3.1. Analysis of Adhesion Using the Loading Criterion
To better understand the results, a standard curve will be used as a model to illustrate the loading phases (see
Figure 3):
Phase 1 presents an increase in the applied force necessary to cause the sample to move. The curve approaches a straight line, i.e., represents the elastic regime of the glued system. During this phase, there is an increase in the stiffness of the sample, which is especially dominated by the stiffness of the mortar.
In phase 2, the bonded system reaches its maximum limit of resistance to simultaneous efforts, and from then on there is a loss of resistance, demonstrated by the downhill section between phases 2 and 3.
Phase 3 is the point where the load capacity of the mortar is transferred to the ceramic plate, and from then on, the sample’s rigidity is stabilized through the mechanical support of the ceramic plate.
Phase 4 marks the end of the test due to the collapse of the ceramic.
Figure 3.
The schematization of the MMF curve of the sandwich samples.
Figure 3.
The schematization of the MMF curve of the sandwich samples.
Should be mentioned that a similar behaviour to the propagation curves of this research was reported by [
21,
22]. The authors also identified the region of influence of the adhesive and the adherent, as well as the region of crack propagation, providing compatibility with what was presented here.
Figure 4 shows a comparison of the curves of the crack-free sandwich samples with a curve obtained from testing three samples of ceramic tiles with dry joints. The results presented in
Figure 4 show that the curve of the ceramic plates coincides with the lower part of the curve of the sandwich samples, that is, the section between phase 3 and the end of phase 4. This fact confirms, firstly, that phase 1 of the sandwich samples is dominated by the behaviour of the adhesive, and, therefore, the resistance offered by the material in this section comes predominantly from the stiffness of the adhesive mortar; secondly, that the section of the curve between phases 2 and 3 marks the rupture of the connection between the mortar and the ceramic tile due to the propagation of the crack; thirdly, that from point 3 the mechanical capacity of the sample is markedly dominated by the ceramic, with the transfer of load capacity from the mortar to the slab occurring at this point; and finally, that in point 4 the collapse that occurred is related to the rupture of the plate.
Based on this understanding of the analysis of curve profiles, the results obtained from the MMF test will be presented and discussed. For a better understanding of the experimental data, only one curve from each study group was chosen for presentation in
Figure 5,
Figure 6,
Figure 7,
Figure 8,
Figure 9,
Figure 10,
Figure 11 and
Figure 12. However, in the discussion of the experimental results obtained, all samples are considered by evaluating the effects of variables (crack size, healing time, and type of mortar) in statistical tests. Furthermore, the average maximum strength values of the samples and their respective standard deviations are presented in
Table 4.
3.1.1. Effect of Crack Size
Figure 5 and
Figure 6 show the results of the crack propagation test as a function of crack size, for AMI and AMII mortars. An analysis of the curves reveals that the highest values of maximum load are from samples without the presence of a previous crack and that the presence of the crack caused the maximum force resisted by the material (Phase 2) to drop abruptly, starting at a size of 15 mm.
It is also possible to observe that the section of the curve between phases 2 and 3 presented a shorter length as the size of the crack previously inserted in the samples increased. This reduction in the length of the section considered reflects the rapid transfer of load from the mortar to the ceramic tile due to the rapid propagation of the crack that occurred in the adhesive material.
On the other hand, the region of the curve between phases 3 and 4 becomes larger as the extent of the previous crack increases; this means that the greater the extent of the damage, the faster the loss of adhesion of the assembly occurs, with the support mechanical maintained by the resistance of the ceramic plate. Furthermore, since this final support comes predominantly from ceramics, the rupture that occurs in phase 4 always occurs at the same level of displacement supported by the sample, regardless of the level of cracking of the adhesive mortar.
Figure 7 and
Figure 8 show the load values of phase 2 and the reduction suffered by the presence of cracks when compared to the maximum load value achieved by the intact samples. Additionally,
Table 4 presents a description of the maximum force values. The test of statistical differences between groups (Kruskal–Wallis test), followed by the multiple comparison test (Conover–Iman test), was performed to verify whether the crack had a significant effect on the maximum load of the samples and in which groups this effect occurred. The same letter inside the bars denotes homogeneous groups.
The statistical test shows that the crack had a significant influence on the maximum load values and that this was already noticeable for the smallest crack size (15 mm). The existence of a 15 mm crack, corresponding to a loss of contact of 12.5%, generated a reduction in the maximum force supported by the mortar–ceramic set of approximately 50% concerning the reference sample (without crack) for both types of mortar with 28 days.
When the crack size was increased to 30 mm, doubling the loss of contact, the load capacity fell, after 28 days, reaching 70% of the reference sample. This percentage of loss remains the same in the AMII samples even with the increase in contact loss (45 mm crack).
