other and the possible enhancement of the C-S-H bridges.
3.3. Structural Build-Up
The term thixotropy reflects the fact that the rheological properties (viscosity) are time-dependent. Thixotropic materials thus become more fluid with an increasing shear time (at a constant shear rate) or more viscous when kept at rest. Therefore, the viscosity of thixotropic material gradually increases with the resting time (build-up), and when it is sheared, it must recover its initial state (break-down). Thixotropy therefore assumes that the evolution of rheological properties over time is reversible. Thus, the application of a shear makes it possible to erase the history of the structuration at rest. This reversible phenomenon is often attributed to reversible physico-chemical phenomena such as flocculation/deflocculation in colloidal suspensions
[23].
The term “thixotropy” is often used for cementitious materials to describe the reversible evolution at the macroscopic scale, e.g., the maintenance of workability
[33][41][54][55][35,44,63,64]. However, due to cement hydration, the initial state cannot be completely recovered. This is referred to as workability loss (or slump loss). In fact, during the low-activity period of cement hydration, also called the dormant period, chemical changes occur in the cementitious material, leading to the formation of hydrates bridges between cement particles
[23].
Various testing procedures and approaches have been reported in the literature. The first procedure, called the hysteresis loop, consists of applying an increasing and decreasing shear rate. The area between the ascending and descending curve is an indicator of the thixotropy. This method can be used as a preliminary attempt to assess the thixotropy
[56][57][65,66]. In fact, the hysteresis area depends not only on time but also on shear history (shear rate, test condition, step duration). The most common test consists of the measurement of the static yield stress (using the stress growth procedure) after different resting periods
[20][21][58][59][20,21,67,68].
4. Conclusions
The non-linearity of flow behavior corresponds to a shear-thinning/shear-thickening phenomenon that can be represented by the Herschel–Bulkley model. If the shear-thinning phenomenon can be related to the flocculation state, the origins of shear thickening are not clearly elucidated. Theories based on order–disorder transition, particle clustering, or viscous/inertial regime transition have been developed to explain the appearance of shear thickening.
Furthermore, oscillation rheology allows for determining the linear viscoelastic domain (LVED) in which both storage and loss moduli remain constant. The end of this linear domain is associated with a critical strain of the order of 10
−2%. This critical strain could be the signature of the breakage of interparticle bonds formed by early hydrates (C-S-H) and/or attractive colloidal forces, especially for cements with supplementary cementitious materials (SCMs) and alternative cements such as calcium sulfoaluminates cements or belite ye’elimite ferrite (BYF) cements.