Introduction

Rheology can be defined as the science that studies the flow and deformation of materials, but it can also be approached as the relationship between deformations and the application of forces in liquid, solid and multiphase materials, describing the behavior of these materials with regard to the storage and dissipation of deformation energy, in other words, the relationship between their elastic and viscous behavior (Mezger, 2014; Ghasemi, 2019).

For cement-based materials, some of their properties in the hardened state are known to be related to their properties in the fresh state. A good example of this fact is adhesive mortars, where the adhesion capacity (bond strength) is related to the viscosity in the fresh state (Modler, 2017; Roussel et al., 2010).

In addition, according to Romano et al. (2021), fresh-state properties analyzed using rheometry techniques can directly influence the usability conditions of cementitious materials, such as transport, application and workability, which are fundamental for the development of properties in the hardened state. The authors therefore advocate the rheological analysis of cementitious materials as a tool for predicting the final properties of these materials.

According to Miranda et al. (2023), knowledge of the rheological properties of cementitious systems still has important uncertainties, such as those relating to the static and dynamic yield stress values, as well as the dependence of the aforementioned properties on time, i.e. the evolution of cement hydration processes. The authors point out that there is a need for discussion on these issues, despite the fact that a large number of studies deal with the relationship between hydration reactions in cementitious systems and the rheological transformations of these materials.

Therefore, the study of the rheology of cement-based materials from two complementary dimensions is essential for the development of the field. First of all, there is a relationship between the properties of the fresh state, assessed using rheometry techniques, and the properties of the hardened state, which are the intended properties of this type of material. In parallel with these studies, we can mention that the relationship between rheological properties and cement hydration phenomena affects the possibility of transporting and applying the materials and, therefore, their properties in the hardened state.

Understanding the consolidation processes of cement-based materials can therefore broaden the application possibilities of these materials, reducing problems related to pathologies such as cracking, peeling and efflorescence, as mentioned in Cardoso, Pileggi and John (2005), when the authors advocate the study of the fresh state properties of mortars. Dai et a.l (2022) studied the rheology of alcali activated slag cement (AASC) through oscilatory rheometry. The authors argue that AASC can be an alternative to the ordinary Portland Cement. However, the new material must have compatible characteristics since the first moments of mixing. Therefore, properties such as initial workability and the hardening process must be analyzed in order to make the best use of the material.

Betioli et al. (2009a, 2009b) state that the polymers EVA and HMEC are widely used in mortars and other cement-based systems to improve properties in both the fresh and hardened states, thus justifying the importance of studying these materials as part of cement-based systems. The authors of the papers sought to evaluate each of the polymers in relation to their chemical and physical actions as part of these systems.

Betioli et al. (2012) state that the use of EVA in cementitious materials interferes with the hydration process by prolonging the induction period and reducing the reactivity rates of the cement. The authors conclude that the significant changes in the cement pastes modified by the use of EVA can be attributed to physical effects, as the polymer had minor effects on hydration during the period studied.

Betioli et al. (2009b) argues that the effects of the HMEC polymer on cement hydration are only partially understood, with studies showing that the effect on the viscosity of the aqueous phase retaining water in the system tends to make the induction and consolidation periods longer. The work reinforces these arguments in its conclusions by pointing out effects on the components of the dynamic modulus (G’ and G’’) in their maximum and minimum values, but also in their variation over the period studied.

This work seeks to advance the second aspect mentioned by evaluating the behavior of adhesive mortars with regard to the development of shear stress throughout their consolidation period using oscillatory rheometry

Theoretical background

Oscillatory tests were described in Mezger (2014) and applied to the study of the rheological behavior of a wide range of materials, from liquids with low viscosity to rigid solids, including multiphase suspensions with viscoelastic behavior such as pastes and mortars.

The oscillatory tests consist of applying a sinusoidal deformation function (γ) reading of the shear stress (τ) required to obtain the respective deformation (Romano et al., 2017; Modler, 2017). The parallel plate model (Figure 1) that schematically represents the oscillatory tests is described in various works, some of which are referenced here like Modler (2017) and Modler, Mohamad and Lubeck (2021).

The conduct of oscillatory tests can be described by Hooke’s Law in its complex form: τ(t)=G*∙γ(t). Where G* is the complex modulus of elasticity, defined from two components: storage modulus (G’) and loss modulus (G’’) (Mezger, 2014).

The storage modulus (G’) is a measure of the strain energy stored by the sample during the shearing process (Mezger, 2014). Such stored energy is used to restore the original shape of the material after the force has been removed. G’, therefore represents the elastic portion of the material’s shear behavior (Modler, 2017).