This significant reduction in the load capacity of the samples demonstrates the high stress-concentrating effect that the existence of flaws in the interface region exerts already in the initial phases of loading. This also reveals the importance of ensuring that the substrate conditions are the best possible, as the gain in adhesion will only be effective if the adhesive mortar covers the entire surface. All of this reinforces the premise that the contact between the surfaces is decisive in the intensity of the bonds existing at the interface, since the acetate sheet, which simulated the existence of the crack, was positioned precisely at the mortar–ceramic interface, directly interfering with adhesion between them.
3.1.2. Effect of Curing Time
Figure 9 and
Figure 10 show the propagation curves as a function of curing time for the two types of mortar.
Figure 11 and
Figure 12 present the results of statistical tests to verify the effect of curing time on the value of the maximum load reached.
The analysis of the propagation curves seems to reveal a small gain in strength depending on the curing time, with the greatest difference being found in samples with AMII, without previous cracking, when the curing time increases from 7 to 28 days. However, statistical analysis shows that the differences observed in the representative curves, due to healing time, were not statistically significant.
A point that draws attention in
Figure 10 is the shape of the propagation curves of the samples with AMII 45 mm, which is more similar to the triangle curve of dry joint ceramic plates. A justification for this change in the shape of the curve can be found in studies carried out by [
23], who observed the same change in their curves when an uneven mixture of propagation modes was performed. In this research, this change can be attributed to the large area of debonding promoted by the 45 mm crack, which caused the ceramic to assume the mechanical support of the sample faster, and may have influenced the contribution of the mode mixture.
3.1.3. Effect of AM Type
Figure 13 shows the results of the MMF test depending on the type of adhesive mortar. The analysis of the representative curves seems to indicate that the AMII mortar presents slightly better mechanical performance than the AMI, for all curing times evaluated. However, when taking into account the load values of all samples, the application of the Mann–Whitney statistical test, used when wanting to compare two groups of independent samples (AMI and AMII), indicated a
pvalue > 0.05, which means that the hypothesis of equality between the average values must be accepted, that is, it is much more likely that the mechanical performance of the two mortars is similar.
In this sense, given the results presented, it is important to highlight the role of interfacial contact on the adhesion between the coating layers, as it was the only variable that influenced the mechanical performance of the samples under study.
3.2. Analysis of Adhesion Using the Energy Criterion
Although load- and stress-based approaches are the subject of a large amount of investigation, this research wishes to investigate whether the analysis of the adhesion of adhesive mortar joints can also be carried out using energy criteria, to quantitatively show the energy that, when placed on the samples, creates fracture surfaces.
For this, the values of potential elastic energy and dissipated energy were extracted from the propagation curves. The elastic energy was obtained from the area under the curve in the section delineated by phases 1 to 3. The dissipated energy was obtained from the difference in areas under the curve of samples with different crack sizes, following the methodology found in [
4].
Figure 14 shows the elastic energy values for the two types of mortar depending on the different crack sizes. In this figure, it can be seen that there is a decrease in elastic potential energy as the contact area between the materials is reduced. The reduction in this energy occurs significantly in samples with 15 mm of previous cracking, as observed in previous discussions with the force parameter.
The reduction in elastic energy occurs because the increase in crack size occurs with energy dissipation by the system. Thus, at the end of propagation, the elastic potential energy stored in the system was permanently reduced. The exponential reduction in energy due to the propagation of a crack or the presence of a bonding failure shows that there is a close relationship between the interface energy and the material adhesive strength since the load values of the ceramic/adhesive mortar assembly also suffered significantly. reduction. Lower elastic energy values of the samples indicate lower adhesion resistance when connecting the materials interface.
The influence of curing time on energy values was not observed, as the curves were all within the standard deviation (pvalue > 0.05). The same can be observed with the type of AM which, in general, with rare exceptions, also presented similar energy performance. A plausible justification for this may be the similarity of the mechanical performance of the mortars, observed by the lack of statistical significance in the MMF test.
In research works presented in the literature in which the mechanical properties of adhesives are different [
12,
24,
25], such as tensile strength and modulus of elasticity, it was possible to verify a difference in the energy performance of the material. In [
12] the ductile adhesive presented a critical energy of 4 to 10 times greater than the brittle adhesive.
However, the observed results in this research demonstrated that when there is a similar mechanical performance of adhesive mortars, the interface energy is intrinsically related to the substrate conditions in providing better mechanical anchoring of the materials in contact.