The loss modulus (G’’) is a measure of the strain energy consumed in the sample during the shearing process. This energy will not be returned after the shear force is removed, so the portion of deformation attributed to it will be permanent. G’’represents the viscous portion of the material’s shear behavior.

There is a relationship between the G’ and the yield stress (τ0) of materials in suspension. The yield stress is the limit of the shear stress applied to a fluid, at which point the material begins to move. Some works like Mezger (2014), Romano et al. (2021) and Banfill (2011) present the relationship between τ0 and G’ in the sense that the deformations occurring before the start of viscous flow of the material are elastic and are therefore described by Hooke’s Law. Viscous deformations start after the flow begins and are described by Newton’s Law for fluids.

Based on these approaches, it is estimated that the proportionality relationship between the two quantities, evaluated in oscillatory processes in mortars, is the one that best represents the description of the behavior of this type of material (τ0≡G’) (Romano et al., 2017). This relationship is considered true by the authors since the entire process is carried out in such a way that the bonds created during consolidation due to the hydration of the cement are not broken during the test. This condition is achieved by keeping the imposed deformation within what Mezger (2014) calls Linear Viscoelastic range (LVE). LVE is identified in the region where the G’ and G’’ curves have a linear behavior.

Cementitious materials show stability under the action of gravity until the limit imposed by the yield stress is not reached. In this way, pastes and mortars behave like Bingham fluids, with a yield stress (τ0) (Banfill, 2006).

Due to the chemical reactions that take place over time and the internal physical transformations, there is an increase in the value of the shear stress when a predetermined deformation is imposed on the sample. This increase is confirmed by the increase in both G’ and G’’ (De Gasperi et al., 2021).

Since G’ is the expression of the elastic response of the material under a shear stress during the consolidation period, it is understood that increasing values of G’ indicate that the behavior of the material is approaching that of an elastic solid (Romano et al., 2021).

Flatt and Bowen (2006) relate the yeld stress to the amount of solid particles in a mixture. The authors state that when a suspension has a high solid content and is set in motion by a shear force, hydrodynamic interactions and particle agglomerations play an important role. This highlights the importance of approaching the physical transformations occurring in mortars in the light of the characteristics related to their composition in terms of the proportion of their components.

The main goal of this work is to apply the oscilatory rheometry technique to achieve a better understanding about the hardening process of the adhesive mortars using the shear stress and the complex modulus components (G’ and G’’) development.

It is salso expected to broaden knowledge about the transformation phenomena occurred during the period of time in which we expect the consolidation to take place.

Materials and experimental program

For the experimental program, eleven adhesive mortars combinations were tested at the Building and Material Laboratory of Federal University of Santa Maria - Brazil. The mixes were composed of Portland cement type CPII-F-40, limestone sand and two polymers commonly used in adhesive mortars, a polymeric látex (ethylene vinyl acetate – EVA) and a cellulose ester (hydroxymethyl ethylcellulose HMEC) (Betiolli et al., 2009a, 2009b). The materials properties of sand, cement and polymers are presented in Table 1.

The independent variables in this work are related to the proportions of components in the mixtures, which were designed aimed to evaluate their influence on the mortars hardening process. Such strategy aims to gain a better understanding of the phenomena linked to the hardening of mortars, as well as to define oscillatory rheometry as an instrument for characterizing these phenomena.

The independente variables were:

1. W/S - water/solid materials ratio (as the volumetric ratio between the water presente at the moment of the mix and the cement amount);

2. A/C - aggregate/cement ratio (as the volumetric ratio between the agregate and cement); and

3. %P - polymer percentage (as the massive ratio of the total amount of polymers used relative to cement).

The tests were performed in an oscillatory rheometer Anton Paar MCR 102 (Figure 2a) where the stress strenght (τ) was mesured throughout the period of time in which we presume that the most important transformations by the hardening process of mortars were occurred. Each mixture was subjected to 200 min of oscillatory test. The oscillatory test rheometer has two circular plates at the top and bottom of the equipment with a diameter of 25 mm and 50 mm, respectively, and a standard metallic ring mold with 4 mm high, as can be seen in Figure 2b.

The mixtures samples were placed between plates gap, where it was squeezed using a compressive force. The test protocol used was the controlled shear deformation (CSD), without lateral restraint (by removing the molding ring), with frequency f=1HZ and shear strain γ=10^(-4). The used compression force was F=0,5N and the data acquisition was done every one minute. The samples were pre-compressed to a height of 3mm to achieve a greater contact area with the equipment plates (Mezger, 2014)

The tests were carried out in a controlled room with a temperature between 20 ºC and 23 ºC. When the molding ring is removed, the sides of the sample (3mm high) cause moisture to be lost to the environment.

The value of the shear strain (γ=〖10〗^(-4)) was designed according to Romano et al. (2021) and Modler, Mohamad and Lubeck (2021) aimed keeping the sample in LVR during all test period.

A factorialdesign model for proportioning of mortars used in the experiments was carried out to set the mix proportions parameters used at the experiments and got a significant wide range of mortar mixes, as presented in Table 2. The lower and upper limits for each variable were determined from a survey of mortar manufacturers. In this way, the mortars on the market have their composition within the limits used in the research. The polymer content used was divided between HMEC and EVA in a 1/10 ratio. The materials mixture followed a protocol which can be described by the following steps, from the materials weighing:

1. dry homogenization of the granular materials by shaking for 2 min;

2. placement of all the water in the previously moist mixer;

3. addition of half the dry homogeneous mixture to the water;

4. mixture in low velocity for 3 minutes;

5. addition of ¼ of the mixture (half of the left amount) to the already mixed part and mixing again in low velocity for 3 minutes; and

6. addition of the resting material (¼ of the total) and mixture in low velocity for 3 minutes more. Mixing was carried out in a planetary mixer with a capacity of 5 liters.

After mixing, the samples were taken to the oscillatory rheometry equipment room. Because of this and the preparation of the sample in the equipment, the oscillatory test began 20 minutes after the materials were mixed.

From the data extracted directly from the rheometer, graphs were produced showing the development of the shear stress throughout the test.

In this process, a parameter was defined which we call the elasticity factor (EF) as the portion of elastic energy developed in the process, characterized by the storage modulus, as shown in Equation 1 (adapted from Modler, 2017).

This parameter shows that the deformation imposed by the test is divided into two parts, one elastic (related to G’) and the other viscous (related to G’’). Thus, by observing the EF values, it is possible to see the mortar’s state transformations. In addition to the continuous increase in shear stress, there is a transition in the behavior of the material, which loses viscous energy and gains elastic energy throughout the test.

We have chosen to present the EF values on the same graph as the shear stress (SS) values in order to facilitate the analysis of the two quantities. The graphical model generated for the EF/SS analysis is shown in Figure 3.

For this work, the analysis of the experimental data was performed in three levels. From the first one, two independent variables were kept constant, while the third variable changed. In the second and third levels, the other variables assumed different values. So, it was possible to investigate the cross influence between variables, allowing to compare one variable with different levels to the other two. Table 2 presents this analysis design.

In order to implement such form of analysis, the mixtures were joined in groups (e.g. M2/M3), in which only one of the independent variables varied (e.g. W/S), and the other two were kept constant (e.g. A/C and %P). The joined groups form a set of mixes named here as a block (e.g. Block 1 is composed of adhesive mortar groups M2/M3 and M4/M5). Within each block, the comparison between the groups varies the second independent variable like A/C ratio and keeps the third one constant as a polymer’s percentage (%P).

Results and discussion

The graphs shown in Figure 4, Figure 5 and Figure 6 are used to carry out the analysis based on the grouping defined in Table 3.

In Figure 4, the curves constructed are used to analyze Block 1 and Block 3 and their groups (M2/M3; M4/M5 and M2/M4; M3/M5, respectively).

Analysing Figure 4 we can observe that the variation of %P enhanced the W/S effect. This is showed by comparison between M2/M3 and M4/M5 when we observe for EF and for SS the same influence from water amount in the mixture, that is, the EF curve being moved down and obtaining lower values of SS during the period of tests.

Analyzing mixtures of Block 1 it is noticed that the increase in %P values points to a greater effect of W/S on both EF and SS curves. Effectively this is in line with consulted references (Modler; Mohamed; Lubeck, 2021; Betioli et al., 2009a, 2012), since the action of polymer occurs mainly on the aqueous phase what improves the workability of the particle suspensions.

The same phenomenon can be seen in Figure 5 (Block 2), which points to a low influence of the amount of sand (A/C) on the observed trends. Thus, following the observation methodology recommended in the experimental design (Table 2), it can be seen from Block 1 and Block 2 that, in accordance with the literature, the amount of water (W/S) influences the formation of the rheological profile of the mixtures, both with regard to EF and SS. The polymer content (%P) acts to increase the influence of W/S, while the amount of sand had no significant influence.

By analyzing Block 3 and Block 4 (Figure 4 and Figure 5) it can be seen that %P causes small effects when taken into consideration in isolation. This small effect refers to an increase in SS values which may be caused by the transition of the aqueous phase due to the formation of the polymer gel and the start of hydration reactions.