An important parameter in predicting the fracture resistance of materials is the critical energy release rate; for this reason, the values of energy dissipated throughout the crack propagation process were calculated and are presented in
Table 5 as the standard deviation value (S.D.). A statistical analysis was also carried out to verify the effect of the variables on the dissipated energy parameter which is presented in
Table 6. This result reveals that the dissipated energies of the samples assume different values as the size of the pre-crack changes (
pvalue < 0.05). Curing time and type of mortar did not have the same influence.
The results presented in
Table 5 show that for the samples to progress from a state without cracking to the state of initial cracking (0/15 mm), greater energy dissipation was necessary when compared to the other states.
From
Table 5, it is also possible to see that after the crack begins to propagate, its advancement does not require the same release of energy, justifying the lower dissipation values when advancing from 15 mm to 45 mm. This can be explained by the fact that crack growth promotes the accumulation of damage, favouring the coalescing of existing microcracks and contributing to their propagation. Furthermore, once the energy release rate reaches a critical value, G
c, the crack propagates in an unstable manner, that is, it grows without the need for an increase in applied load.
The statistical analysis results presented in
Table 6 confirm the previous analysis and, as shown by [
26], the energy dissipated (E
d) during the crack propagation process is equal to the critical fracture energy (G
c) of the material, and even that the critical fracture energy can assume the highest value among the dissipated energies by the material throughout the damage propagation process. Therefore,
Table 7 presents the G
c values for each AM type and curing times.
Critical fracture energy values confirm the fact that neither the AM type nor the curing time were influencing factors on the energy parameters of the material, as all Gc identified fall within an average value of 0.053 ± 0.031 J. This result is in agreement with the maximum load and elastic energy values observed, which were also not affected by these same variables. In this research, the value of 0.053 ± 0.031 J can be assumed to be the critical fracture energy of the ceramic–adhesive mortar interface, recognizing that it is necessary for the load applied to these samples to dispense energy equal to or greater than this value so that it is possible for a 15 mm crack to propagate and create a fracture surface.
By way of comparison with the results of this research,
Table 8 provides a summary of critical fracture energy (G
c) values obtained for different adhesives and substrates.
In this work, it was evident that there is a close relationship between surface energy and adhesion. Thus, the worse the interfacial contact, the greater the energy dissipated through the interface and the lower the amount of energy potentially absorbed by the sample. Therefore, to improve the material’s energetic performance and increase the value of its critical fracture energy, it is necessary to improve the interfacial contact conditions. This was observed in studies [
30], in which the surface treatment carried out on a group of samples provided an increase in the critical fracture energy of the samples.
3.3. Limitations of the Study and Future Study Plan
Based on the experimental results presented and discussed above, it is possible to list some limitations of the research, highlighting the following:
The existing literature concerning the systematic study of the critical energy of fault propagation in ceramic contacts is scarce or non-existent, as far as the authors were able to verify. In this sense, the research focused on identifying the variation range of energies involved in the evolution of the damage, simulated by reducing the bonded area. Additionally, despite the need to expand the study with a greater number of samples to be tested, especially with shorter damage induction intervals, to assess more accurate values of the determining property of contact conditions (namely, the critical contact energy), the experimental values obtained in this work were close to the experimental values of other systems.
Still on the previous point, it is important to highlight that statistical analyses were carried out with the set of samples involved in the study to confirm the accuracy of the experimental campaign and the significance of the studied variables (tensile strength and energy).
Only one type of ceramic coating (Bib group), without additional surface treatments, was used to prepare the samples, therefore, other contact conditions could not have their effect investigated on the parameters taken for discussion.
The monitoring of the crack propagation could not be carried out. The crack propagations possibly occurred at a microscopic level, so that information about the type of failure can only be purely descriptive, obtaining, from visual analysis, validation that the adhesive failure occurred in all samples, at the upper contact where the acetate film was placed.
However, it was possible to identify, through the experimental tests, that the critical contact energy prevails over the properties of the isolated materials in the structural integrity of the bonded systems. Additionally, given the significance of this parameter for the bonded systems, it should be taken into account that the analysis is quite complex and requires the use of multiple approaches.
To identify the mechanical aspects, taking into account that the characteristics of the contact reside on scales that are often micrometric, it is necessary to expand the study with the use of non-destructive wave propagation techniques, with variation in frequency and amplitude of mechanical waves, which can expand the development of damage detection tools and even allow the creation of numerical models that include contact elements. In turn, the physicochemical aspects allow us to understand the role of mechanical anchoring, through the study of the roughness of the substrates as well as the potential chemical compatibility of the adhesives and their interactions on this scale. To this end, microscopic and microanalytical techniques are essential, such as atomic force microscopy, scanning electron microscopy as well as the chemical contrasts allowed by the use of energy-dispersive spectroscopy, for example.