The importance of the hydration-related phenomena and their interactions with the polymer gel can be seen by comparing the EF and SS curves, as the variations in SS values appear in the same period as the greatest EF variations, i.e. when each of the mixtures enters a period of more accelerated transformations in terms of their viscoelastic behavior.

Still observing Block 3 and Block 4, we can note, as the second and third dimension of influence that neither W/S nor A/C influenced the %P action.

In the case of W/S, it is understood that the cross-influence occurs in the %P→W/S direction and not the other way around, since there is a direct action of the polymer on the aqueous phase.

With regard to A/C, the observation of the data is contrary to conclusions collected in the literature, which confirm that the solids content in a mixture influences its rheological characteristics (Barbhuiya; Das, 2023).

Estellé et al. (2008) concluded that the volumetric concentration of the particles in suspension directly influences the rheological behavior of the material. Mixtures with lower concentrations had a rheological profile similar to that of the gel itself, i.e. a homogeneous fluid. Mixtures with higher concentrations had their behavior altered to that of a heterogeneous fluid.

In this study, it was not possible to observe the cross-influence of A/C with W/S or %P and not its direct influence on the characteristics measured. We therefore analyzed Figure 6, which shows Block 5, in order to observe, in isolation, the action of A/C on the characteristics studied in this work.

Although directly and in isolation (the W/S and %P values are the intermediate values used in the work), it can be seen in Figure 6 that the relationship between the quantities of aggregates and cement did not show a clear trend of influence. In order to resolve this incongruity, we can outline some lines of action.

First of all, it is possible to broaden the A/C spectrum, thus evaluating the possible influence of this parameter on the properties investigated. In parallel with this action, it will be possible to conclude on the suitability of the methods chosen here for this analysis.

By analyzing the entire set of data, it can be seen that the EF parameter represents a promising way of understanding the consolidation process of the mixtures used in this work. In all cases, it can be seen that there is a variation in EF that is consistent with consolidation and the expected transformations in cement-based materials.

It should be borne in mind that the variation in EF reached detection limits by the oscillatory rheometry method in shorter times than the variation in SS, which may indicate that the oscillatory method is able to detect the hardening itself with greater amplitude than the changes in state indicated by EF.

Modler, Mohamad and Lubeck (2021) used the phase angle measured in oscillatory rheometry together with its derivative to demonstrate that this type of test can detect changes in state in the initial periods, but has limits in this detection similar to those that emerged in this work.

Conclusions

Romano et al. (2017) indicated that there is a direct proportional correlation between the yield stress (τ0) of particle suspensions such as pastes and mortars and the storage modulus (G’), and that the increase in the values of this parameter may represent the development of the transition of this type of material from fluid to elastic solid. The technical difficulties encountered in measuring τ0 justify the use of G’ to describe the transition process.

The use of EF in the present work agrees with the conclusions of the aforementioned work, as well as the statements found in Mezger (2014) who defines the storage modulus as part of the elastic behavior of viscoelastic materials, which elastically absorb stresses below τ0.

The aim here was to analyze the same consolidation process through the development of shear stress (SS) measured during the oscillatory rheometry test. The stresses developed indicate the increasing formation of physical bonds through cement hydration, indicating that the test can be used to evaluate the process in question.

Unlike SS, the EF graphs indicated that oscillatory rheometry seems to reach a limit for observing the fluid→solid transition, since it showed a final plateau while SS has constant growth.

At the beginning of the period, however, EF values showed significant variation while SS did not show significant variations measurable by oscillatory rheometry. This branching occurs in the initial periods, after the cement grains have come into contact with water and the first phases of hydrated material have formed. This observation is in line with Betioli et al. (2009a) when the authors mention physical transformations in cementitious materials from the moment the dry material comes into contact with water.

Based on the data obtained, the analysis of the graphs thus constructed and the above considerations, it is possible to draw the following conclusions for this work:

1. oscillatory rheometry is a promising tool for analyzing adhesive mortars, especially with regard to their consolidation process, and it is capable of detecting small variations arising from different compositions such as those used here;

2. it is necessary to expand the proposed experimental program in order to verify the limitations of observation, especially with regard to the relationship between aggregates and cement, for which it was not possible to detect the form of influence on the results;

3. the amount of water is the most important variable in the formation of the rheological profile of the materials tested, which agrees with most of the references which define the aqueous phase as a fundamental parameter, especially in the early stages of the process, right after mixing; and

4. the polymer content acts as a coadjuvant in the rheological evaluation, since these materials interfere directly with the behavior of the aqueous phase. Thus, the amount of polymer tends to optimize the role of water in the mixture, which also agrees with what is established in the references.

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